Support Vector Machine (SVM algorithm)¶
In machine learning, support-vector machines (SVMs, also support-vector networks) are supervised learning models with associated learning algorithms that analyze data used for classification and regression analysis. Developed at AT&T Bell Laboratories by Vapnik with colleagues (Boser et al., 1992, Guyon et al., 1993, Vapnik et al., 1997), it presents one of the most robust prediction methods, based on the statistical learning framework or VC theory proposed by Vapnik and Chervonekis (1974) and Vapnik (1982, 1995). Given a set of training examples, each marked as belonging to one or the other of two categories, an SVM training algorithm builds a model that assigns new examples to one category or the other, making it a non-probabilistic binary linear classifier (although methods such as Platt scaling exist to use SVM in a probabilistic classification setting). An SVM model is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible. New examples are then mapped into that same space and predicted to belong to a category based on the side of the gap on which they fall.
In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces.
When data are unlabelled, supervised learning is not possible, and an unsupervised learning approach is required, which attempts to find natural clustering of the data to groups, and then map new data to these formed groups. The support-vector clustering[2] algorithm, created by Hava Siegelmann and Vladimir Vapnik, applies the statistics of support vectors, developed in the support vector machines algorithm, to categorize unlabeled data, and is one of the most widely used clustering algorithms in industrial applications.
Here we are going to implement SVM using Telecom Churn Dataset.
0. Loading required libraries¶
In [3]:
library(DBI)
library(corrgram)
library(caret) # contains SVM function
library(gridExtra)
library(ggpubr)
1. Setting up the code parallelizing¶
Today is a good practice to start parallelizing your code. The common motivation behind parallel computing is that something is taking too long time. For somebody that means any computation that takes more than 3 minutes – this because parallelization is incredibly simple and most tasks that take time are embarrassingly parallel. Here are a few common tasks that fit the description:
- Bootstrapping
- Cross-validation
- Multivariate Imputation by Chained Equations (MICE)
- Fitting multiple regression models
For Windows users
In [ ]:
# process in parallel on Windows
library(doParallel)
cl <- makeCluster(detectCores(), type='PSOCK')
registerDoParallel(cl)
For Mac OSX and Unix like systems users
In [6]:
# process in parallel on Mac OSX and UNIX like systems
library(doMC)
registerDoMC(cores = 4)
2. Importing Data¶
In [8]:
#Set working directory where CSV is located
#getwd()
#setwd("...YOUR WORKING DIRECTORY WITH A DATASET...")
#getwd()
In [7]:
# Load the DataSets:
dataSet <- read.csv("TelcoCustomerChurnDataset.csv", header = TRUE, sep = ',')
colnames(dataSet) #Check the dataframe column names
- 'Account_Length'
- 'Vmail_Message'
- 'Day_Mins'
- 'Eve_Mins'
- 'Night_Mins'
- 'Intl_Mins'
- 'CustServ_Calls'
- 'Churn'
- 'Intl_Plan'
- 'Vmail_Plan'
- 'Day_Calls'
- 'Day_Charge'
- 'Eve_Calls'
- 'Eve_Charge'
- 'Night_Calls'
- 'Night_Charge'
- 'Intl_Calls'
- 'Intl_Charge'
- 'State'
- 'Area_Code'
- 'Phone'
3. Exploring the dataset¶
In [8]:
# Print top 10 rows in the dataSet
head(dataSet, 10)
| Account_Length | Vmail_Message | Day_Mins | Eve_Mins | Night_Mins | Intl_Mins | CustServ_Calls | Churn | Intl_Plan | Vmail_Plan | ⋯ | Day_Charge | Eve_Calls | Eve_Charge | Night_Calls | Night_Charge | Intl_Calls | Intl_Charge | State | Area_Code | Phone | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| <int> | <int> | <dbl> | <dbl> | <dbl> | <dbl> | <int> | <fct> | <fct> | <fct> | ⋯ | <dbl> | <int> | <dbl> | <int> | <dbl> | <int> | <dbl> | <fct> | <int> | <fct> | |
| 1 | 128 | 25 | 265.1 | 197.4 | 244.7 | 10.0 | 1 | no | no | yes | ⋯ | 45.07 | 99 | 16.78 | 91 | 11.01 | 3 | 2.70 | KS | 415 | 382-4657 |
| 2 | 107 | 26 | 161.6 | 195.5 | 254.4 | 13.7 | 1 | no | no | yes | ⋯ | 27.47 | 103 | 16.62 | 103 | 11.45 | 3 | 3.70 | OH | 415 | 371-7191 |
| 3 | 137 | 0 | 243.4 | 121.2 | 162.6 | 12.2 | 0 | no | no | no | ⋯ | 41.38 | 110 | 10.30 | 104 | 7.32 | 5 | 3.29 | NJ | 415 | 358-1921 |
| 4 | 84 | 0 | 299.4 | 61.9 | 196.9 | 6.6 | 2 | no | yes | no | ⋯ | 50.90 | 88 | 5.26 | 89 | 8.86 | 7 | 1.78 | OH | 408 | 375-9999 |
| 5 | 75 | 0 | 166.7 | 148.3 | 186.9 | 10.1 | 3 | no | yes | no | ⋯ | 28.34 | 122 | 12.61 | 121 | 8.41 | 3 | 2.73 | OK | 415 | 330-6626 |
| 6 | 118 | 0 | 223.4 | 220.6 | 203.9 | 6.3 | 0 | no | yes | no | ⋯ | 37.98 | 101 | 18.75 | 118 | 9.18 | 6 | 1.70 | AL | 510 | 391-8027 |
| 7 | 121 | 24 | 218.2 | 348.5 | 212.6 | 7.5 | 3 | no | no | yes | ⋯ | 37.09 | 108 | 29.62 | 118 | 9.57 | 7 | 2.03 | MA | 510 | 355-9993 |
| 8 | 147 | 0 | 157.0 | 103.1 | 211.8 | 7.1 | 0 | no | yes | no | ⋯ | 26.69 | 94 | 8.76 | 96 | 9.53 | 6 | 1.92 | MO | 415 | 329-9001 |
| 9 | 117 | 0 | 184.5 | 351.6 | 215.8 | 8.7 | 1 | no | no | no | ⋯ | 31.37 | 80 | 29.89 | 90 | 9.71 | 4 | 2.35 | LA | 408 | 335-4719 |
| 10 | 141 | 37 | 258.6 | 222.0 | 326.4 | 11.2 | 0 | no | yes | yes | ⋯ | 43.96 | 111 | 18.87 | 97 | 14.69 | 5 | 3.02 | WV | 415 | 330-8173 |
In [9]:
# Print last 10 rows in the dataSet
tail(dataSet, 10)
| Account_Length | Vmail_Message | Day_Mins | Eve_Mins | Night_Mins | Intl_Mins | CustServ_Calls | Churn | Intl_Plan | Vmail_Plan | ⋯ | Day_Charge | Eve_Calls | Eve_Charge | Night_Calls | Night_Charge | Intl_Calls | Intl_Charge | State | Area_Code | Phone | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| <int> | <int> | <dbl> | <dbl> | <dbl> | <dbl> | <int> | <fct> | <fct> | <fct> | ⋯ | <dbl> | <int> | <dbl> | <int> | <dbl> | <int> | <dbl> | <fct> | <int> | <fct> | |
| 3324 | 117 | 0 | 118.4 | 249.3 | 227.0 | 13.6 | 5 | yes | no | no | ⋯ | 20.13 | 97 | 21.19 | 56 | 10.22 | 3 | 3.67 | IN | 415 | 362-5899 |
| 3325 | 159 | 0 | 169.8 | 197.7 | 193.7 | 11.6 | 1 | no | no | no | ⋯ | 28.87 | 105 | 16.80 | 82 | 8.72 | 4 | 3.13 | WV | 415 | 377-1164 |
| 3326 | 78 | 0 | 193.4 | 116.9 | 243.3 | 9.3 | 2 | no | no | no | ⋯ | 32.88 | 88 | 9.94 | 109 | 10.95 | 4 | 2.51 | OH | 408 | 368-8555 |
| 3327 | 96 | 0 | 106.6 | 284.8 | 178.9 | 14.9 | 1 | no | no | no | ⋯ | 18.12 | 87 | 24.21 | 92 | 8.05 | 7 | 4.02 | OH | 415 | 347-6812 |
| 3328 | 79 | 0 | 134.7 | 189.7 | 221.4 | 11.8 | 2 | no | no | no | ⋯ | 22.90 | 68 | 16.12 | 128 | 9.96 | 5 | 3.19 | SC | 415 | 348-3830 |
| 3329 | 192 | 36 | 156.2 | 215.5 | 279.1 | 9.9 | 2 | no | no | yes | ⋯ | 26.55 | 126 | 18.32 | 83 | 12.56 | 6 | 2.67 | AZ | 415 | 414-4276 |
| 3330 | 68 | 0 | 231.1 | 153.4 | 191.3 | 9.6 | 3 | no | no | no | ⋯ | 39.29 | 55 | 13.04 | 123 | 8.61 | 4 | 2.59 | WV | 415 | 370-3271 |
| 3331 | 28 | 0 | 180.8 | 288.8 | 191.9 | 14.1 | 2 | no | no | no | ⋯ | 30.74 | 58 | 24.55 | 91 | 8.64 | 6 | 3.81 | RI | 510 | 328-8230 |
| 3332 | 184 | 0 | 213.8 | 159.6 | 139.2 | 5.0 | 2 | no | yes | no | ⋯ | 36.35 | 84 | 13.57 | 137 | 6.26 | 10 | 1.35 | CT | 510 | 364-6381 |
| 3333 | 74 | 25 | 234.4 | 265.9 | 241.4 | 13.7 | 0 | no | no | yes | ⋯ | 39.85 | 82 | 22.60 | 77 | 10.86 | 4 | 3.70 | TN | 415 | 400-4344 |
In [10]:
# Dimention of Dataset
dim(dataSet)
- 3333
- 21
In [11]:
# Check Data types of each column
table(unlist(lapply(dataSet, class)))
factor integer numeric
5 8 8
In [12]:
# Check Data types of individual column
data.class(dataSet$Account_Length)
data.class(dataSet$Vmail_Message)
data.class(dataSet$Day_Mins)
data.class(dataSet$Eve_Mins)
data.class(dataSet$Night_Mins)
data.class(dataSet$Intl_Mins)
data.class(dataSet$CustServ_Calls)
data.class(dataSet$Intl_Plan)
data.class(dataSet$Vmail_Plan)
data.class(dataSet$Day_Calls)
data.class(dataSet$Day_Charge)
data.class(dataSet$Eve_Calls)
data.class(dataSet$Eve_Charge)
data.class(dataSet$Night_Calls)
data.class(dataSet$Night_Charge)
data.class(dataSet$Intl_Calls)
data.class(dataSet$Intl_Charge)
data.class(dataSet$State)
data.class(dataSet$Phone)
data.class(dataSet$Churn)
'numeric'
'numeric'
'numeric'
'numeric'
'numeric'
'numeric'
'numeric'
'factor'
'factor'
'numeric'
'numeric'
'numeric'
'numeric'
'numeric'
'numeric'
'numeric'
'numeric'
'factor'
'factor'
'factor'
Converting variables Intl_Plan, Vmail_Plan, State to numeric data type.
In [13]:
dataSet$Intl_Plan <- as.numeric(dataSet$Intl_Plan)
dataSet$Vmail_Plan <- as.numeric(dataSet$Vmail_Plan)
dataSet$State <- as.numeric(dataSet$State)
In [14]:
# Check Data types of each column
table(unlist(lapply(dataSet, class)))
factor integer numeric
2 8 11
4. Exploring or Summarising dataset with descriptive statistics¶
In [15]:
# Find out if there is missing value in rows
rowSums(is.na(dataSet))
- 0
- 0
- 0
- 0
- 0
- 0
- 0
- 0
- 0
- 0
- 0
- 0
- 0
- 0
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- ⋯
- 0
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- 0
- 0
- 0
- 0
- 0
- 0
In [16]:
# Find out if there is missing value in columns
colSums(is.na(dataSet))
- Account_Length
- 0
- Vmail_Message
- 0
- Day_Mins
- 0
- Eve_Mins
- 0
- Night_Mins
- 0
- Intl_Mins
- 0
- CustServ_Calls
- 0
- Churn
- 0
- Intl_Plan
- 0
- Vmail_Plan
- 0
- Day_Calls
- 0
- Day_Charge
- 0
- Eve_Calls
- 0
- Eve_Charge
- 0
- Night_Calls
- 0
- Night_Charge
- 0
- Intl_Calls
- 0
- Intl_Charge
- 0
- State
- 0
- Area_Code
- 0
- Phone
- 0
Missing value checking using different packages (mice and VIM)
In [17]:
#Checking missing value with the mice package
library(mice)
md.pattern(dataSet)
Attaching package: ‘mice’
The following objects are masked from ‘package:base’:
cbind, rbind
/\ /\
{ `---' }
{ O O }
==> V <== No need for mice. This data set is completely observed.
\ \|/ /
`-----'
| Account_Length | Vmail_Message | Day_Mins | Eve_Mins | Night_Mins | Intl_Mins | CustServ_Calls | Churn | Intl_Plan | Vmail_Plan | ⋯ | Eve_Calls | Eve_Charge | Night_Calls | Night_Charge | Intl_Calls | Intl_Charge | State | Area_Code | Phone | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 3333 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ⋯ | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ⋯ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
In [18]:
#Checking missing value with the VIM package
library(VIM)
mice_plot <- aggr(dataSet, col=c('navyblue','yellow'),
numbers=TRUE, sortVars=TRUE,
labels=names(dataSet[1:21]), cex.axis=.9,
gap=3, ylab=c("Missing data","Pattern"))
Loading required package: colorspace
Loading required package: grid
VIM is ready to use.
Suggestions and bug-reports can be submitted at: https://github.com/statistikat/VIM/issues
Attaching package: ‘VIM’
The following object is masked from ‘package:datasets’:
sleep
Variables sorted by number of missings:
Variable Count
Account_Length 0
Vmail_Message 0
Day_Mins 0
Eve_Mins 0
Night_Mins 0
Intl_Mins 0
CustServ_Calls 0
Churn 0
Intl_Plan 0
Vmail_Plan 0
Day_Calls 0
Day_Charge 0
Eve_Calls 0
Eve_Charge 0
Night_Calls 0
Night_Charge 0
Intl_Calls 0
Intl_Charge 0
State 0
Area_Code 0
Phone 0
After the observation, we can claim that dataset contains no missing values.
Summary of dataset
In [19]:
# Selecting just columns with numeric data type
numericalCols <- colnames(dataSet[c(1:7,9:20)])
Difference between the lapply and sapply functions (we will use them in the next 2 cells):
We use lapply - when we want to apply a function to each element of a list in turn and get a list back.
We use sapply - when we want to apply a function to each element of a list in turn, but we want a vector back, rather than a list.
Finding statistics metrics with lapply function
In [20]:
#Sum
lapply(dataSet[numericalCols], FUN = sum)
- $Account_Length
- 336849
- $Vmail_Message
- 26994
- $Day_Mins
- 599190.4
- $Eve_Mins
- 669867.5
- $Night_Mins
- 669506.5
- $Intl_Mins
- 34120.9
- $CustServ_Calls
- 5209
- $Intl_Plan
- 3656
- $Vmail_Plan
- 4255
- $Day_Calls
- 334752
- $Day_Charge
- 101864.17
- $Eve_Calls
- 333681
- $Eve_Charge
- 56939.44
- $Night_Calls
- 333659
- $Night_Charge
- 30128.07
- $Intl_Calls
- 14930
- $Intl_Charge
- 9214.35
- $State
- 90189
- $Area_Code
- 1457129
In [21]:
#Mean
lapply(dataSet[numericalCols], FUN = mean)
- $Account_Length
- 101.064806480648
- $Vmail_Message
- 8.0990099009901
- $Day_Mins
- 179.775097509751
- $Eve_Mins
- 200.980348034803
- $Night_Mins
- 200.87203720372
- $Intl_Mins
- 10.2372937293729
- $CustServ_Calls
- 1.56285628562856
- $Intl_Plan
- 1.0969096909691
- $Vmail_Plan
- 1.27662766276628
- $Day_Calls
- 100.435643564356
- $Day_Charge
- 30.5623072307231
- $Eve_Calls
- 100.114311431143
- $Eve_Charge
- 17.0835403540354
- $Night_Calls
- 100.107710771077
- $Night_Charge
- 9.03932493249325
- $Intl_Calls
- 4.47944794479448
- $Intl_Charge
- 2.76458145814581
- $State
- 27.0594059405941
- $Area_Code
- 437.182418241824
In [22]:
#median
lapply(dataSet[numericalCols], FUN = median)
- $Account_Length
- 101
- $Vmail_Message
- 0
- $Day_Mins
- 179.4
- $Eve_Mins
- 201.4
- $Night_Mins
- 201.2
- $Intl_Mins
- 10.3
- $CustServ_Calls
- 1
- $Intl_Plan
- 1
- $Vmail_Plan
- 1
- $Day_Calls
- 101
- $Day_Charge
- 30.5
- $Eve_Calls
- 100
- $Eve_Charge
- 17.12
- $Night_Calls
- 100
- $Night_Charge
- 9.05
- $Intl_Calls
- 4
- $Intl_Charge
- 2.78
- $State
- 27
- $Area_Code
- 415
In [23]:
#Min
lapply(dataSet[numericalCols], FUN = min)
- $Account_Length
- 1
- $Vmail_Message
- 0
- $Day_Mins
- 0
- $Eve_Mins
- 0
- $Night_Mins
- 23.2
- $Intl_Mins
- 0
- $CustServ_Calls
- 0
- $Intl_Plan
- 1
- $Vmail_Plan
- 1
- $Day_Calls
- 0
- $Day_Charge
- 0
- $Eve_Calls
- 0
- $Eve_Charge
- 0
- $Night_Calls
- 33
- $Night_Charge
- 1.04
- $Intl_Calls
- 0
- $Intl_Charge
- 0
- $State
- 1
- $Area_Code
- 408
In [24]:
#Max
lapply(dataSet[numericalCols], FUN = max)
- $Account_Length
- 243
- $Vmail_Message
- 51
- $Day_Mins
- 350.8
- $Eve_Mins
- 363.7
- $Night_Mins
- 395
- $Intl_Mins
- 20
- $CustServ_Calls
- 9
- $Intl_Plan
- 2
- $Vmail_Plan
- 2
- $Day_Calls
- 165
- $Day_Charge
- 59.64
- $Eve_Calls
- 170
- $Eve_Charge
- 30.91
- $Night_Calls
- 175
- $Night_Charge
- 17.77
- $Intl_Calls
- 20
- $Intl_Charge
- 5.4
- $State
- 51
- $Area_Code
- 510
In [25]:
#Length
lapply(dataSet[numericalCols], FUN = length)
- $Account_Length
- 3333
- $Vmail_Message
- 3333
- $Day_Mins
- 3333
- $Eve_Mins
- 3333
- $Night_Mins
- 3333
- $Intl_Mins
- 3333
- $CustServ_Calls
- 3333
- $Intl_Plan
- 3333
- $Vmail_Plan
- 3333
- $Day_Calls
- 3333
- $Day_Charge
- 3333
- $Eve_Calls
- 3333
- $Eve_Charge
- 3333
- $Night_Calls
- 3333
- $Night_Charge
- 3333
- $Intl_Calls
- 3333
- $Intl_Charge
- 3333
- $State
- 3333
- $Area_Code
- 3333
Finding statistics metrics with sapply function
In [26]:
# Sum
sapply(dataSet[numericalCols], FUN = sum)
- Account_Length
- 336849
- Vmail_Message
- 26994
- Day_Mins
- 599190.4
- Eve_Mins
- 669867.5
- Night_Mins
- 669506.5
- Intl_Mins
- 34120.9
- CustServ_Calls
- 5209
- Intl_Plan
- 3656
- Vmail_Plan
- 4255
- Day_Calls
- 334752
- Day_Charge
- 101864.17
- Eve_Calls
- 333681
- Eve_Charge
- 56939.44
- Night_Calls
- 333659
- Night_Charge
- 30128.07
- Intl_Calls
- 14930
- Intl_Charge
- 9214.35
- State
- 90189
- Area_Code
- 1457129
In [27]:
# Mean
sapply(dataSet[numericalCols], FUN = mean)
- Account_Length
- 101.064806480648
- Vmail_Message
- 8.0990099009901
- Day_Mins
- 179.775097509751
- Eve_Mins
- 200.980348034803
- Night_Mins
- 200.87203720372
- Intl_Mins
- 10.2372937293729
- CustServ_Calls
- 1.56285628562856
- Intl_Plan
- 1.0969096909691
- Vmail_Plan
- 1.27662766276628
- Day_Calls
- 100.435643564356
- Day_Charge
- 30.5623072307231
- Eve_Calls
- 100.114311431143
- Eve_Charge
- 17.0835403540354
- Night_Calls
- 100.107710771077
- Night_Charge
- 9.03932493249325
- Intl_Calls
- 4.47944794479448
- Intl_Charge
- 2.76458145814581
- State
- 27.0594059405941
- Area_Code
- 437.182418241824
In [28]:
# Median
sapply(dataSet[numericalCols], FUN = median)
- Account_Length
- 101
- Vmail_Message
- 0
- Day_Mins
- 179.4
- Eve_Mins
- 201.4
- Night_Mins
- 201.2
- Intl_Mins
- 10.3
- CustServ_Calls
- 1
- Intl_Plan
- 1
- Vmail_Plan
- 1
- Day_Calls
- 101
- Day_Charge
- 30.5
- Eve_Calls
- 100
- Eve_Charge
- 17.12
- Night_Calls
- 100
- Night_Charge
- 9.05
- Intl_Calls
- 4
- Intl_Charge
- 2.78
- State
- 27
- Area_Code
- 415
In [29]:
# Min
sapply(dataSet[numericalCols], FUN = min)
- Account_Length
- 1
- Vmail_Message
- 0
- Day_Mins
- 0
- Eve_Mins
- 0
- Night_Mins
- 23.2
- Intl_Mins
- 0
- CustServ_Calls
- 0
- Intl_Plan
- 1
- Vmail_Plan
- 1
- Day_Calls
- 0
- Day_Charge
- 0
- Eve_Calls
- 0
- Eve_Charge
- 0
- Night_Calls
- 33
- Night_Charge
- 1.04
- Intl_Calls
- 0
- Intl_Charge
- 0
- State
- 1
- Area_Code
- 408
In [30]:
# Max
sapply(dataSet[numericalCols], FUN = max)
- Account_Length
- 243
- Vmail_Message
- 51
- Day_Mins
- 350.8
- Eve_Mins
- 363.7
- Night_Mins
- 395
- Intl_Mins
- 20
- CustServ_Calls
- 9
- Intl_Plan
- 2
- Vmail_Plan
- 2
- Day_Calls
- 165
- Day_Charge
- 59.64
- Eve_Calls
- 170
- Eve_Charge
- 30.91
- Night_Calls
- 175
- Night_Charge
- 17.77
- Intl_Calls
- 20
- Intl_Charge
- 5.4
- State
- 51
- Area_Code
- 510
In [31]:
# Length
sapply(dataSet[numericalCols], FUN = length)
- Account_Length
- 3333
- Vmail_Message
- 3333
- Day_Mins
- 3333
- Eve_Mins
- 3333
- Night_Mins
- 3333
- Intl_Mins
- 3333
- CustServ_Calls
- 3333
- Intl_Plan
- 3333
- Vmail_Plan
- 3333
- Day_Calls
- 3333
- Day_Charge
- 3333
- Eve_Calls
- 3333
- Eve_Charge
- 3333
- Night_Calls
- 3333
- Night_Charge
- 3333
- Intl_Calls
- 3333
- Intl_Charge
- 3333
- State
- 3333
- Area_Code
- 3333
In the next few cells, you will find three different options on how to aggregate data.
In [32]:
# OPTION 1: (Using Aggregate FUNCTION - all variables together)
aggregate(dataSet[numericalCols], list(dataSet$Churn), summary)
| Group.1 | Account_Length | Vmail_Message | Day_Mins | Eve_Mins | Night_Mins | Intl_Mins | CustServ_Calls | Intl_Plan | Vmail_Plan | Day_Calls | Day_Charge | Eve_Calls | Eve_Charge | Night_Calls | Night_Charge | Intl_Calls | Intl_Charge | State | Area_Code |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| <fct> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> | <dbl[,6]> |
| no | 1, 73, 100, 100.7937, 127, 243 | 0, 0, 0, 8.604561, 22, 51 | 0, 142.825, 177.2, 175.1758, 210.30, 315.6 | 0.0, 164.5, 199.6, 199.0433, 233.20, 361.8 | 23.2, 165.90, 200.25, 200.1332, 234.90, 395.0 | 0, 8.4, 10.2, 10.15888, 12.0, 18.9 | 0, 1, 1, 1.449825, 2, 8 | 1, 1, 1, 1.065263, 1, 2 | 1, 1, 1, 1.295439, 2, 2 | 0, 87.0, 100, 100.2832, 114.0, 163 | 0, 24.2825, 30.12, 29.78042, 35.75, 53.65 | 0, 87, 100, 100.0386, 114, 170 | 0.00, 13.980, 16.97, 16.91891, 19.820, 30.75 | 33, 87, 100, 100.0582, 113, 175 | 1.04, 7.470, 9.01, 9.006074, 10.570, 17.77 | 0, 3, 4, 4.532982, 6, 19 | 0.00, 2.27, 2.75, 2.743404, 3.24, 5.1 | 1, 14, 27, 27.01193, 40, 51 | 408, 408, 415, 437.0747, 510, 510 |
| yes | 1, 76, 103, 102.6646, 127, 225 | 0, 0, 0, 5.115942, 0, 48 | 0, 153.250, 217.6, 206.9141, 265.95, 350.8 | 70.9, 177.1, 211.3, 212.4101, 249.45, 363.7 | 47.4, 171.25, 204.80, 205.2317, 239.85, 354.9 | 2, 8.8, 10.6, 10.70000, 12.8, 20.0 | 0, 1, 2, 2.229814, 4, 9 | 1, 1, 1, 1.283644, 2, 2 | 1, 1, 1, 1.165631, 1, 2 | 0, 87.5, 103, 101.3354, 116.5, 165 | 0, 26.0550, 36.99, 35.17592, 45.21, 59.64 | 48, 87, 101, 100.5611, 114, 168 | 6.03, 15.055, 17.96, 18.05497, 21.205, 30.91 | 49, 85, 100, 100.3996, 115, 158 | 2.13, 7.705, 9.22, 9.235528, 10.795, 15.97 | 1, 2, 4, 4.163561, 5, 20 | 0.54, 2.38, 2.86, 2.889545, 3.46, 5.4 | 1, 17, 27, 27.33954, 39, 51 | 408, 408, 415, 437.8178, 510, 510 |
In [33]:
# OPTION 2: (Using Aggregate FUNCTION - variables separately)
aggregate(dataSet$Intl_Mins, list(dataSet$Churn), summary)
aggregate(dataSet$Day_Mins, list(dataSet$Churn), summary)
aggregate(dataSet$Night_Mins, list(dataSet$Churn), summary)
| Group.1 | x |
|---|---|
| <fct> | <dbl[,6]> |
| no | 0, 8.4, 10.2, 10.15888, 12.0, 18.9 |
| yes | 2, 8.8, 10.6, 10.70000, 12.8, 20.0 |
| Group.1 | x |
|---|---|
| <fct> | <dbl[,6]> |
| no | 0, 142.825, 177.2, 175.1758, 210.30, 315.6 |
| yes | 0, 153.250, 217.6, 206.9141, 265.95, 350.8 |
| Group.1 | x |
|---|---|
| <fct> | <dbl[,6]> |
| no | 23.2, 165.90, 200.25, 200.1332, 234.90, 395.0 |
| yes | 47.4, 171.25, 204.80, 205.2317, 239.85, 354.9 |
In [34]:
# OPTION 3: (Using "by" FUNCTION instead of "Aggregate" FUNCTION)
by(dataSet$Intl_Mins, dataSet[8], FUN = summary)
by(dataSet$Day_Mins, dataSet[8], FUN = summary)
by(dataSet$Night_Mins, dataSet[8], FUN = summary)
Churn: no
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00 8.40 10.20 10.16 12.00 18.90
------------------------------------------------------------
Churn: yes
Min. 1st Qu. Median Mean 3rd Qu. Max.
2.0 8.8 10.6 10.7 12.8 20.0
Churn: no
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0 142.8 177.2 175.2 210.3 315.6
------------------------------------------------------------
Churn: yes
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0 153.2 217.6 206.9 265.9 350.8
Churn: no Min. 1st Qu. Median Mean 3rd Qu. Max. 23.2 165.9 200.2 200.1 234.9 395.0 ------------------------------------------------------------ Churn: yes Min. 1st Qu. Median Mean 3rd Qu. Max. 47.4 171.2 204.8 205.2 239.8 354.9
Find out correlation
In [35]:
# Correlations/covariances among numeric variables
library(Hmisc)
cor(dataSet[c(2,5,11,13,16,18)], use="complete.obs", method="kendall")
cov(dataSet[c(2,5,11,13,16,18)], use="complete.obs")
Loading required package: survival
Attaching package: ‘survival’
The following object is masked from ‘package:caret’:
cluster
Loading required package: Formula
Attaching package: ‘Hmisc’
The following objects are masked from ‘package:base’:
format.pval, units
| Vmail_Message | Night_Mins | Day_Calls | Eve_Calls | Night_Charge | Intl_Charge | |
|---|---|---|---|---|---|---|
| Vmail_Message | 1.000000000 | 0.003718463 | -0.009573189 | -5.382921e-03 | 0.003710434 | -1.263503e-03 |
| Night_Mins | 0.003718463 | 1.000000000 | 0.012550159 | 3.291091e-03 | 0.999625309 | -7.103399e-03 |
| Day_Calls | -0.009573189 | 0.012550159 | 1.000000000 | 9.253492e-03 | 0.012531632 | 1.038631e-02 |
| Eve_Calls | -0.005382921 | 0.003291091 | 0.009253492 | 1.000000e+00 | 0.003310838 | -9.536135e-05 |
| Night_Charge | 0.003710434 | 0.999625309 | 0.012531632 | 3.310838e-03 | 1.000000000 | -7.097366e-03 |
| Intl_Charge | -0.001263503 | -0.007103399 | 0.010386309 | -9.536135e-05 | -0.007097366 | 1.000000e+00 |
| Vmail_Message | Night_Mins | Day_Calls | Eve_Calls | Night_Charge | Intl_Charge | |
|---|---|---|---|---|---|---|
| Vmail_Message | 187.37134656 | 5.3174453 | -2.6229779 | -1.59925653 | 0.23873433 | 0.02975334 |
| Night_Mins | 5.31744529 | 2557.7140018 | 23.2812431 | -2.10859729 | 115.09955435 | -0.57867377 |
| Day_Calls | -2.62297790 | 23.2812431 | 402.7681409 | 2.58373944 | 1.04716693 | 0.32775442 |
| Eve_Calls | -1.59925653 | -2.1085973 | 2.5837394 | 396.91099860 | -0.09322113 | 0.13025644 |
| Night_Charge | 0.23873433 | 115.0995543 | 1.0471669 | -0.09322113 | 5.17959717 | -0.02605168 |
| Intl_Charge | 0.02975334 | -0.5786738 | 0.3277544 | 0.13025644 | -0.02605168 | 0.56817315 |
In [36]:
# Correlations with significance levels
rcorr(as.matrix(dataSet[c(2,5,11,13,16,18)]), type="pearson")
Vmail_Message Night_Mins Day_Calls Eve_Calls Night_Charge
Vmail_Message 1.00 0.01 -0.01 -0.01 0.01
Night_Mins 0.01 1.00 0.02 0.00 1.00
Day_Calls -0.01 0.02 1.00 0.01 0.02
Eve_Calls -0.01 0.00 0.01 1.00 0.00
Night_Charge 0.01 1.00 0.02 0.00 1.00
Intl_Charge 0.00 -0.02 0.02 0.01 -0.02
Intl_Charge
Vmail_Message 0.00
Night_Mins -0.02
Day_Calls 0.02
Eve_Calls 0.01
Night_Charge -0.02
Intl_Charge 1.00
n= 3333
P
Vmail_Message Night_Mins Day_Calls Eve_Calls Night_Charge
Vmail_Message 0.6576 0.5816 0.7350 0.6583
Night_Mins 0.6576 0.1855 0.9039 0.0000
Day_Calls 0.5816 0.1855 0.7092 0.1857
Eve_Calls 0.7350 0.9039 0.7092 0.9056
Night_Charge 0.6583 0.0000 0.1857 0.9056
Intl_Charge 0.8678 0.3810 0.2111 0.6167 0.3808
Intl_Charge
Vmail_Message 0.8678
Night_Mins 0.3810
Day_Calls 0.2111
Eve_Calls 0.6167
Night_Charge 0.3808
Intl_Charge
5. Visualising DataSet¶
In [37]:
# Pie Chart from data
mytable <- table(dataSet$Churn)
lbls <- paste(names(mytable), "\n", mytable, sep="")
pie(mytable, labels = lbls, col=rainbow(length(lbls)),
main="Pie Chart of Classes\n (with sample sizes)")
In [38]:
# Barplot of categorical data
par(mfrow=c(1,1))
barplot(table(dataSet$Churn), ylab = "Count",
col=c("darkblue","red"))
barplot(prop.table(table(dataSet$Churn)), ylab = "Proportion",
col=c("darkblue","red"))
barplot(table(dataSet$Churn), xlab = "Count", horiz = TRUE,
col=c("darkblue","red"))
barplot(prop.table(table(dataSet$Churn)), xlab = "Proportion", horiz = TRUE,
col=c("darkblue","red"))
In [39]:
# Scatterplot Matrices from the glus Package
library(gclus)
dta <- dataSet[c(2,5,11,13,16,18)] # get data
dta.r <- abs(cor(dta)) # get correlations
dta.col <- dmat.color(dta.r) # get colors
# reorder variables so those with highest correlation are closest to the diagonal
dta.o <- order.single(dta.r)
cpairs(dta, dta.o, panel.colors=dta.col, gap=.5,
main="Variables Ordered and Colored by Correlation" )
Loading required package: cluster
Visualise correlations
In [40]:
corrgram(dataSet[c(2,5,11,13,16,18)], order=TRUE, lower.panel=panel.shade,
upper.panel=panel.pie, text.panel=panel.txt, main=" ")
In [41]:
# More graphs on correlatios amaong data
# Using "Hmisc"
res2 <- rcorr(as.matrix(dataSet[,c(2,5,11,13,16,18)]))
# Extract the correlation coefficients
res2$r
# Extract p-values
res2$P
| Vmail_Message | Night_Mins | Day_Calls | Eve_Calls | Night_Charge | Intl_Charge | |
|---|---|---|---|---|---|---|
| Vmail_Message | 1.000000000 | 0.007681136 | -0.009548068 | -0.005864351 | 0.007663290 | 0.002883658 |
| Night_Mins | 0.007681136 | 1.000000000 | 0.022937845 | -0.002092768 | 0.999999215 | -0.015179849 |
| Day_Calls | -0.009548068 | 0.022937845 | 1.000000000 | 0.006462114 | 0.022926638 | 0.021666095 |
| Eve_Calls | -0.005864351 | -0.002092768 | 0.006462114 | 1.000000000 | -0.002055984 | 0.008673858 |
| Night_Charge | 0.007663290 | 0.999999215 | 0.022926638 | -0.002055984 | 1.000000000 | -0.015186139 |
| Intl_Charge | 0.002883658 | -0.015179849 | 0.021666095 | 0.008673858 | -0.015186139 | 1.000000000 |
| Vmail_Message | Night_Mins | Day_Calls | Eve_Calls | Night_Charge | Intl_Charge | |
|---|---|---|---|---|---|---|
| Vmail_Message | NA | 0.6575570 | 0.5816089 | 0.7350335 | 0.6583020 | 0.8678283 |
| Night_Mins | 0.6575570 | NA | 0.1855268 | 0.9038694 | 0.0000000 | 0.3809828 |
| Day_Calls | 0.5816089 | 0.1855268 | NA | 0.7091964 | 0.1857418 | 0.2111142 |
| Eve_Calls | 0.7350335 | 0.9038694 | 0.7091964 | NA | 0.9055511 | 0.6166654 |
| Night_Charge | 0.6583020 | 0.0000000 | 0.1857418 | 0.9055511 | NA | 0.3807855 |
| Intl_Charge | 0.8678283 | 0.3809828 | 0.2111142 | 0.6166654 | 0.3807855 | NA |
In [42]:
# Using "corrplot"
library(corrplot)
library(RColorBrewer)
corrplot(res2$r, type = "upper", order = "hclust", col=brewer.pal(n=8, name="RdYlBu"),
tl.col = "black", tl.srt = 45)
corrplot(res2$r, type = "lower", order = "hclust", col=brewer.pal(n=8, name="RdYlBu"),
tl.col = "black", tl.srt = 45)
corrplot 0.84 loaded
In [43]:
# Using PerformanceAnalytics
library(PerformanceAnalytics)
data <- dataSet[, c(2,5,11,13,16,18)]
chart.Correlation(data, histogram=TRUE, pch=19)
Loading required package: xts
Loading required package: zoo
Attaching package: ‘zoo’
The following objects are masked from ‘package:base’:
as.Date, as.Date.numeric
Attaching package: ‘PerformanceAnalytics’
The following object is masked from ‘package:graphics’:
legend
In [44]:
# Using Colored Headmap
col <- colorRampPalette(c("blue", "white", "red"))(20)
heatmap(x = res2$r, col = col, symm = TRUE)
We should notice that Night_Mins and Night_Charge have a strong, linear, positive relationship.
6. Pre-Processing of DataSet i.e. train (75%) : test (25%) split¶
In [45]:
train_test_index <- createDataPartition(dataSet$Churn, p=0.75, list=FALSE)
training_dataset <- dataSet[, c(1:20)][train_test_index,]
testing_dataset <- dataSet[, c(1:20)][-train_test_index,]
In [46]:
dim(training_dataset)
dim(testing_dataset)
- 2501
- 20
- 832
- 20
7. Cross Validation and control parameter setup¶
In [47]:
control <- trainControl(method="repeatedcv", # repeatedcv / adaptive_cv
number=2, repeats = 2,
verbose = TRUE, search = "grid",
allowParallel = TRUE)
metric <- "Accuracy"
tuneLength = 2
8. Algorithm : SVM¶
In [49]:
getModelInfo("svmLinear"); getModelInfo("svmRadial"); getModelInfo("svmPoly");
- $lssvmLinear
- $label
- 'Least Squares Support Vector Machine'
- $library
- 'kernlab'
- $type
- 'Classification'
- $parameters
A data.frame: 1 × 3 parameter class label <chr> <chr> <chr> tau numeric Regularization Parameter - $grid
function (x, y, len = NULL, search = "grid") { if (search == "grid") { out <- expand.grid(tau = 2^((1:len) - 5)) } else { out <- data.frame(tau = 2^runif(len, min = -5, max = 10)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { kernlab::lssvm(x = as.matrix(x), y = y, tau = param$tau, kernel = kernlab::polydot(degree = 1, scale = 1, offset = 1), ...) }- $predict
function (modelFit, newdata, submodels = NULL) { out <- kernlab::predict(modelFit, as.matrix(newdata)) if (is.matrix(out)) out <- out[, 1] out }- $prob
- NULL
- $predictors
function (x, ...) { if (hasTerms(x) & !is.null(x@terms)) { out <- predictors.terms(x@terms) } else { out <- colnames(attr(x, "xmatrix")) } if (is.null(out)) out <- names(attr(x, "scaling")$x.scale$`scaled:center`) if (is.null(out)) out <- NA out }- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Linear Classifier'
- $levels
function (x) lev(x)- $sort
function (x) x
- $svmLinear
- $label
- 'Support Vector Machines with Linear Kernel'
- $library
- 'kernlab'
- $type
-
- 'Regression'
- 'Classification'
- $parameters
A data.frame: 1 × 3 parameter class label <chr> <chr> <chr> C numeric Cost - $grid
function (x, y, len = NULL, search = "grid") { if (search == "grid") { out <- data.frame(C = 1) } else { out <- data.frame(C = 2^runif(len, min = -5, max = 10)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { if (any(names(list(...)) == "prob.model") | is.numeric(y)) { out <- kernlab::ksvm(x = as.matrix(x), y = y, kernel = kernlab::vanilladot(), C = param$C, ...) } else { out <- kernlab::ksvm(x = as.matrix(x), y = y, kernel = kernlab::vanilladot(), C = param$C, prob.model = classProbs, ...) } out }- $predict
function (modelFit, newdata, submodels = NULL) { svmPred <- function(obj, x) { hasPM <- !is.null(unlist(obj@prob.model)) if (hasPM) { pred <- kernlab::lev(obj)[apply(kernlab::predict(obj, x, type = "probabilities"), 1, which.max)] } else pred <- kernlab::predict(obj, x) pred } out <- try(svmPred(modelFit, newdata), silent = TRUE) if (is.character(kernlab::lev(modelFit))) { if (class(out)[1] == "try-error") { warning("kernlab class prediction calculations failed; returning NAs") out <- rep("", nrow(newdata)) out[seq(along = out)] <- NA } } else { if (class(out)[1] == "try-error") { warning("kernlab prediction calculations failed; returning NAs") out <- rep(NA, nrow(newdata)) } } if (is.matrix(out)) out <- out[, 1] out }- $prob
function (modelFit, newdata, submodels = NULL) { out <- try(kernlab::predict(modelFit, newdata, type = "probabilities"), silent = TRUE) if (class(out)[1] != "try-error") { if (any(out < 0)) { out[out < 0] <- 0 out <- t(apply(out, 1, function(x) x/sum(x))) } out <- out[, kernlab::lev(modelFit), drop = FALSE] } else { warning("kernlab class probability calculations failed; returning NAs") out <- matrix(NA, nrow(newdata) * length(kernlab::lev(modelFit)), ncol = length(kernlab::lev(modelFit))) colnames(out) <- kernlab::lev(modelFit) } out }- $predictors
function (x, ...) { if (hasTerms(x) & !is.null(x@terms)) { out <- predictors.terms(x@terms) } else { out <- colnames(attr(x, "xmatrix")) } if (is.null(out)) out <- names(attr(x, "scaling")$x.scale$`scaled:center`) if (is.null(out)) out <- NA out }- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Linear Regression'
- 'Linear Classifier'
- 'Robust Methods'
- $levels
function (x) kernlab::lev(x)- $sort
function (x) { x[order(x$C), ] }
- $svmLinear2
- $label
- 'Support Vector Machines with Linear Kernel'
- $library
- 'e1071'
- $type
-
- 'Regression'
- 'Classification'
- $parameters
A data.frame: 1 × 3 parameter class label <chr> <chr> <chr> cost numeric Cost - $grid
function (x, y, len = NULL, search = "grid") { if (search == "grid") { out <- expand.grid(cost = 2^((1:len) - 3)) } else { out <- data.frame(cost = 2^runif(len, min = -5, max = 10)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { if (any(names(list(...)) == "probability") | is.numeric(y)) { out <- e1071::svm(x = as.matrix(x), y = y, kernel = "linear", cost = param$cost, ...) } else { out <- e1071::svm(x = as.matrix(x), y = y, kernel = "linear", cost = param$cost, probability = classProbs, ...) } out }- $predict
function (modelFit, newdata, submodels = NULL) { predict(modelFit, newdata) }- $prob
function (modelFit, newdata, submodels = NULL) { out <- predict(modelFit, newdata, probability = TRUE) attr(out, "probabilities") }- $predictors
function (x, ...) { out <- if (!is.null(x$terms)) predictors.terms(x$terms) else x$xNames if (is.null(out)) out <- names(attr(x, "scaling")$x.scale$`scaled:center`) if (is.null(out)) out <- NA out }- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Linear Regression'
- 'Linear Classifier'
- 'Robust Methods'
- $levels
function (x) x$levels- $sort
function (x) { x[order(x$cost), ] }
- $svmLinear3
- $label
- 'L2 Regularized Support Vector Machine (dual) with Linear Kernel'
- $library
- 'LiblineaR'
- $type
-
- 'Regression'
- 'Classification'
- $parameters
A data.frame: 2 × 3 parameter class label <chr> <chr> <chr> cost numeric Cost Loss character Loss Function - $grid
function (x, y, len = NULL, search = "grid") { if (search == "grid") { out <- expand.grid(cost = 2^((1:len) - 3), Loss = c("L1", "L2")) } else { out <- data.frame(cost = 2^runif(len, min = -10, max = 10), Loss = sample(c("L1", "L2"), size = len, replace = TRUE)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { if (param$Loss == "L2") { model_type <- if (is.factor(y)) 2 else 12 } else model_type <- if (is.factor(y)) 3 else 13 out <- LiblineaR::LiblineaR(data = as.matrix(x), target = y, cost = param$cost, type = model_type, ...) out }- $predict
function (modelFit, newdata, submodels = NULL) { predict(modelFit, newdata)$predictions }- $prob
- NULL
- $predictors
function (x, ...) { out <- colnames(x$W) out[out != "Bias"] }- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Linear Regression'
- 'Linear Classifier'
- 'Robust Methods'
- $levels
function (x) x$levels- $sort
function (x) { x[order(x$cost), ] }
- $svmLinearWeights
- $label
- 'Linear Support Vector Machines with Class Weights'
- $library
- 'e1071'
- $type
- 'Classification'
- $parameters
A data.frame: 2 × 3 parameter class label <chr> <chr> <chr> cost numeric Cost weight numeric Class Weight - $grid
function (x, y, len = NULL, search = "grid") { if (search == "grid") { out <- expand.grid(cost = 2^((1:len) - 3), weight = 1:len) } else { out <- data.frame(cost = 2^runif(len, min = -5, max = 10), weight = runif(len, min = 1, max = 25)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { if (length(levels(y)) != 2) stop("Currently implemented for 2-class problems") cwts <- c(1, param$weight) names(cwts) <- levels(y) out <- e1071::svm(x = as.matrix(x), y = y, kernel = "linear", cost = param$cost, probability = classProbs, class.weights = cwts, ...) out }- $predict
function (modelFit, newdata, submodels = NULL) { predict(modelFit, newdata) }- $prob
function (modelFit, newdata, submodels = NULL) { out <- predict(modelFit, newdata, probability = TRUE) attr(out, "probabilities") }- $predictors
function (x, ...) { out <- if (!is.null(x$terms)) predictors.terms(x$terms) else x$xNames if (is.null(out)) out <- names(attr(x, "scaling")$x.scale$`scaled:center`) if (is.null(out)) out <- NA out }- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Linear Classifier'
- 'Robust Methods'
- 'Cost Sensitive Learning'
- 'Two Class Only'
- $levels
function (x) x$levels- $sort
function (x) { x[order(x$cost, x$weight), ] }
- $svmLinearWeights2
- $label
- 'L2 Regularized Linear Support Vector Machines with Class Weights'
- $library
- 'LiblineaR'
- $type
- 'Classification'
- $parameters
A data.frame: 3 × 3 parameter class label <chr> <chr> <chr> cost numeric Cost Loss character Loss Function weight numeric Class Weight - $grid
function (x, y, len = NULL, search = "grid") { if (search == "grid") { out <- expand.grid(cost = 2^((1:len) - 3), Loss = c("L1", "L2"), weight = 1:len) } else { out <- data.frame(cost = 2^runif(len, min = -10, max = 10), Loss = sample(c("L1", "L2"), size = len, replace = TRUE), weight = runif(len, min = 1, max = 25)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { model_type <- if (param$Loss == "L2") 2 else 3 if (length(levels(y)) != 2) stop("Currently implemented for 2-class problems") cwts <- c(1, param$weight) names(cwts) <- levels(y) out <- LiblineaR::LiblineaR(data = as.matrix(x), target = y, cost = param$cost, type = model_type, wi = cwts, ...) out }- $predict
function (modelFit, newdata, submodels = NULL) { predict(modelFit, newdata)$predictions }- $prob
- NULL
- $predictors
function (x, ...) { out <- colnames(x$W) out[out != "Bias"] }- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Linear Classifier'
- 'Robust Methods'
- 'Cost Sensitive Learning'
- 'Two Class Only'
- $levels
function (x) x$levels- $sort
function (x) { x[order(x$cost), ] }
- $lssvmRadial
- $label
- 'Least Squares Support Vector Machine with Radial Basis Function Kernel'
- $library
- 'kernlab'
- $type
- 'Classification'
- $parameters
A data.frame: 2 × 3 parameter class label <chr> <chr> <chr> sigma numeric Sigma tau numeric Regularization Parameter - $grid
function (x, y, len = NULL, search = "grid") { sigmas <- kernlab::sigest(as.matrix(x), na.action = na.omit, scaled = TRUE) if (search == "grid") { out <- expand.grid(sigma = seq(min(sigmas), max(sigmas), length = min(6, len)), tau = 2^((1:len) - 5)) } else { rng <- extendrange(log(sigmas), f = 0.75) out <- data.frame(sigma = exp(runif(len, min = rng[1], max = rng[2])), tau = 2^runif(len, min = -5, max = 10)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { kernlab::lssvm(x = as.matrix(x), y = y, tau = param$tau, kernel = "rbfdot", kpar = list(sigma = param$sigma), ...) }- $predict
function (modelFit, newdata, submodels = NULL) { out <- kernlab::predict(modelFit, as.matrix(newdata)) if (is.matrix(out)) out <- out[, 1] out }- $prob
- NULL
- $predictors
function (x, ...) { if (hasTerms(x) & !is.null(x@terms)) { out <- predictors.terms(x@terms) } else { out <- colnames(attr(x, "xmatrix")) } if (is.null(out)) out <- names(attr(x, "scaling")$x.scale$`scaled:center`) if (is.null(out)) out <- NA out }- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Radial Basis Function'
- $levels
function (x) lev(x)- $sort
function (x) x
- $svmRadial
- $label
- 'Support Vector Machines with Radial Basis Function Kernel'
- $library
- 'kernlab'
- $type
-
- 'Regression'
- 'Classification'
- $parameters
A data.frame: 2 × 3 parameter class label <chr> <chr> <chr> sigma numeric Sigma C numeric Cost - $grid
function (x, y, len = NULL, search = "grid") { sigmas <- kernlab::sigest(as.matrix(x), na.action = na.omit, scaled = TRUE) if (search == "grid") { out <- expand.grid(sigma = mean(as.vector(sigmas[-2])), C = 2^((1:len) - 3)) } else { rng <- extendrange(log(sigmas), f = 0.75) out <- data.frame(sigma = exp(runif(len, min = rng[1], max = rng[2])), C = 2^runif(len, min = -5, max = 10)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { if (any(names(list(...)) == "prob.model") | is.numeric(y)) { out <- kernlab::ksvm(x = as.matrix(x), y = y, kernel = "rbfdot", kpar = list(sigma = param$sigma), C = param$C, ...) } else { out <- kernlab::ksvm(x = as.matrix(x), y = y, kernel = "rbfdot", kpar = list(sigma = param$sigma), C = param$C, prob.model = classProbs, ...) } out }- $predict
function (modelFit, newdata, submodels = NULL) { svmPred <- function(obj, x) { hasPM <- !is.null(unlist(obj@prob.model)) if (hasPM) { pred <- kernlab::lev(obj)[apply(kernlab::predict(obj, x, type = "probabilities"), 1, which.max)] } else pred <- kernlab::predict(obj, x) pred } out <- try(svmPred(modelFit, newdata), silent = TRUE) if (is.character(kernlab::lev(modelFit))) { if (class(out)[1] == "try-error") { warning("kernlab class prediction calculations failed; returning NAs") out <- rep("", nrow(newdata)) out[seq(along = out)] <- NA } } else { if (class(out)[1] == "try-error") { warning("kernlab prediction calculations failed; returning NAs") out <- rep(NA, nrow(newdata)) } } if (is.matrix(out)) out <- out[, 1] out }- $prob
function (modelFit, newdata, submodels = NULL) { out <- try(kernlab::predict(modelFit, newdata, type = "probabilities"), silent = TRUE) if (class(out)[1] != "try-error") { if (any(out < 0)) { out[out < 0] <- 0 out <- t(apply(out, 1, function(x) x/sum(x))) } out <- out[, kernlab::lev(modelFit), drop = FALSE] } else { warning("kernlab class probability calculations failed; returning NAs") out <- matrix(NA, nrow(newdata) * length(kernlab::lev(modelFit)), ncol = length(kernlab::lev(modelFit))) colnames(out) <- kernlab::lev(modelFit) } out }- $predictors
function (x, ...) { if (hasTerms(x) & !is.null(x@terms)) { out <- predictors.terms(x@terms) } else { out <- colnames(attr(x, "xmatrix")) } if (is.null(out)) out <- names(attr(x, "scaling")$x.scale$`scaled:center`) if (is.null(out)) out <- NA out }- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Radial Basis Function'
- 'Robust Methods'
- $levels
function (x) kernlab::lev(x)- $sort
function (x) { x[order(x$C, -x$sigma), ] }
- $svmRadialCost
- $label
- 'Support Vector Machines with Radial Basis Function Kernel'
- $library
- 'kernlab'
- $type
-
- 'Regression'
- 'Classification'
- $parameters
A data.frame: 1 × 3 parameter class label <chr> <chr> <chr> C numeric Cost - $grid
function (x, y, len = NULL, search = "grid") { if (search == "grid") { out <- data.frame(C = 2^((1:len) - 3)) } else { out <- data.frame(C = 2^runif(len, min = -5, max = 10)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { if (any(names(list(...)) == "prob.model") | is.numeric(y)) { out <- kernlab::ksvm(x = as.matrix(x), y = y, kernel = "rbfdot", C = param$C, ...) } else { out <- kernlab::ksvm(x = as.matrix(x), y = y, kernel = "rbfdot", C = param$C, prob.model = classProbs, ...) } out }- $predict
function (modelFit, newdata, submodels = NULL) { svmPred <- function(obj, x) { hasPM <- !is.null(unlist(obj@prob.model)) if (hasPM) { pred <- kernlab::lev(obj)[apply(kernlab::predict(obj, x, type = "probabilities"), 1, which.max)] } else pred <- kernlab::predict(obj, x) pred } out <- try(svmPred(modelFit, newdata), silent = TRUE) if (is.character(kernlab::lev(modelFit))) { if (class(out)[1] == "try-error") { warning("kernlab class prediction calculations failed; returning NAs") out <- rep("", nrow(newdata)) out[seq(along = out)] <- NA } } else { if (class(out)[1] == "try-error") { warning("kernlab prediction calculations failed; returning NAs") out <- rep(NA, nrow(newdata)) } } if (is.matrix(out)) out <- out[, 1] out }- $prob
function (modelFit, newdata, submodels = NULL) { out <- try(kernlab::predict(modelFit, newdata, type = "probabilities"), silent = TRUE) if (class(out)[1] != "try-error") { if (any(out < 0)) { out[out < 0] <- 0 out <- t(apply(out, 1, function(x) x/sum(x))) } out <- out[, kernlab::lev(modelFit), drop = FALSE] } else { warning("kernlab class probability calculations failed; returning NAs") out <- matrix(NA, nrow(newdata) * length(kernlab::lev(modelFit)), ncol = length(kernlab::lev(modelFit))) colnames(out) <- kernlab::lev(modelFit) } out }- $predictors
function (x, ...) { if (hasTerms(x) & !is.null(x@terms)) { out <- predictors.terms(x@terms) } else { out <- colnames(attr(x, "xmatrix")) } if (is.null(out)) out <- names(attr(x, "scaling")$x.scale$`scaled:center`) if (is.null(out)) out <- NA out }- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Radial Basis Function'
- $levels
function (x) kernlab::lev(x)- $sort
function (x) { x[order(x$C), ] }
- $svmRadialSigma
- $label
- 'Support Vector Machines with Radial Basis Function Kernel'
- $library
- 'kernlab'
- $type
-
- 'Regression'
- 'Classification'
- $parameters
A data.frame: 2 × 3 parameter class label <chr> <chr> <chr> sigma numeric Sigma C numeric Cost - $grid
function (x, y, len = NULL, search = "grid") { sigmas <- kernlab::sigest(as.matrix(x), na.action = na.omit, scaled = TRUE) if (search == "grid") { out <- expand.grid(sigma = seq(min(sigmas), max(sigmas), length = min(6, len)), C = 2^((1:len) - 3)) } else { rng <- extendrange(log(sigmas), f = 0.75) out <- data.frame(sigma = exp(runif(len, min = rng[1], max = rng[2])), C = 2^runif(len, min = -5, max = 10)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { if (any(names(list(...)) == "prob.model") | is.numeric(y)) { out <- kernlab::ksvm(x = as.matrix(x), y = y, kernel = "rbfdot", kpar = list(sigma = param$sigma), C = param$C, ...) } else { out <- kernlab::ksvm(x = as.matrix(x), y = y, kernel = "rbfdot", kpar = list(sigma = param$sigma), C = param$C, prob.model = classProbs, ...) } out }- $predict
function (modelFit, newdata, submodels = NULL) { svmPred <- function(obj, x) { hasPM <- !is.null(unlist(obj@prob.model)) if (hasPM) { pred <- kernlab::lev(obj)[apply(kernlab::predict(obj, x, type = "probabilities"), 1, which.max)] } else pred <- kernlab::predict(obj, x) pred } out <- try(svmPred(modelFit, newdata), silent = TRUE) if (is.character(kernlab::lev(modelFit))) { if (class(out)[1] == "try-error") { warning("kernlab class prediction calculations failed; returning NAs") out <- rep("", nrow(newdata)) out[seq(along = out)] <- NA } } else { if (class(out)[1] == "try-error") { warning("kernlab prediction calculations failed; returning NAs") out <- rep(NA, nrow(newdata)) } } if (is.matrix(out)) out <- out[, 1] out }- $prob
function (modelFit, newdata, submodels = NULL) { out <- try(kernlab::predict(modelFit, newdata, type = "probabilities"), silent = TRUE) if (class(out)[1] != "try-error") { if (any(out < 0)) { out[out < 0] <- 0 out <- t(apply(out, 1, function(x) x/sum(x))) } out <- out[, kernlab::lev(modelFit), drop = FALSE] } else { warning("kernlab class probability calculations failed; returning NAs") out <- matrix(NA, nrow(newdata) * length(kernlab::lev(modelFit)), ncol = length(kernlab::lev(modelFit))) colnames(out) <- kernlab::lev(modelFit) } out }- $predictors
function (x, ...) { if (hasTerms(x) & !is.null(x@terms)) { out <- predictors.terms(x@terms) } else { out <- colnames(attr(x, "xmatrix")) } if (is.null(out)) out <- names(attr(x, "scaling")$x.scale$`scaled:center`) if (is.null(out)) out <- NA out }- $notes
- 'This SVM model tunes over the cost parameter and the RBF kernel parameter sigma. In the latter case, using `tuneLength` will, at most, evaluate six values of the kernel parameter. This enables a broad search over the cost parameter and a relatively narrow search over `sigma`'
- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Radial Basis Function'
- 'Robust Methods'
- $levels
function (x) kernlab::lev(x)- $sort
function (x) { x[order(x$C, -x$sigma), ] }
- $svmRadialWeights
- $label
- 'Support Vector Machines with Class Weights'
- $library
- 'kernlab'
- $type
- 'Classification'
- $parameters
A data.frame: 3 × 3 parameter class label <chr> <chr> <chr> sigma numeric Sigma C numeric Cost Weight numeric Weight - $grid
function (x, y, len = NULL, search = "grid") { sigmas <- kernlab::sigest(as.matrix(x), na.action = na.omit, scaled = TRUE) if (search == "grid") { out <- expand.grid(sigma = mean(as.vector(sigmas[-2])), C = 2^((1:len) - 3), Weight = 1:len) } else { rng <- extendrange(log(sigmas), f = 0.75) out <- data.frame(sigma = exp(runif(len, min = rng[1], max = rng[2])), C = 2^runif(len, min = -5, max = 10), Weight = runif(len, min = 1, max = 25)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { if (param$Weight != 1) { wts <- c(param$Weight, 1) names(wts) <- levels(y) } else wts <- NULL if (any(names(list(...)) == "prob.model") | is.numeric(y)) { out <- kernlab::ksvm(x = as.matrix(x), y = y, kernel = "rbfdot", kpar = list(sigma = param$sigma), class.weights = wts, C = param$C, ...) } else { out <- kernlab::ksvm(x = as.matrix(x), y = y, kernel = "rbfdot", kpar = list(sigma = param$sigma), class.weights = wts, C = param$C, prob.model = classProbs, ...) } out }- $predict
function (modelFit, newdata, submodels = NULL) { out <- kernlab::predict(modelFit, newdata) if (is.matrix(out)) out <- out[, 1] out }- $prob
function (modelFit, newdata, submodels = NULL) { out <- try(kernlab::predict(modelFit, newdata, type = "probabilities"), silent = TRUE) if (class(out)[1] != "try-error") { if (any(out < 0)) { out[out < 0] <- 0 out <- t(apply(out, 1, function(x) x/sum(x))) } out <- out[, kernlab::lev(modelFit), drop = FALSE] } else { warning("kernlab class probability calculations failed; returning NAs") out <- matrix(NA, nrow(newdata) * length(kernlab::lev(modelFit)), ncol = length(kernlab::lev(modelFit))) colnames(out) <- kernlab::lev(modelFit) } out }- $predictors
function (x, ...) { if (hasTerms(x) & !is.null(x@terms)) { out <- predictors.terms(x@terms) } else { out <- colnames(attr(x, "xmatrix")) } if (is.null(out)) out <- names(attr(x, "scaling")$x.scale$`scaled:center`) if (is.null(out)) out <- NA out }- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Radial Basis Function'
- 'Cost Sensitive Learning'
- 'Two Class Only'
- $levels
function (x) kernlab::lev(x)- $sort
function (x) x[order(x$C, -x$sigma, x$Weight), ]
- $lssvmPoly
- $label
- 'Least Squares Support Vector Machine with Polynomial Kernel'
- $library
- 'kernlab'
- $type
- 'Classification'
- $parameters
A data.frame: 3 × 3 parameter class label <chr> <chr> <chr> degree numeric Polynomial Degree scale numeric Scale tau numeric Regularization Parameter - $grid
function (x, y, len = NULL, search = "grid") { if (search == "grid") { out <- expand.grid(degree = seq(1, min(len, 3)), scale = 10^((1:len) - 4), tau = 2^((1:len) - 5)) } else { out <- data.frame(degree = sample(1:3, size = len, replace = TRUE), scale = 10^runif(len, min = -5, log10(2)), tau = 2^runif(len, min = -5, max = 10)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { kernlab::lssvm(x = as.matrix(x), y = y, tau = param$tau, kernel = kernlab::polydot(degree = param$degree, scale = param$scale, offset = 1), ...) }- $predict
function (modelFit, newdata, submodels = NULL) { out <- kernlab::predict(modelFit, as.matrix(newdata)) if (is.matrix(out)) out <- out[, 1] out }- $prob
- NULL
- $predictors
function (x, ...) { if (hasTerms(x) & !is.null(x@terms)) { out <- predictors.terms(x@terms) } else { out <- colnames(attr(x, "xmatrix")) } if (is.null(out)) out <- names(attr(x, "scaling")$xscale$`scaled:center`) if (is.null(out)) out <- NA out }- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Polynomial Model'
- $levels
function (x) lev(x)- $sort
function (x) x
- $svmPoly
- $label
- 'Support Vector Machines with Polynomial Kernel'
- $library
- 'kernlab'
- $type
-
- 'Regression'
- 'Classification'
- $parameters
A data.frame: 3 × 3 parameter class label <chr> <chr> <chr> degree numeric Polynomial Degree scale numeric Scale C numeric Cost - $grid
function (x, y, len = NULL, search = "grid") { if (search == "grid") { out <- expand.grid(degree = seq(1, min(len, 3)), scale = 10^((1:len) - 4), C = 2^((1:len) - 3)) } else { out <- data.frame(degree = sample(1:3, size = len, replace = TRUE), scale = 10^runif(len, min = -5, log10(2)), C = 2^runif(len, min = -5, max = 10)) } out }- $loop
- NULL
- $fit
function (x, y, wts, param, lev, last, classProbs, ...) { if (any(names(list(...)) == "prob.model") | is.numeric(y)) { out <- kernlab::ksvm(x = as.matrix(x), y = y, kernel = kernlab::polydot(degree = param$degree, scale = param$scale, offset = 1), C = param$C, ...) } else { out <- kernlab::ksvm(x = as.matrix(x), y = y, kernel = kernlab::polydot(degree = param$degree, scale = param$scale, offset = 1), C = param$C, prob.model = classProbs, ...) } out }- $predict
function (modelFit, newdata, submodels = NULL) { svmPred <- function(obj, x) { hasPM <- !is.null(unlist(obj@prob.model)) if (hasPM) { pred <- kernlab::lev(obj)[apply(kernlab::predict(obj, x, type = "probabilities"), 1, which.max)] } else pred <- kernlab::predict(obj, x) pred } out <- try(svmPred(modelFit, newdata), silent = TRUE) if (is.character(kernlab::lev(modelFit))) { if (class(out)[1] == "try-error") { warning("kernlab class prediction calculations failed; returning NAs") out <- rep("", nrow(newdata)) out[seq(along = out)] <- NA } } else { if (class(out)[1] == "try-error") { warning("kernlab prediction calculations failed; returning NAs") out <- rep(NA, nrow(newdata)) } } if (is.matrix(out)) out <- out[, 1] out }- $prob
function (modelFit, newdata, submodels = NULL) { out <- try(kernlab::predict(modelFit, newdata, type = "probabilities"), silent = TRUE) if (class(out)[1] != "try-error") { if (any(out < 0)) { out[out < 0] <- 0 out <- t(apply(out, 1, function(x) x/sum(x))) } out <- out[, kernlab::lev(modelFit), drop = FALSE] } else { warning("kernlab class probability calculations failed; returning NAs") out <- matrix(NA, nrow(newdata) * length(kernlab::lev(modelFit)), ncol = length(kernlab::lev(modelFit))) colnames(out) <- kernlab::lev(modelFit) } out }- $predictors
function (x, ...) { if (hasTerms(x) & !is.null(x@terms)) { out <- predictors.terms(x@terms) } else { out <- colnames(attr(x, "xmatrix")) } if (is.null(out)) out <- names(attr(x, "scaling")$xscale$`scaled:center`) if (is.null(out)) out <- NA out }- $tags
-
- 'Kernel Method'
- 'Support Vector Machines'
- 'Polynomial Model'
- 'Robust Methods'
- $levels
function (x) kernlab::lev(x)- $sort
function (x) x[order(x$degree, x$C, x$scale), ]
In [50]:
names(getModelInfo("svm"))
- 'lssvmLinear'
- 'lssvmPoly'
- 'lssvmRadial'
- 'ORFsvm'
- 'svmBoundrangeString'
- 'svmExpoString'
- 'svmLinear'
- 'svmLinear2'
- 'svmLinear3'
- 'svmLinearWeights'
- 'svmLinearWeights2'
- 'svmPoly'
- 'svmRadial'
- 'svmRadialCost'
- 'svmRadialSigma'
- 'svmRadialWeights'
- 'svmSpectrumString'
1) Training - without explicit parameter tuning / using default
In [73]:
# svmLinear
fit.svmLinear <- caret::train(Churn~., data=training_dataset, method="svmLinear",
metric=metric,
trControl=control,
verbose = TRUE
)
print(fit.svmLinear)
Aggregating results Fitting final model on full training set Support Vector Machines with Linear Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' No pre-processing Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1250, 1251, 1251, 1250 Resampling results: Accuracy Kappa 0.8548582 0 Tuning parameter 'C' was held constant at a value of 1
In [74]:
# svmRadial
fit.svmRadial <- caret::train(Churn~., data=training_dataset, method="svmRadial",
metric=metric,
trControl=control,
verbose = TRUE
)
print(fit.svmRadial)
Aggregating results Selecting tuning parameters Fitting sigma = 0.0331, C = 1 on full training set Support Vector Machines with Radial Basis Function Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' No pre-processing Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1251, 1250, 1250, 1251 Resampling results across tuning parameters: C Accuracy Kappa 0.25 0.8558574 0.0116202 0.50 0.8756486 0.2422584 1.00 0.8956422 0.4350147 Tuning parameter 'sigma' was held constant at a value of 0.03310822 Accuracy was used to select the optimal model using the largest value. The final values used for the model were sigma = 0.03310822 and C = 1.
In [75]:
# svmPoly
fit.svmPoly <- caret::train(Churn~., data=training_dataset, method="svmPoly",
metric=metric,
trControl=control,
verbose = TRUE
)
print(fit.svmPoly)
Aggregating results Selecting tuning parameters Fitting degree = 3, scale = 0.1, C = 0.25 on full training set Support Vector Machines with Polynomial Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' No pre-processing Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1251, 1250, 1250, 1251 Resampling results across tuning parameters: degree scale C Accuracy Kappa 1 0.001 0.25 0.8548582 0.000000000 1 0.001 0.50 0.8548582 0.000000000 1 0.001 1.00 0.8548582 0.000000000 1 0.010 0.25 0.8548582 0.000000000 1 0.010 0.50 0.8548582 0.000000000 1 0.010 1.00 0.8548582 0.000000000 1 0.100 0.25 0.8548582 0.000000000 1 0.100 0.50 0.8548582 0.000000000 1 0.100 1.00 0.8548582 0.000000000 2 0.001 0.25 0.8548582 0.000000000 2 0.001 0.50 0.8548582 0.000000000 2 0.001 1.00 0.8548582 0.000000000 2 0.010 0.25 0.8548582 0.000000000 2 0.010 0.50 0.8548582 0.000000000 2 0.010 1.00 0.8574571 0.030040180 2 0.100 0.25 0.9058395 0.548116063 2 0.100 0.50 0.9054406 0.565423514 2 0.100 1.00 0.9024419 0.559400967 3 0.001 0.25 0.8548582 0.000000000 3 0.001 0.50 0.8548582 0.000000000 3 0.001 1.00 0.8548582 0.000000000 3 0.010 0.25 0.8554580 0.007026524 3 0.010 0.50 0.8636552 0.105467971 3 0.010 1.00 0.8794483 0.283427083 3 0.100 0.25 0.9090373 0.598891399 3 0.100 0.50 0.9032388 0.587678103 3 0.100 1.00 0.8926424 0.555832982 Accuracy was used to select the optimal model using the largest value. The final values used for the model were degree = 3, scale = 0.1 and C = 0.25.
2) Training - with explicit parameter tuning using preProcess method
In [76]:
# svmLinear
fit.svmLinear_preProc <- caret::train(Churn~., data=training_dataset, method="svmLinear",
metric=metric,
trControl=control,
preProc=c("center", "scale", "pca"),
verbose = TRUE
)
print(fit.svmLinear_preProc)
Aggregating results Fitting final model on full training set Support Vector Machines with Linear Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' Pre-processing: centered (19), scaled (19), principal component signal extraction (19) Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1251, 1250, 1250, 1251 Resampling results: Accuracy Kappa 0.8548582 0 Tuning parameter 'C' was held constant at a value of 1
In [77]:
# svmRadial
fit.svmRadial_preProc <- caret::train(Churn~., data=training_dataset, method="svmRadial",
metric=metric,
trControl=control,
preProc=c("center", "scale", "pca"),
verbose = TRUE
)
print(fit.svmRadial_preProc)
Aggregating results Selecting tuning parameters Fitting sigma = 0.0491, C = 1 on full training set Support Vector Machines with Radial Basis Function Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' Pre-processing: centered (19), scaled (19), principal component signal extraction (19) Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1251, 1250, 1250, 1251 Resampling results across tuning parameters: C Accuracy Kappa 0.25 0.8548582 0.0000000 0.50 0.8642526 0.1058326 1.00 0.8900433 0.3778059 Tuning parameter 'sigma' was held constant at a value of 0.0490987 Accuracy was used to select the optimal model using the largest value. The final values used for the model were sigma = 0.0490987 and C = 1.
In [78]:
# svmPoly
fit.svmPoly_preProc <- caret::train(Churn~., data=training_dataset, method="svmPoly",
metric=metric,
trControl=control,
preProc=c("center", "scale", "pca"),
verbose = TRUE
)
print(fit.svmPoly_preProc)
Aggregating results Selecting tuning parameters Fitting degree = 3, scale = 0.1, C = 0.25 on full training set Support Vector Machines with Polynomial Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' Pre-processing: centered (19), scaled (19), principal component signal extraction (19) Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1251, 1250, 1251, 1250 Resampling results across tuning parameters: degree scale C Accuracy Kappa 1 0.001 0.25 0.8548582 0.00000000 1 0.001 0.50 0.8548582 0.00000000 1 0.001 1.00 0.8548582 0.00000000 1 0.010 0.25 0.8548582 0.00000000 1 0.010 0.50 0.8548582 0.00000000 1 0.010 1.00 0.8548582 0.00000000 1 0.100 0.25 0.8548582 0.00000000 1 0.100 0.50 0.8548582 0.00000000 1 0.100 1.00 0.8548582 0.00000000 2 0.001 0.25 0.8548582 0.00000000 2 0.001 0.50 0.8548582 0.00000000 2 0.001 1.00 0.8548582 0.00000000 2 0.010 0.25 0.8548582 0.00000000 2 0.010 0.50 0.8548582 0.00000000 2 0.010 1.00 0.8548582 0.00000000 2 0.100 0.25 0.8926459 0.42965743 2 0.100 0.50 0.8984433 0.50078337 2 0.100 1.00 0.8992428 0.52311505 3 0.001 0.25 0.8548582 0.00000000 3 0.001 0.50 0.8548582 0.00000000 3 0.001 1.00 0.8548582 0.00000000 3 0.010 0.25 0.8548582 0.00000000 3 0.010 0.50 0.8548582 0.00000000 3 0.010 1.00 0.8574576 0.03020616 3 0.100 0.25 0.9032409 0.53728468 3 0.100 0.50 0.9016409 0.55131624 3 0.100 1.00 0.8960430 0.54436065 Accuracy was used to select the optimal model using the largest value. The final values used for the model were degree = 3, scale = 0.1 and C = 0.25.
3) Training - with explicit parameter tuning using preProcess method & Automatic Grid i.e. tuneLength
In [79]:
# svmLinear
fit.svmLinear_automaticGrid <- caret::train(Churn~., data=training_dataset, method="svmLinear",
metric=metric,
trControl=control,
preProc=c("center", "scale", "pca"),
tuneLength = tuneLength,
verbose = TRUE
)
print(fit.svmLinear_automaticGrid)
Aggregating results Fitting final model on full training set Support Vector Machines with Linear Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' Pre-processing: centered (19), scaled (19), principal component signal extraction (19) Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1250, 1251, 1250, 1251 Resampling results: Accuracy Kappa 0.8548582 0 Tuning parameter 'C' was held constant at a value of 1
In [80]:
# svmRadial
fit.svmRadial_automaticGrid <- caret::train(Churn~., data=training_dataset, method="svmRadial",
metric=metric,
trControl=control,
preProc=c("center", "scale", "pca"),
tuneLength = tuneLength,
verbose = TRUE
)
print(fit.svmRadial_automaticGrid)
Aggregating results Selecting tuning parameters Fitting sigma = 0.0499, C = 0.5 on full training set Support Vector Machines with Radial Basis Function Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' Pre-processing: centered (19), scaled (19), principal component signal extraction (19) Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1251, 1250, 1251, 1250 Resampling results across tuning parameters: C Accuracy Kappa 0.25 0.8548582 0.0000000 0.50 0.8636534 0.1035911 Tuning parameter 'sigma' was held constant at a value of 0.04993854 Accuracy was used to select the optimal model using the largest value. The final values used for the model were sigma = 0.04993854 and C = 0.5.
In [81]:
# svmPoly
fit.svmPoly_automaticGrid <- caret::train(Churn~., data=training_dataset, method="svmPoly",
metric=metric,
trControl=control,
preProc=c("center", "scale", "pca"),
tuneLength = tuneLength,
verbose = TRUE
)
print(fit.svmPoly_automaticGrid)
Aggregating results Selecting tuning parameters Fitting degree = 1, scale = 0.001, C = 0.25 on full training set Support Vector Machines with Polynomial Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' Pre-processing: centered (19), scaled (19), principal component signal extraction (19) Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1250, 1251, 1250, 1251 Resampling results across tuning parameters: degree scale C Accuracy Kappa 1 0.001 0.25 0.8548582 0 1 0.001 0.50 0.8548582 0 1 0.010 0.25 0.8548582 0 1 0.010 0.50 0.8548582 0 2 0.001 0.25 0.8548582 0 2 0.001 0.50 0.8548582 0 2 0.010 0.25 0.8548582 0 2 0.010 0.50 0.8548582 0 Accuracy was used to select the optimal model using the largest value. The final values used for the model were degree = 1, scale = 0.001 and C = 0.25.
4) Training - with explicit parameter tuning using preProcess method & Manual Grid i.e. tuneGrid
Grid needs to parameterise manually for each particular algorithm
In [82]:
# svmLinear
grid <- expand.grid(C=c(seq(from = 1, to = 5, by = 0.5)))
fit.svmLinear_manualGrid <- caret::train(Churn~., data=training_dataset, method="svmLinear",
metric=metric,
trControl=control,
preProc=c("center", "scale", "pca"),
tuneGrid = grid,
verbose = TRUE
)
print(fit.svmLinear_manualGrid)
plot(fit.svmLinear_manualGrid)
Aggregating results Selecting tuning parameters Fitting C = 1 on full training set Support Vector Machines with Linear Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' Pre-processing: centered (19), scaled (19), principal component signal extraction (19) Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1250, 1251, 1250, 1251 Resampling results across tuning parameters: C Accuracy Kappa 1.0 0.8548582 0 1.5 0.8548582 0 2.0 0.8548582 0 2.5 0.8548582 0 3.0 0.8548582 0 3.5 0.8548582 0 4.0 0.8548582 0 4.5 0.8548582 0 5.0 0.8548582 0 Accuracy was used to select the optimal model using the largest value. The final value used for the model was C = 1.
In [83]:
# svmRadial
grid <- expand.grid(C = c(seq(from = 1, to = 5, by = 0.5)),
sigma = c(seq(from = 0.1, to = 1, by = 0.1))
)
fit.svmRadial_manualGrid <- caret::train(Churn~., data=training_dataset, method="svmRadial",
metric=metric,
trControl=control,
preProc=c("center", "scale", "pca"),
tuneGrid = grid,
verbose = TRUE
)
print(fit.svmRadial_manualGrid)
plot(fit.svmRadial_manualGrid)
Aggregating results Selecting tuning parameters Fitting sigma = 0.1, C = 3 on full training set Support Vector Machines with Radial Basis Function Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' Pre-processing: centered (19), scaled (19), principal component signal extraction (19) Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1251, 1250, 1251, 1250 Resampling results across tuning parameters: C sigma Accuracy Kappa 1.0 0.1 0.8910436 0.395101052 1.0 0.2 0.8770491 0.263986504 1.0 0.3 0.8616558 0.082270494 1.0 0.4 0.8560579 0.014053048 1.0 0.5 0.8550582 0.002353195 1.0 0.6 0.8548582 0.000000000 1.0 0.7 0.8548582 0.000000000 1.0 0.8 0.8548582 0.000000000 1.0 0.9 0.8548582 0.000000000 1.0 1.0 0.8548582 0.000000000 1.5 0.1 0.8994398 0.479467316 1.5 0.2 0.8900443 0.398313543 1.5 0.3 0.8710515 0.207242730 1.5 0.4 0.8614560 0.085221306 1.5 0.5 0.8558579 0.017438650 1.5 0.6 0.8550582 0.002353195 1.5 0.7 0.8548582 0.000000000 1.5 0.8 0.8548582 0.000000000 1.5 0.9 0.8548582 0.000000000 1.5 1.0 0.8548582 0.000000000 2.0 0.1 0.9000395 0.504361056 2.0 0.2 0.8922428 0.427059231 2.0 0.3 0.8718508 0.224707540 2.0 0.4 0.8614560 0.095038285 2.0 0.5 0.8556580 0.018936195 2.0 0.6 0.8544584 0.001146119 2.0 0.7 0.8548584 0.001955066 2.0 0.8 0.8548582 0.000000000 2.0 0.9 0.8548582 0.000000000 2.0 1.0 0.8548582 0.000000000 2.5 0.1 0.9020390 0.522895363 2.5 0.2 0.8914432 0.424427823 2.5 0.3 0.8720508 0.228016585 2.5 0.4 0.8614561 0.100069704 2.5 0.5 0.8556580 0.018936195 2.5 0.6 0.8544584 0.001146119 2.5 0.7 0.8548584 0.001955066 2.5 0.8 0.8548582 0.000000000 2.5 0.9 0.8548582 0.000000000 2.5 1.0 0.8548582 0.000000000 3.0 0.1 0.9034380 0.536488374 3.0 0.2 0.8902432 0.420058273 3.0 0.3 0.8716510 0.228112624 3.0 0.4 0.8612563 0.099602705 3.0 0.5 0.8556580 0.018936195 3.0 0.6 0.8544584 0.001146119 3.0 0.7 0.8548584 0.001955066 3.0 0.8 0.8548582 0.000000000 3.0 0.9 0.8548582 0.000000000 3.0 1.0 0.8548582 0.000000000 3.5 0.1 0.9014385 0.532802322 3.5 0.2 0.8898435 0.420461089 3.5 0.3 0.8710513 0.227597045 3.5 0.4 0.8612563 0.099602705 3.5 0.5 0.8556580 0.018936195 3.5 0.6 0.8544584 0.001146119 3.5 0.7 0.8548584 0.001955066 3.5 0.8 0.8548582 0.000000000 3.5 0.9 0.8548582 0.000000000 3.5 1.0 0.8548582 0.000000000 4.0 0.1 0.9002382 0.534163603 4.0 0.2 0.8878440 0.414978448 4.0 0.3 0.8710510 0.230432537 4.0 0.4 0.8610563 0.099096612 4.0 0.5 0.8556580 0.018936195 4.0 0.6 0.8544584 0.001146119 4.0 0.7 0.8548584 0.001955066 4.0 0.8 0.8548582 0.000000000 4.0 0.9 0.8548582 0.000000000 4.0 1.0 0.8548582 0.000000000 4.5 0.1 0.9004384 0.539666102 4.5 0.2 0.8872443 0.413919157 4.5 0.3 0.8712508 0.232350709 4.5 0.4 0.8610563 0.099096612 4.5 0.5 0.8556580 0.018936195 4.5 0.6 0.8544584 0.001146119 4.5 0.7 0.8548584 0.001955066 4.5 0.8 0.8548582 0.000000000 4.5 0.9 0.8548582 0.000000000 4.5 1.0 0.8548582 0.000000000 5.0 0.1 0.9000390 0.539396659 5.0 0.2 0.8878440 0.418393524 5.0 0.3 0.8710508 0.230455586 5.0 0.4 0.8610563 0.099096612 5.0 0.5 0.8556580 0.018936195 5.0 0.6 0.8544584 0.001146119 5.0 0.7 0.8548584 0.001955066 5.0 0.8 0.8548582 0.000000000 5.0 0.9 0.8548582 0.000000000 5.0 1.0 0.8548582 0.000000000 Accuracy was used to select the optimal model using the largest value. The final values used for the model were sigma = 0.1 and C = 3.
In [84]:
# svmPoly
grid <- expand.grid(C = c(seq(from = 1, to = 5, by = 0.25)),
scale = c(seq(from = 0.001, to = 0.010, by = 0.001)),
degree = c(seq(from = 1, to = 10, by = 1))
)
fit.svmPoly_manualGrid <- caret::train(Churn~., data=training_dataset, method="svmPoly",
metric=metric,
trControl=control,
preProc=c("center", "scale", "pca"),
tuneGrid = grid,
verbose = TRUE
)
print(fit.svmPoly_manualGrid)
plot(fit.svmPoly_manualGrid)
Aggregating results Selecting tuning parameters Fitting degree = 10, scale = 0.009, C = 4.25 on full training set Support Vector Machines with Polynomial Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' Pre-processing: centered (19), scaled (19), principal component signal extraction (19) Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1250, 1251, 1250, 1251 Resampling results across tuning parameters: C scale degree Accuracy Kappa 1.00 0.001 1 0.8548582 0.000000000 1.00 0.001 2 0.8548582 0.000000000 1.00 0.001 3 0.8548582 0.000000000 1.00 0.001 4 0.8548582 0.000000000 1.00 0.001 5 0.8548582 0.000000000 1.00 0.001 6 0.8548582 0.000000000 1.00 0.001 7 0.8548582 0.000000000 1.00 0.001 8 0.8548582 0.000000000 1.00 0.001 9 0.8548582 0.000000000 1.00 0.001 10 0.8548582 0.000000000 1.00 0.002 1 0.8548582 0.000000000 1.00 0.002 2 0.8548582 0.000000000 1.00 0.002 3 0.8548582 0.000000000 1.00 0.002 4 0.8548582 0.000000000 1.00 0.002 5 0.8548582 0.000000000 1.00 0.002 6 0.8548582 0.000000000 1.00 0.002 7 0.8548582 0.000000000 1.00 0.002 8 0.8548582 0.000000000 1.00 0.002 9 0.8548582 0.000000000 1.00 0.002 10 0.8548582 0.000000000 1.00 0.003 1 0.8548582 0.000000000 1.00 0.003 2 0.8548582 0.000000000 1.00 0.003 3 0.8548582 0.000000000 1.00 0.003 4 0.8548582 0.000000000 1.00 0.003 5 0.8548582 0.000000000 1.00 0.003 6 0.8548582 0.000000000 1.00 0.003 7 0.8548582 0.000000000 1.00 0.003 8 0.8560579 0.014016854 1.00 0.003 9 0.8570574 0.027457856 1.00 0.003 10 0.8600563 0.063246904 1.00 0.004 1 0.8548582 0.000000000 1.00 0.004 2 0.8548582 0.000000000 1.00 0.004 3 0.8548582 0.000000000 1.00 0.004 4 0.8548582 0.000000000 1.00 0.004 5 0.8548582 0.000000000 1.00 0.004 6 0.8558580 0.011696471 1.00 0.004 7 0.8572574 0.031645341 1.00 0.004 8 0.8620553 0.086992444 1.00 0.004 9 0.8658547 0.146646561 1.00 0.004 10 0.8712523 0.213636693 1.00 0.005 1 0.8548582 0.000000000 1.00 0.005 2 0.8548582 0.000000000 1.00 0.005 3 0.8548582 0.000000000 1.00 0.005 4 0.8548582 0.000000000 1.00 0.005 5 0.8558580 0.011696471 1.00 0.005 6 0.8592566 0.054318694 1.00 0.005 7 0.8636548 0.119865678 1.00 0.005 8 0.8702532 0.203009851 1.00 0.005 9 0.8750502 0.258235867 1.00 0.005 10 0.8816481 0.327107215 1.00 0.006 1 0.8548582 0.000000000 1.00 0.006 2 0.8548582 0.000000000 1.00 0.006 3 0.8548582 0.000000000 1.00 0.006 4 0.8550582 0.002353195 1.00 0.006 5 0.8580571 0.040763415 1.00 0.006 6 0.8638548 0.125111764 1.00 0.006 7 0.8720523 0.222717083 1.00 0.006 8 0.8762497 0.272764890 1.00 0.006 9 0.8838470 0.348722418 1.00 0.006 10 0.8864459 0.377695450 1.00 0.007 1 0.8548582 0.000000000 1.00 0.007 2 0.8548582 0.000000000 1.00 0.007 3 0.8548582 0.000000000 1.00 0.007 4 0.8564576 0.020546433 1.00 0.007 5 0.8624552 0.099687622 1.00 0.007 6 0.8712524 0.213764196 1.00 0.007 7 0.8776491 0.285345622 1.00 0.007 8 0.8842470 0.352115948 1.00 0.007 9 0.8880451 0.393810533 1.00 0.007 10 0.8908438 0.423250231 1.00 0.008 1 0.8548582 0.000000000 1.00 0.008 2 0.8548582 0.000000000 1.00 0.008 3 0.8548582 0.000000000 1.00 0.008 4 0.8592566 0.054318694 1.00 0.008 5 0.8680537 0.174675046 1.00 0.008 6 0.8756500 0.264873106 1.00 0.008 7 0.8842470 0.353084396 1.00 0.008 8 0.8878454 0.394043677 1.00 0.008 9 0.8908440 0.426580259 1.00 0.008 10 0.8922432 0.443012573 1.00 0.009 1 0.8548582 0.000000000 1.00 0.009 2 0.8548582 0.000000000 1.00 0.009 3 0.8558580 0.011696471 1.00 0.009 4 0.8628550 0.102260835 1.00 0.009 5 0.8732515 0.237044193 1.00 0.009 6 0.8832476 0.342652685 1.00 0.009 7 0.8868457 0.382810897 1.00 0.009 8 0.8906440 0.424347031 1.00 0.009 9 0.8922432 0.443012573 1.00 0.009 10 0.8960425 0.471488371 1.00 0.010 1 0.8548582 0.000000000 1.00 0.010 2 0.8548582 0.000000000 1.00 0.010 3 0.8564576 0.020546433 1.00 0.010 4 0.8662545 0.152052900 1.00 0.010 5 0.8756500 0.267345526 1.00 0.010 6 0.8848468 0.359151466 1.00 0.010 7 0.8904441 0.416700875 1.00 0.010 8 0.8910436 0.435063437 1.00 0.010 9 0.8950427 0.465229136 1.00 0.010 10 0.8966417 0.480257219 1.25 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0.147458132 4.25 0.003 7 0.8730518 0.234980995 4.25 0.003 8 0.8786494 0.299946615 4.25 0.003 9 0.8854460 0.365820579 4.25 0.003 10 0.8886460 0.395616297 4.25 0.004 1 0.8548582 0.000000000 4.25 0.004 2 0.8548582 0.000000000 4.25 0.004 3 0.8550582 0.002353195 4.25 0.004 4 0.8610560 0.074230165 4.25 0.004 5 0.8688539 0.187817864 4.25 0.004 6 0.8770499 0.282385798 4.25 0.004 7 0.8860459 0.370669178 4.25 0.004 8 0.8882456 0.398889627 4.25 0.004 9 0.8910438 0.431593520 4.25 0.004 10 0.8912433 0.447034593 4.25 0.005 1 0.8548582 0.000000000 4.25 0.005 2 0.8548582 0.000000000 4.25 0.005 3 0.8568574 0.025122989 4.25 0.005 4 0.8684537 0.178049675 4.25 0.005 5 0.8782496 0.295237693 4.25 0.005 6 0.8872459 0.383278115 4.25 0.005 7 0.8900446 0.418822158 4.25 0.005 8 0.8916433 0.447409035 4.25 0.005 9 0.8938428 0.468012736 4.25 0.005 10 0.8954422 0.479870400 4.25 0.006 1 0.8548582 0.000000000 4.25 0.006 2 0.8548582 0.000000000 4.25 0.006 3 0.8628552 0.098705222 4.25 0.006 4 0.8750504 0.258017346 4.25 0.006 5 0.8872460 0.384138391 4.25 0.006 6 0.8900443 0.420634370 4.25 0.006 7 0.8922430 0.455521622 4.25 0.006 8 0.8946422 0.476559675 4.25 0.006 9 0.8960411 0.483430032 4.25 0.006 10 0.8978412 0.500973263 4.25 0.007 1 0.8548582 0.000000000 4.25 0.007 2 0.8552582 0.004688062 4.25 0.007 3 0.8676544 0.169489642 4.25 0.007 4 0.8826475 0.339974208 4.25 0.007 5 0.8888451 0.409756213 4.25 0.007 6 0.8918430 0.450493869 4.25 0.007 7 0.8950420 0.479193346 4.25 0.007 8 0.8972408 0.490721518 4.25 0.007 9 0.8986406 0.508312552 4.25 0.007 10 0.8958419 0.503278954 4.25 0.008 1 0.8548582 0.000000000 4.25 0.008 2 0.8560579 0.015905667 4.25 0.008 3 0.8726521 0.231378649 4.25 0.008 4 0.8876460 0.387207766 4.25 0.008 5 0.8912438 0.441216579 4.25 0.008 6 0.8942428 0.471360709 4.25 0.008 7 0.8964409 0.486812385 4.25 0.008 8 0.8986406 0.508312552 4.25 0.008 9 0.8956417 0.503294492 4.25 0.008 10 0.8982393 0.528920735 4.25 0.009 1 0.8548582 0.000000000 4.25 0.009 2 0.8576574 0.034176538 4.25 0.009 3 0.8768499 0.281892086 4.25 0.009 4 0.8890449 0.410363653 4.25 0.009 5 0.8930428 0.460318347 4.25 0.009 6 0.8952420 0.480749955 4.25 0.009 7 0.8976411 0.501675594 4.25 0.009 8 0.8964417 0.505707902 4.25 0.009 9 0.8984393 0.529492322 4.25 0.009 10 0.9010382 0.551562222 4.25 0.010 1 0.8548582 0.000000000 4.25 0.010 2 0.8620558 0.086636279 4.25 0.010 3 0.8832472 0.345836859 4.25 0.010 4 0.8918436 0.439109305 4.25 0.010 5 0.8936427 0.468809018 4.25 0.010 6 0.8970409 0.492168688 4.25 0.010 7 0.8976409 0.509938728 4.25 0.010 8 0.8964406 0.516270809 4.25 0.010 9 0.8996388 0.544365021 4.25 0.010 10 0.8954408 0.536769853 4.50 0.001 1 0.8548582 0.000000000 4.50 0.001 2 0.8548582 0.000000000 4.50 0.001 3 0.8548582 0.000000000 4.50 0.001 4 0.8548582 0.000000000 4.50 0.001 5 0.8548582 0.000000000 4.50 0.001 6 0.8548582 0.000000000 4.50 0.001 7 0.8548582 0.000000000 4.50 0.001 8 0.8548582 0.000000000 4.50 0.001 9 0.8548582 0.000000000 4.50 0.001 10 0.8550582 0.002353195 4.50 0.002 1 0.8548582 0.000000000 4.50 0.002 2 0.8548582 0.000000000 4.50 0.002 3 0.8548582 0.000000000 4.50 0.002 4 0.8548582 0.000000000 4.50 0.002 5 0.8548582 0.000000000 4.50 0.002 6 0.8560579 0.015887588 4.50 0.002 7 0.8596566 0.058729676 4.50 0.002 8 0.8646547 0.126845907 4.50 0.002 9 0.8692534 0.185777607 4.50 0.002 10 0.8734515 0.238535420 4.50 0.003 1 0.8548582 0.000000000 4.50 0.003 2 0.8548582 0.000000000 4.50 0.003 3 0.8548582 0.000000000 4.50 0.003 4 0.8558580 0.011696471 4.50 0.003 5 0.8608560 0.072057445 4.50 0.003 6 0.8666547 0.160110312 4.50 0.003 7 0.8736512 0.244659730 4.50 0.003 8 0.8802481 0.313943999 4.50 0.003 9 0.8866457 0.375484443 4.50 0.003 10 0.8882456 0.395325779 4.50 0.004 1 0.8548582 0.000000000 4.50 0.004 2 0.8548582 0.000000000 4.50 0.004 3 0.8552582 0.004688062 4.50 0.004 4 0.8620558 0.086733121 4.50 0.004 5 0.8704531 0.206145013 4.50 0.004 6 0.8788492 0.301753392 4.50 0.004 7 0.8870459 0.381590401 4.50 0.004 8 0.8898448 0.411921178 4.50 0.004 9 0.8912438 0.436422045 4.50 0.004 10 0.8916433 0.452869020 4.50 0.005 1 0.8548582 0.000000000 4.50 0.005 2 0.8548582 0.000000000 4.50 0.005 3 0.8574574 0.031954022 4.50 0.005 4 0.8690537 0.188290097 4.50 0.005 5 0.8796484 0.309828555 4.50 0.005 6 0.8882460 0.390818803 4.50 0.005 7 0.8906440 0.425933708 4.50 0.005 8 0.8914432 0.449260334 4.50 0.005 9 0.8944425 0.473649399 4.50 0.005 10 0.8958416 0.481967262 4.50 0.006 1 0.8548582 0.000000000 4.50 0.006 2 0.8548582 0.000000000 4.50 0.006 3 0.8636547 0.113603679 4.50 0.006 4 0.8762499 0.271355902 4.50 0.006 5 0.8878459 0.387821507 4.50 0.006 6 0.8904440 0.427089339 4.50 0.006 7 0.8924432 0.456922140 4.50 0.006 8 0.8954419 0.481254526 4.50 0.006 9 0.8972408 0.490721518 4.50 0.006 10 0.8980411 0.505028882 4.50 0.007 1 0.8548582 0.000000000 4.50 0.007 2 0.8552582 0.004688062 4.50 0.007 3 0.8690536 0.186765249 4.50 0.007 4 0.8858464 0.367019116 4.50 0.007 5 0.8890449 0.412981943 4.50 0.007 6 0.8926428 0.457550459 4.50 0.007 7 0.8956417 0.482683926 4.50 0.007 8 0.8970412 0.490840306 4.50 0.007 9 0.8974409 0.504639798 4.50 0.007 10 0.8962417 0.505851129 4.50 0.008 1 0.8548582 0.000000000 4.50 0.008 2 0.8566576 0.022820477 4.50 0.008 3 0.8734513 0.241324214 4.50 0.008 4 0.8888456 0.398254890 4.50 0.008 5 0.8912438 0.442753430 4.50 0.008 6 0.8944424 0.475063638 4.50 0.008 7 0.8972408 0.491425372 4.50 0.008 8 0.8976408 0.505900645 4.50 0.008 9 0.8964414 0.509689120 4.50 0.008 10 0.8984393 0.533162673 4.50 0.009 1 0.8548582 0.000000000 4.50 0.009 2 0.8588569 0.049698540 4.50 0.009 3 0.8784491 0.298338140 4.50 0.009 4 0.8886451 0.410853430 4.50 0.009 5 0.8928430 0.461072811 4.50 0.009 6 0.8948417 0.480307516 4.50 0.009 7 0.8976411 0.503659126 4.50 0.009 8 0.8956419 0.505223812 4.50 0.009 9 0.8988390 0.534357042 4.50 0.009 10 0.8996388 0.547265556 4.50 0.010 1 0.8548582 0.000000000 4.50 0.010 2 0.8626553 0.096455100 4.50 0.010 3 0.8854467 0.364776118 4.50 0.010 4 0.8916438 0.442458654 4.50 0.010 5 0.8944424 0.474368731 4.50 0.010 6 0.8966409 0.492356948 4.50 0.010 7 0.8970411 0.508799773 4.50 0.010 8 0.8980393 0.526918484 4.50 0.010 9 0.9006385 0.550778247 4.50 0.010 10 0.8956406 0.539564747 4.75 0.001 1 0.8548582 0.000000000 4.75 0.001 2 0.8548582 0.000000000 4.75 0.001 3 0.8548582 0.000000000 4.75 0.001 4 0.8548582 0.000000000 4.75 0.001 5 0.8548582 0.000000000 4.75 0.001 6 0.8548582 0.000000000 4.75 0.001 7 0.8548582 0.000000000 4.75 0.001 8 0.8548582 0.000000000 4.75 0.001 9 0.8548582 0.000000000 4.75 0.001 10 0.8552582 0.004688062 4.75 0.002 1 0.8548582 0.000000000 4.75 0.002 2 0.8548582 0.000000000 4.75 0.002 3 0.8548582 0.000000000 4.75 0.002 4 0.8548582 0.000000000 4.75 0.002 5 0.8548582 0.000000000 4.75 0.002 6 0.8564576 0.020546433 4.75 0.002 7 0.8606560 0.069834930 4.75 0.002 8 0.8650548 0.135429537 4.75 0.002 9 0.8690537 0.191129789 4.75 0.002 10 0.8740510 0.248559119 4.75 0.003 1 0.8548582 0.000000000 4.75 0.003 2 0.8548582 0.000000000 4.75 0.003 3 0.8548582 0.000000000 4.75 0.003 4 0.8560580 0.013995319 4.75 0.003 5 0.8618558 0.084608543 4.75 0.003 6 0.8690536 0.183827455 4.75 0.003 7 0.8748504 0.256347507 4.75 0.003 8 0.8820476 0.332705391 4.75 0.003 9 0.8870459 0.381657060 4.75 0.003 10 0.8882456 0.398889627 4.75 0.004 1 0.8548582 0.000000000 4.75 0.004 2 0.8548582 0.000000000 4.75 0.004 3 0.8556582 0.009358009 4.75 0.004 4 0.8628552 0.098705222 4.75 0.004 5 0.8714529 0.217851419 4.75 0.004 6 0.8804481 0.315448610 4.75 0.004 7 0.8874457 0.384886328 4.75 0.004 8 0.8896449 0.414849836 4.75 0.004 9 0.8916436 0.442452442 4.75 0.004 10 0.8928432 0.460453781 4.75 0.005 1 0.8548582 0.000000000 4.75 0.005 2 0.8548582 0.000000000 4.75 0.005 3 0.8584569 0.045218768 4.75 0.005 4 0.8702531 0.204393501 4.75 0.005 5 0.8814478 0.326337015 4.75 0.005 6 0.8884457 0.396009930 4.75 0.005 7 0.8906438 0.431202070 4.75 0.005 8 0.8922432 0.455523127 4.75 0.005 9 0.8946422 0.476506637 4.75 0.005 10 0.8958412 0.482725729 4.75 0.006 1 0.8548582 0.000000000 4.75 0.006 2 0.8548582 0.000000000 4.75 0.006 3 0.8650547 0.132094621 4.75 0.006 4 0.8770499 0.283680335 4.75 0.006 5 0.8888456 0.397406289 4.75 0.006 6 0.8914438 0.437848041 4.75 0.006 7 0.8926433 0.459827973 4.75 0.006 8 0.8954419 0.482056457 4.75 0.006 9 0.8968412 0.490204879 4.75 0.006 10 0.8982408 0.506377447 4.75 0.007 1 0.8548582 0.000000000 4.75 0.007 2 0.8556582 0.009358009 4.75 0.007 3 0.8694534 0.195162512 4.75 0.007 4 0.8852464 0.365192444 4.75 0.007 5 0.8894444 0.418773907 4.75 0.007 6 0.8924430 0.458458154 4.75 0.007 7 0.8952419 0.481438208 4.75 0.007 8 0.8966412 0.491739780 4.75 0.007 9 0.8978406 0.508468806 4.75 0.007 10 0.8970411 0.513485499 4.75 0.008 1 0.8548582 0.000000000 4.75 0.008 2 0.8566576 0.022820477 4.75 0.008 3 0.8746505 0.254420785 4.75 0.008 4 0.8884456 0.398655708 4.75 0.008 5 0.8916433 0.448191114 4.75 0.008 6 0.8956417 0.481883821 4.75 0.008 7 0.8968409 0.491547698 4.75 0.008 8 0.8978406 0.508468806 4.75 0.008 9 0.8974406 0.517698999 4.75 0.008 10 0.8990392 0.537322287 4.75 0.009 1 0.8548582 0.000000000 4.75 0.009 2 0.8600564 0.063151862 4.75 0.009 3 0.8804486 0.316771987 4.75 0.009 4 0.8894446 0.417574878 4.75 0.009 5 0.8934428 0.464385915 4.75 0.009 6 0.8962411 0.488225186 4.75 0.009 7 0.8982408 0.507704127 4.75 0.009 8 0.8974411 0.516444736 4.75 0.009 9 0.8988392 0.536136741 4.75 0.009 10 0.8984393 0.542238779 4.75 0.010 1 0.8548582 0.000000000 4.75 0.010 2 0.8628552 0.103643168 4.75 0.010 3 0.8860462 0.372627199 4.75 0.010 4 0.8914438 0.442630490 4.75 0.010 5 0.8950419 0.479314460 4.75 0.010 6 0.8964414 0.493124600 4.75 0.010 7 0.8966414 0.507519443 4.75 0.010 8 0.8988392 0.533130103 4.75 0.010 9 0.8996388 0.547128817 4.75 0.010 10 0.8950409 0.538252839 5.00 0.001 1 0.8548582 0.000000000 5.00 0.001 2 0.8548582 0.000000000 5.00 0.001 3 0.8548582 0.000000000 5.00 0.001 4 0.8548582 0.000000000 5.00 0.001 5 0.8548582 0.000000000 5.00 0.001 6 0.8548582 0.000000000 5.00 0.001 7 0.8548582 0.000000000 5.00 0.001 8 0.8548582 0.000000000 5.00 0.001 9 0.8548582 0.000000000 5.00 0.001 10 0.8556582 0.009358009 5.00 0.002 1 0.8548582 0.000000000 5.00 0.002 2 0.8548582 0.000000000 5.00 0.002 3 0.8548582 0.000000000 5.00 0.002 4 0.8548582 0.000000000 5.00 0.002 5 0.8550582 0.002353195 5.00 0.002 6 0.8566576 0.022820477 5.00 0.002 7 0.8618558 0.082915837 5.00 0.002 8 0.8656547 0.146092379 5.00 0.002 9 0.8704531 0.206145013 5.00 0.002 10 0.8748504 0.256347507 5.00 0.003 1 0.8548582 0.000000000 5.00 0.003 2 0.8548582 0.000000000 5.00 0.003 3 0.8548582 0.000000000 5.00 0.003 4 0.8560579 0.015887588 5.00 0.003 5 0.8626553 0.096592384 5.00 0.003 6 0.8688539 0.187817864 5.00 0.003 7 0.8754502 0.262799823 5.00 0.003 8 0.8840467 0.350523495 5.00 0.003 9 0.8872460 0.383123590 5.00 0.003 10 0.8898448 0.412842945 5.00 0.004 1 0.8548582 0.000000000 5.00 0.004 2 0.8548582 0.000000000 5.00 0.004 3 0.8558580 0.011696471 5.00 0.004 4 0.8634550 0.109947626 5.00 0.004 5 0.8726521 0.231378649 5.00 0.004 6 0.8822475 0.333283308 5.00 0.004 7 0.8880460 0.389263894 5.00 0.004 8 0.8898446 0.418192526 5.00 0.004 9 0.8914435 0.445969991 5.00 0.004 10 0.8926433 0.459731536 5.00 0.005 1 0.8548582 0.000000000 5.00 0.005 2 0.8548582 0.000000000 5.00 0.005 3 0.8598566 0.060918807 5.00 0.005 4 0.8712529 0.213459077 5.00 0.005 5 0.8826475 0.339974208 5.00 0.005 6 0.8882456 0.397081957 5.00 0.005 7 0.8916438 0.440812611 5.00 0.005 8 0.8926432 0.459832791 5.00 0.005 9 0.8952419 0.480631137 5.00 0.005 10 0.8964409 0.486812385 5.00 0.006 1 0.8548582 0.000000000 5.00 0.006 2 0.8548582 0.000000000 5.00 0.006 3 0.8646550 0.134456950 5.00 0.006 4 0.8786491 0.298902319 5.00 0.006 5 0.8882457 0.395314036 5.00 0.006 6 0.8914438 0.441835815 5.00 0.006 7 0.8932433 0.463011790 5.00 0.006 8 0.8952420 0.480695585 5.00 0.006 9 0.8968412 0.492375207 5.00 0.006 10 0.8980406 0.508454825 5.00 0.007 1 0.8548582 0.000000000 5.00 0.007 2 0.8560580 0.013995319 5.00 0.007 3 0.8712529 0.213459077 5.00 0.007 4 0.8874456 0.384686489 5.00 0.007 5 0.8902441 0.427343953 5.00 0.007 6 0.8928432 0.461070095 5.00 0.007 7 0.8950420 0.480066863 5.00 0.007 8 0.8972412 0.496251382 5.00 0.007 9 0.8980404 0.510550661 5.00 0.007 10 0.8972406 0.516493627 5.00 0.008 1 0.8548582 0.000000000 5.00 0.008 2 0.8568576 0.025077147 5.00 0.008 3 0.8758500 0.266422036 5.00 0.008 4 0.8876457 0.396236433 5.00 0.008 5 0.8916432 0.448222796 5.00 0.008 6 0.8952419 0.480631137 5.00 0.008 7 0.8964411 0.491070278 5.00 0.008 8 0.8976408 0.509292898 5.00 0.008 9 0.8974406 0.518434260 5.00 0.008 10 0.8996387 0.542729938 5.00 0.009 1 0.8548582 0.000000000 5.00 0.009 2 0.8608561 0.071896757 5.00 0.009 3 0.8826475 0.337756825 5.00 0.009 4 0.8902446 0.425408992 5.00 0.009 5 0.8936428 0.465746417 5.00 0.009 6 0.8968409 0.492926736 5.00 0.009 7 0.8982406 0.510362305 5.00 0.009 8 0.8974408 0.517720395 5.00 0.009 9 0.8996387 0.542786938 5.00 0.009 10 0.8982388 0.544138687 5.00 0.010 1 0.8548582 0.000000000 5.00 0.010 2 0.8648545 0.127092987 5.00 0.010 3 0.8872459 0.383089427 5.00 0.010 4 0.8916435 0.445571043 5.00 0.010 5 0.8948419 0.477944746 5.00 0.010 6 0.8964412 0.495865625 5.00 0.010 7 0.8974411 0.512544710 5.00 0.010 8 0.8982392 0.533078032 5.00 0.010 9 0.8980393 0.541614769 5.00 0.010 10 0.8950408 0.538912055 Accuracy was used to select the optimal model using the largest value. The final values used for the model were degree = 10, scale = 0.009 and C = 4.25.
Collect the results of trained models
In [85]:
results <- resamples(list( trained_Model_1 = fit.svmLinear
, trained_Model_2 = fit.svmRadial
, trained_Model_3 = fit.svmPoly
, trained_Model_4 = fit.svmLinear_preProc
, trained_Model_5 = fit.svmRadial_preProc
, trained_Model_6 = fit.svmRadial_preProc
, trained_Model_7 = fit.svmLinear_automaticGrid
, trained_Model_8 = fit.svmRadial_automaticGrid
, trained_Model_9 = fit.svmPoly_automaticGrid
, trained_Model_10 = fit.svmLinear_manualGrid
, trained_Model_11 = fit.svmRadial_manualGrid
, trained_Model_12 = fit.svmPoly_manualGrid
))
Summarize the fitted models
In [86]:
summary(results)
Call:
summary.resamples(object = results)
Models: trained_Model_1, trained_Model_2, trained_Model_3, trained_Model_4, trained_Model_5, trained_Model_6, trained_Model_7, trained_Model_8, trained_Model_9, trained_Model_10, trained_Model_11, trained_Model_12
Number of resamples: 4
Accuracy
Min. 1st Qu. Median Mean 3rd Qu. Max.
trained_Model_1 0.8545164 0.8545164 0.8548582 0.8548582 0.8552000 0.8552000
trained_Model_2 0.8904876 0.8928219 0.8960406 0.8956422 0.8988609 0.9000000
trained_Model_3 0.9032774 0.9038193 0.9072358 0.9090373 0.9124537 0.9184000
trained_Model_4 0.8545164 0.8545164 0.8548582 0.8548582 0.8552000 0.8552000
trained_Model_5 0.8816000 0.8882657 0.8916867 0.8900433 0.8934643 0.8952000
trained_Model_6 0.8816000 0.8882657 0.8916867 0.8900433 0.8934643 0.8952000
trained_Model_7 0.8545164 0.8545164 0.8548582 0.8548582 0.8552000 0.8552000
trained_Model_8 0.8592000 0.8616000 0.8632544 0.8636534 0.8653078 0.8689049
trained_Model_9 0.8545164 0.8545164 0.8548582 0.8548582 0.8552000 0.8552000
trained_Model_10 0.8545164 0.8545164 0.8548582 0.8548582 0.8552000 0.8552000
trained_Model_11 0.8912000 0.8990590 0.9048761 0.9034380 0.9092552 0.9128000
trained_Model_12 0.8952000 0.8988000 0.9004396 0.9010382 0.9026779 0.9080735
NA's
trained_Model_1 0
trained_Model_2 0
trained_Model_3 0
trained_Model_4 0
trained_Model_5 0
trained_Model_6 0
trained_Model_7 0
trained_Model_8 0
trained_Model_9 0
trained_Model_10 0
trained_Model_11 0
trained_Model_12 0
Kappa
Min. 1st Qu. Median Mean 3rd Qu. Max.
trained_Model_1 0.00000000 0.00000000 0.0000000 0.0000000 0.0000000 0.0000000
trained_Model_2 0.40525167 0.40907562 0.4326150 0.4350147 0.4585541 0.4695772
trained_Model_3 0.55522418 0.56871090 0.5979642 0.5988914 0.6281447 0.6444130
trained_Model_4 0.00000000 0.00000000 0.0000000 0.0000000 0.0000000 0.0000000
trained_Model_5 0.29086714 0.36655898 0.4012314 0.3778059 0.4124783 0.4178937
trained_Model_6 0.29086714 0.36655898 0.4012314 0.3778059 0.4124783 0.4178937
trained_Model_7 0.00000000 0.00000000 0.0000000 0.0000000 0.0000000 0.0000000
trained_Model_8 0.05362505 0.08019566 0.0983517 0.1035911 0.1217471 0.1640358
trained_Model_9 0.00000000 0.00000000 0.0000000 0.0000000 0.0000000 0.0000000
trained_Model_10 0.00000000 0.00000000 0.0000000 0.0000000 0.0000000 0.0000000
trained_Model_11 0.49325432 0.50752411 0.5343763 0.5364884 0.5633406 0.5839466
trained_Model_12 0.53572647 0.53917530 0.5412529 0.5515622 0.5536398 0.5880166
NA's
trained_Model_1 0
trained_Model_2 0
trained_Model_3 0
trained_Model_4 0
trained_Model_5 0
trained_Model_6 0
trained_Model_7 0
trained_Model_8 0
trained_Model_9 0
trained_Model_10 0
trained_Model_11 0
trained_Model_12 0
Plot and rank the fitted models
In [87]:
dotplot(results)
In [88]:
bwplot(results)
Assign the best trained model based on Accuracy
In [89]:
best_trained_model <- fit.svmRadial_manualGrid
9. Test skill of the BEST trained model on validation/testing dataset¶
In [90]:
predictions <- predict(best_trained_model, newdata=testing_dataset)
Evaluate the BEST trained model and print results
In [91]:
res_ <- caret::confusionMatrix(table(predictions, testing_dataset$Churn))
print("Results from the BEST trained model ... ...\n");
print(round(res_$overall, digits = 3))
[1] "Results from the BEST trained model ... ...\n"
Accuracy Kappa AccuracyLower AccuracyUpper AccuracyNull
0.907 0.559 0.886 0.926 0.856
AccuracyPValue McnemarPValue
0.000 0.000
10. Save the model to disk¶
In [92]:
#getwd()
saveRDS(best_trained_model, "./best_trained_model.rds")
In [93]:
# load the model
#getwd()
saved_model <- readRDS("./best_trained_model.rds")
print(saved_model)
Support Vector Machines with Radial Basis Function Kernel 2501 samples 19 predictor 2 classes: 'no', 'yes' Pre-processing: centered (19), scaled (19), principal component signal extraction (19) Resampling: Cross-Validated (2 fold, repeated 2 times) Summary of sample sizes: 1251, 1250, 1251, 1250 Resampling results across tuning parameters: C sigma Accuracy Kappa 1.0 0.1 0.8910436 0.395101052 1.0 0.2 0.8770491 0.263986504 1.0 0.3 0.8616558 0.082270494 1.0 0.4 0.8560579 0.014053048 1.0 0.5 0.8550582 0.002353195 1.0 0.6 0.8548582 0.000000000 1.0 0.7 0.8548582 0.000000000 1.0 0.8 0.8548582 0.000000000 1.0 0.9 0.8548582 0.000000000 1.0 1.0 0.8548582 0.000000000 1.5 0.1 0.8994398 0.479467316 1.5 0.2 0.8900443 0.398313543 1.5 0.3 0.8710515 0.207242730 1.5 0.4 0.8614560 0.085221306 1.5 0.5 0.8558579 0.017438650 1.5 0.6 0.8550582 0.002353195 1.5 0.7 0.8548582 0.000000000 1.5 0.8 0.8548582 0.000000000 1.5 0.9 0.8548582 0.000000000 1.5 1.0 0.8548582 0.000000000 2.0 0.1 0.9000395 0.504361056 2.0 0.2 0.8922428 0.427059231 2.0 0.3 0.8718508 0.224707540 2.0 0.4 0.8614560 0.095038285 2.0 0.5 0.8556580 0.018936195 2.0 0.6 0.8544584 0.001146119 2.0 0.7 0.8548584 0.001955066 2.0 0.8 0.8548582 0.000000000 2.0 0.9 0.8548582 0.000000000 2.0 1.0 0.8548582 0.000000000 2.5 0.1 0.9020390 0.522895363 2.5 0.2 0.8914432 0.424427823 2.5 0.3 0.8720508 0.228016585 2.5 0.4 0.8614561 0.100069704 2.5 0.5 0.8556580 0.018936195 2.5 0.6 0.8544584 0.001146119 2.5 0.7 0.8548584 0.001955066 2.5 0.8 0.8548582 0.000000000 2.5 0.9 0.8548582 0.000000000 2.5 1.0 0.8548582 0.000000000 3.0 0.1 0.9034380 0.536488374 3.0 0.2 0.8902432 0.420058273 3.0 0.3 0.8716510 0.228112624 3.0 0.4 0.8612563 0.099602705 3.0 0.5 0.8556580 0.018936195 3.0 0.6 0.8544584 0.001146119 3.0 0.7 0.8548584 0.001955066 3.0 0.8 0.8548582 0.000000000 3.0 0.9 0.8548582 0.000000000 3.0 1.0 0.8548582 0.000000000 3.5 0.1 0.9014385 0.532802322 3.5 0.2 0.8898435 0.420461089 3.5 0.3 0.8710513 0.227597045 3.5 0.4 0.8612563 0.099602705 3.5 0.5 0.8556580 0.018936195 3.5 0.6 0.8544584 0.001146119 3.5 0.7 0.8548584 0.001955066 3.5 0.8 0.8548582 0.000000000 3.5 0.9 0.8548582 0.000000000 3.5 1.0 0.8548582 0.000000000 4.0 0.1 0.9002382 0.534163603 4.0 0.2 0.8878440 0.414978448 4.0 0.3 0.8710510 0.230432537 4.0 0.4 0.8610563 0.099096612 4.0 0.5 0.8556580 0.018936195 4.0 0.6 0.8544584 0.001146119 4.0 0.7 0.8548584 0.001955066 4.0 0.8 0.8548582 0.000000000 4.0 0.9 0.8548582 0.000000000 4.0 1.0 0.8548582 0.000000000 4.5 0.1 0.9004384 0.539666102 4.5 0.2 0.8872443 0.413919157 4.5 0.3 0.8712508 0.232350709 4.5 0.4 0.8610563 0.099096612 4.5 0.5 0.8556580 0.018936195 4.5 0.6 0.8544584 0.001146119 4.5 0.7 0.8548584 0.001955066 4.5 0.8 0.8548582 0.000000000 4.5 0.9 0.8548582 0.000000000 4.5 1.0 0.8548582 0.000000000 5.0 0.1 0.9000390 0.539396659 5.0 0.2 0.8878440 0.418393524 5.0 0.3 0.8710508 0.230455586 5.0 0.4 0.8610563 0.099096612 5.0 0.5 0.8556580 0.018936195 5.0 0.6 0.8544584 0.001146119 5.0 0.7 0.8548584 0.001955066 5.0 0.8 0.8548582 0.000000000 5.0 0.9 0.8548582 0.000000000 5.0 1.0 0.8548582 0.000000000 Accuracy was used to select the optimal model using the largest value. The final values used for the model were sigma = 0.1 and C = 3.
In [94]:
# make a predictions on "new data" using the final model
final_predictions <- predict(saved_model, dataSet[1:20])
confusionMatrix(table(final_predictions, dataSet$Churn))
res_ <- confusionMatrix(table(final_predictions, dataSet$Churn))
print("Results from the BEST trained model ... ...\n");
print(round(res_$overall, digits = 3))
Confusion Matrix and Statistics
final_predictions no yes
no 2831 110
yes 19 373
Accuracy : 0.9613
95% CI : (0.9542, 0.9676)
No Information Rate : 0.8551
P-Value [Acc > NIR] : < 2.2e-16
Kappa : 0.8306
Mcnemar's Test P-Value : 2.299e-15
Sensitivity : 0.9933
Specificity : 0.7723
Pos Pred Value : 0.9626
Neg Pred Value : 0.9515
Prevalence : 0.8551
Detection Rate : 0.8494
Detection Prevalence : 0.8824
Balanced Accuracy : 0.8828
'Positive' Class : no
[1] "Results from the BEST trained model ... ...\n"
Accuracy Kappa AccuracyLower AccuracyUpper AccuracyNull
0.961 0.831 0.954 0.968 0.855
AccuracyPValue McnemarPValue
0.000 0.000
In [95]:
print(res_$table)
fourfoldplot(res_$table, color = c("#CC6666", "#99CC99"),
conf.level = 0, margin = 1, main = "Confusion Matrix")
final_predictions no yes
no 2831 110
yes 19 373
