Spam detection - Classification Algorithms
Alema Fissuh
2023-02-07
Spam detection - Classification machine learning algorithms
The Spam data with description are in https://archive.ics.uci.edu/ml/datasets/Spambase
We can also get its formatted version from a package “kernlab”
#install.packages("kernlab")
library(kernlab)data(spam) # getting spam data from kernlab package
dim(spam) # to see the number of rows and columns / dimension## [1] 4601 58names(spam) # to see the column names## [1] "make" "address" "all"
## [4] "num3d" "our" "over"
## [7] "remove" "internet" "order"
## [10] "mail" "receive" "will"
## [13] "people" "report" "addresses"
## [16] "free" "business" "email"
## [19] "you" "credit" "your"
## [22] "font" "num000" "money"
## [25] "hp" "hpl" "george"
## [28] "num650" "lab" "labs"
## [31] "telnet" "num857" "data"
## [34] "num415" "num85" "technology"
## [37] "num1999" "parts" "pm"
## [40] "direct" "cs" "meeting"
## [43] "original" "project" "re"
## [46] "edu" "table" "conference"
## [49] "charSemicolon" "charRoundbracket" "charSquarebracket"
## [52] "charExclamation" "charDollar" "charHash"
## [55] "capitalAve" "capitalLong" "capitalTotal"
## [58] "type"head(spam) # to see the first 6 rows/observations## make address all num3d our over remove internet order mail receive will
## 1 0.00 0.64 0.64 0 0.32 0.00 0.00 0.00 0.00 0.00 0.00 0.64
## 2 0.21 0.28 0.50 0 0.14 0.28 0.21 0.07 0.00 0.94 0.21 0.79
## 3 0.06 0.00 0.71 0 1.23 0.19 0.19 0.12 0.64 0.25 0.38 0.45
## 4 0.00 0.00 0.00 0 0.63 0.00 0.31 0.63 0.31 0.63 0.31 0.31
## 5 0.00 0.00 0.00 0 0.63 0.00 0.31 0.63 0.31 0.63 0.31 0.31
## 6 0.00 0.00 0.00 0 1.85 0.00 0.00 1.85 0.00 0.00 0.00 0.00
## people report addresses free business email you credit your font num000
## 1 0.00 0.00 0.00 0.32 0.00 1.29 1.93 0.00 0.96 0 0.00
## 2 0.65 0.21 0.14 0.14 0.07 0.28 3.47 0.00 1.59 0 0.43
## 3 0.12 0.00 1.75 0.06 0.06 1.03 1.36 0.32 0.51 0 1.16
## 4 0.31 0.00 0.00 0.31 0.00 0.00 3.18 0.00 0.31 0 0.00
## 5 0.31 0.00 0.00 0.31 0.00 0.00 3.18 0.00 0.31 0 0.00
## 6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 0.00
## money hp hpl george num650 lab labs telnet num857 data num415 num85
## 1 0.00 0 0 0 0 0 0 0 0 0 0 0
## 2 0.43 0 0 0 0 0 0 0 0 0 0 0
## 3 0.06 0 0 0 0 0 0 0 0 0 0 0
## 4 0.00 0 0 0 0 0 0 0 0 0 0 0
## 5 0.00 0 0 0 0 0 0 0 0 0 0 0
## 6 0.00 0 0 0 0 0 0 0 0 0 0 0
## technology num1999 parts pm direct cs meeting original project re edu
## 1 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
## 2 0 0.07 0 0 0.00 0 0 0.00 0 0.00 0.00
## 3 0 0.00 0 0 0.06 0 0 0.12 0 0.06 0.06
## 4 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
## 5 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
## 6 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
## table conference charSemicolon charRoundbracket charSquarebracket
## 1 0 0 0.00 0.000 0
## 2 0 0 0.00 0.132 0
## 3 0 0 0.01 0.143 0
## 4 0 0 0.00 0.137 0
## 5 0 0 0.00 0.135 0
## 6 0 0 0.00 0.223 0
## charExclamation charDollar charHash capitalAve capitalLong capitalTotal type
## 1 0.778 0.000 0.000 3.756 61 278 spam
## 2 0.372 0.180 0.048 5.114 101 1028 spam
## 3 0.276 0.184 0.010 9.821 485 2259 spam
## 4 0.137 0.000 0.000 3.537 40 191 spam
## 5 0.135 0.000 0.000 3.537 40 191 spam
## 6 0.000 0.000 0.000 3.000 15 54 spamattach(spam)
table(type) # to see the number of spam and none spam types## type
## nonspam spam
## 2788 1813str(spam) # to see the structure of the entire data frame## 'data.frame': 4601 obs. of 58 variables:
## $ make : num 0 0.21 0.06 0 0 0 0 0 0.15 0.06 ...
## $ address : num 0.64 0.28 0 0 0 0 0 0 0 0.12 ...
## $ all : num 0.64 0.5 0.71 0 0 0 0 0 0.46 0.77 ...
## $ num3d : num 0 0 0 0 0 0 0 0 0 0 ...
## $ our : num 0.32 0.14 1.23 0.63 0.63 1.85 1.92 1.88 0.61 0.19 ...
## $ over : num 0 0.28 0.19 0 0 0 0 0 0 0.32 ...
## $ remove : num 0 0.21 0.19 0.31 0.31 0 0 0 0.3 0.38 ...
## $ internet : num 0 0.07 0.12 0.63 0.63 1.85 0 1.88 0 0 ...
## $ order : num 0 0 0.64 0.31 0.31 0 0 0 0.92 0.06 ...
## $ mail : num 0 0.94 0.25 0.63 0.63 0 0.64 0 0.76 0 ...
## $ receive : num 0 0.21 0.38 0.31 0.31 0 0.96 0 0.76 0 ...
## $ will : num 0.64 0.79 0.45 0.31 0.31 0 1.28 0 0.92 0.64 ...
## $ people : num 0 0.65 0.12 0.31 0.31 0 0 0 0 0.25 ...
## $ report : num 0 0.21 0 0 0 0 0 0 0 0 ...
## $ addresses : num 0 0.14 1.75 0 0 0 0 0 0 0.12 ...
## $ free : num 0.32 0.14 0.06 0.31 0.31 0 0.96 0 0 0 ...
## $ business : num 0 0.07 0.06 0 0 0 0 0 0 0 ...
## $ email : num 1.29 0.28 1.03 0 0 0 0.32 0 0.15 0.12 ...
## $ you : num 1.93 3.47 1.36 3.18 3.18 0 3.85 0 1.23 1.67 ...
## $ credit : num 0 0 0.32 0 0 0 0 0 3.53 0.06 ...
## $ your : num 0.96 1.59 0.51 0.31 0.31 0 0.64 0 2 0.71 ...
## $ font : num 0 0 0 0 0 0 0 0 0 0 ...
## $ num000 : num 0 0.43 1.16 0 0 0 0 0 0 0.19 ...
## $ money : num 0 0.43 0.06 0 0 0 0 0 0.15 0 ...
## $ hp : num 0 0 0 0 0 0 0 0 0 0 ...
## $ hpl : num 0 0 0 0 0 0 0 0 0 0 ...
## $ george : num 0 0 0 0 0 0 0 0 0 0 ...
## $ num650 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ lab : num 0 0 0 0 0 0 0 0 0 0 ...
## $ labs : num 0 0 0 0 0 0 0 0 0 0 ...
## $ telnet : num 0 0 0 0 0 0 0 0 0 0 ...
## $ num857 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ data : num 0 0 0 0 0 0 0 0 0.15 0 ...
## $ num415 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ num85 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ technology : num 0 0 0 0 0 0 0 0 0 0 ...
## $ num1999 : num 0 0.07 0 0 0 0 0 0 0 0 ...
## $ parts : num 0 0 0 0 0 0 0 0 0 0 ...
## $ pm : num 0 0 0 0 0 0 0 0 0 0 ...
## $ direct : num 0 0 0.06 0 0 0 0 0 0 0 ...
## $ cs : num 0 0 0 0 0 0 0 0 0 0 ...
## $ meeting : num 0 0 0 0 0 0 0 0 0 0 ...
## $ original : num 0 0 0.12 0 0 0 0 0 0.3 0 ...
## $ project : num 0 0 0 0 0 0 0 0 0 0.06 ...
## $ re : num 0 0 0.06 0 0 0 0 0 0 0 ...
## $ edu : num 0 0 0.06 0 0 0 0 0 0 0 ...
## $ table : num 0 0 0 0 0 0 0 0 0 0 ...
## $ conference : num 0 0 0 0 0 0 0 0 0 0 ...
## $ charSemicolon : num 0 0 0.01 0 0 0 0 0 0 0.04 ...
## $ charRoundbracket : num 0 0.132 0.143 0.137 0.135 0.223 0.054 0.206 0.271 0.03 ...
## $ charSquarebracket: num 0 0 0 0 0 0 0 0 0 0 ...
## $ charExclamation : num 0.778 0.372 0.276 0.137 0.135 0 0.164 0 0.181 0.244 ...
## $ charDollar : num 0 0.18 0.184 0 0 0 0.054 0 0.203 0.081 ...
## $ charHash : num 0 0.048 0.01 0 0 0 0 0 0.022 0 ...
## $ capitalAve : num 3.76 5.11 9.82 3.54 3.54 ...
## $ capitalLong : num 61 101 485 40 40 15 4 11 445 43 ...
## $ capitalTotal : num 278 1028 2259 191 191 ...
## $ type : Factor w/ 2 levels "nonspam","spam": 2 2 2 2 2 2 2 2 2 2 ...LOGISTIC REGRESSION
logreg = glm( type ~ ., data=spam, family = "binomial" ) # running logistic regression## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurrednames(logreg) # to see the names of the model object output## [1] "coefficients" "residuals" "fitted.values"
## [4] "effects" "R" "rank"
## [7] "qr" "family" "linear.predictors"
## [10] "deviance" "aic" "null.deviance"
## [13] "iter" "weights" "prior.weights"
## [16] "df.residual" "df.null" "y"
## [19] "converged" "boundary" "model"
## [22] "call" "formula" "terms"
## [25] "data" "offset" "control"
## [28] "method" "contrasts" "xlevels"prob.spam = fitted.values(logreg) # the fitted probabilities of the model
head(prob.spam) # to see the first 6 probabilities obtained## 1 2 3 4 5 6
## 0.6189824 0.9880333 0.9999977 0.7786119 0.7785570 0.6686157class.spam = ifelse( prob.spam > 0.5, "spam", "nonspam" ) # Use 0.5 as the cutoff for classifying
head(class.spam)## 1 2 3 4 5 6
## "spam" "spam" "spam" "spam" "spam" "spam"table(class.spam, type)## type
## class.spam nonspam spam
## nonspam 2666 194
## spam 122 1619mean( type == class.spam ) # Correct classification rate = 93% ## [1] 0.9313193The Correct classification rate is 93%. However, it is better be validated by CV.
## What are error rates among spam and benign emails?
sum( type=="nonspam" & class.spam=="spam" ) / sum( type=="nonspam" )## [1] 0.04375897sum( type=="spam" & class.spam=="nonspam" ) / sum( type=="spam" )## [1] 0.107005Reducing the error rate for nonspam emails, with loss function L(1,0)=1, L(0,1)=10
class.spam = ifelse( prob.spam > 10/11, "spam", "nonspam" )
table(class.spam, type)## type
## class.spam nonspam spam
## nonspam 2759 674
## spam 29 1139mean( type == class.spam ) # The overall error rate## [1] 0.8472071sum( type=="nonspam" & class.spam=="spam" ) / sum( type=="nonspam" ) #the error rate for being emails ## [1] 0.01040172sum( type=="spam" & class.spam=="nonspam" ) / sum( type=="spam" ) # the error rate of classifying spam emails as nonspam## [1] 0.3717595The overall error rate increased, and the error rate of misclassifying spam emails as nonspam increased substantially, but the error rate for being emails is only 1% now.
DECISION TREES - classification tree algorithm
#install.packages("tree")
library(tree)
tr = tree( type ~ ., data=spam )
plot(tr)
text(tr)
summary(tr)##
## Classification tree:
## tree(formula = type ~ ., data = spam)
## Variables actually used in tree construction:
## [1] "charDollar" "remove" "charExclamation" "hp"
## [5] "capitalLong" "our" "capitalAve" "free"
## [9] "george" "edu"
## Number of terminal nodes: 13
## Residual mean deviance: 0.4879 = 2238 / 4588
## Misclassification error rate: 0.08259 = 380 / 4601Misclassification error rate: 0.08259 = 380 / 4601
Optimization – random forests
#install.packages("randomForest")
library(randomForest)## randomForest 4.7-1.1## Type rfNews() to see new features/changes/bug fixes.rf = randomForest( type ~ ., data=spam )names(rf)## [1] "call" "type" "predicted" "err.rate"
## [5] "confusion" "votes" "oob.times" "classes"
## [9] "importance" "importanceSD" "localImportance" "proximity"
## [13] "ntree" "mtry" "forest" "y"
## [17] "test" "inbag" "terms"importance(rf) ## MeanDecreaseGini
## make 7.8978626
## address 11.7285799
## all 27.6757990
## num3d 1.7299575
## our 60.0124292
## over 15.9645788
## remove 166.6937100
## internet 27.7286671
## order 9.7409332
## mail 16.9984869
## receive 20.7983030
## will 22.9667989
## people 7.2867589
## report 4.5789773
## addresses 2.5292543
## free 145.6777294
## business 27.3220002
## email 17.7410217
## you 59.2223406
## credit 10.3568390
## your 131.0754942
## font 5.7979131
## num000 49.9561970
## money 75.4034532
## hp 104.3969645
## hpl 40.5402989
## george 45.3540006
## num650 11.3869206
## lab 4.3991936
## labs 7.3919751
## telnet 4.4924007
## num857 1.5985785
## data 5.9151665
## num415 1.7707652
## num85 7.4793902
## technology 7.6448474
## num1999 28.1301628
## parts 1.0489031
## pm 6.9789365
## direct 2.5130790
## cs 2.2707389
## meeting 11.6676949
## original 3.1639730
## project 3.9801021
## re 20.7317135
## edu 40.9623212
## table 0.5347235
## conference 2.8664228
## charSemicolon 10.5399412
## charRoundbracket 24.6733040
## charSquarebracket 6.0698685
## charExclamation 258.2145015
## charDollar 198.6380084
## charHash 7.6491697
## capitalAve 147.6482807
## capitalLong 126.6579448
## capitalTotal 81.8965802varImpPlot(rf) # To see which variables are most significant in a tree based classification
rf##
## Call:
## randomForest(formula = type ~ ., data = spam)
## Type of random forest: classification
## Number of trees: 500
## No. of variables tried at each split: 7
##
## OOB estimate of error rate: 4.54%
## Confusion matrix:
## nonspam spam class.error
## nonspam 2709 79 0.02833572
## spam 130 1683 0.07170436The lowest classification rate we could get so far
# Searching for the optimal solution
dim(spam) ## [1] 4601 58There are 58 variables overall in the data set, minus type and 57 variables.
Let’s sample m = root of 57, rounded = 8.
rf3 = randomForest(type ~ ., data=spam, mtry=8) #
plot(rf3)
mtry is m, the number of X-variables available at each node
*How many trees to grow? The default is 500, but error is rather flat after 50.
Random forest tool has multiple output:
names(rf3) ## [1] "call" "type" "predicted" "err.rate"
## [5] "confusion" "votes" "oob.times" "classes"
## [9] "importance" "importanceSD" "localImportance" "proximity"
## [13] "ntree" "mtry" "forest" "y"
## [17] "test" "inbag" "terms"We would like to minimize the mean squared error and to maximize R2, the percent of total variation explained by the forest.
which.min(rf3$err.rate)## [1] 770 rf50 = randomForest(type ~ ., data=spam, mtry=8,ntree=50) #
plot(rf50)
which.min(rf50$err.rate)## [1] 89After ntree = 30, the error is becoming flat - it is not anymore decreasing.
rf30 = randomForest(type ~ ., data=spam, mtry=8,ntree=30) #
plot(rf30)
rf30 ##
## Call:
## randomForest(formula = type ~ ., data = spam, mtry = 8, ntree = 30)
## Type of random forest: classification
## Number of trees: 30
## No. of variables tried at each split: 8
##
## OOB estimate of error rate: 5.15%
## Confusion matrix:
## nonspam spam class.error
## nonspam 2691 97 0.03479197
## spam 140 1673 0.07722008OOB estimate of error rate: 5.37% - it went up!
DISCRIMINANT ANALYSIS
LDA
library(MASS)
LDA = lda( type ~ ., data=spam, CV=TRUE )
names(LDA)## [1] "class" "posterior" "terms" "call" "xlevels"attach(spam)## The following objects are masked from spam (pos = 6):
##
## address, addresses, all, business, capitalAve, capitalLong,
## capitalTotal, charDollar, charExclamation, charHash,
## charRoundbracket, charSemicolon, charSquarebracket, conference,
## credit, cs, data, direct, edu, email, font, free, george, hp, hpl,
## internet, lab, labs, mail, make, meeting, money, num000, num1999,
## num3d, num415, num650, num85, num857, order, original, our, over,
## parts, people, pm, project, re, receive, remove, report, table,
## technology, telnet, type, will, you, yourtable( type, LDA$class ) #Confusion Matrix##
## type nonspam spam
## nonspam 2657 131
## spam 391 1422or
table(spam$type, LDA$class ) #Confusion Matrix##
## nonspam spam
## nonspam 2657 131
## spam 391 1422mean(spam$type == LDA$class) # correct classification rate /Accuracy ~ 88.5%## [1] 0.8865464mean( type != LDA$class ) # This error rate is higher ~11.5%## [1] 0.1134536QDA
QDA = qda( type ~ ., data=spam, CV=TRUE )
names(QDA)## [1] "class" "posterior" "terms" "call" "xlevels"table( type, QDA$class ) # Confusion Matrix##
## type nonspam spam
## nonspam 2090 691
## spam 87 1722mean( type != QDA$class ) # NA appeared - there may be NA values introduced## [1] NAsummary(QDA$class) # let us see if NA is introduced## nonspam spam NA's
## 2177 2413 11Yes! 11 NA values are introduced. There are missing values, predictions not computed by QDA. We’ll remove these points in the following way
mean( type != QDA$class, na.rm=TRUE ) # This error rate is even higher ~17%## [1] 0.1694989No improvement with QDA; linear models are ok.
##GEOMETRY of LDA and QDA
head(spam)## make address all num3d our over remove internet order mail receive will
## 1 0.00 0.64 0.64 0 0.32 0.00 0.00 0.00 0.00 0.00 0.00 0.64
## 2 0.21 0.28 0.50 0 0.14 0.28 0.21 0.07 0.00 0.94 0.21 0.79
## 3 0.06 0.00 0.71 0 1.23 0.19 0.19 0.12 0.64 0.25 0.38 0.45
## 4 0.00 0.00 0.00 0 0.63 0.00 0.31 0.63 0.31 0.63 0.31 0.31
## 5 0.00 0.00 0.00 0 0.63 0.00 0.31 0.63 0.31 0.63 0.31 0.31
## 6 0.00 0.00 0.00 0 1.85 0.00 0.00 1.85 0.00 0.00 0.00 0.00
## people report addresses free business email you credit your font num000
## 1 0.00 0.00 0.00 0.32 0.00 1.29 1.93 0.00 0.96 0 0.00
## 2 0.65 0.21 0.14 0.14 0.07 0.28 3.47 0.00 1.59 0 0.43
## 3 0.12 0.00 1.75 0.06 0.06 1.03 1.36 0.32 0.51 0 1.16
## 4 0.31 0.00 0.00 0.31 0.00 0.00 3.18 0.00 0.31 0 0.00
## 5 0.31 0.00 0.00 0.31 0.00 0.00 3.18 0.00 0.31 0 0.00
## 6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 0.00
## money hp hpl george num650 lab labs telnet num857 data num415 num85
## 1 0.00 0 0 0 0 0 0 0 0 0 0 0
## 2 0.43 0 0 0 0 0 0 0 0 0 0 0
## 3 0.06 0 0 0 0 0 0 0 0 0 0 0
## 4 0.00 0 0 0 0 0 0 0 0 0 0 0
## 5 0.00 0 0 0 0 0 0 0 0 0 0 0
## 6 0.00 0 0 0 0 0 0 0 0 0 0 0
## technology num1999 parts pm direct cs meeting original project re edu
## 1 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
## 2 0 0.07 0 0 0.00 0 0 0.00 0 0.00 0.00
## 3 0 0.00 0 0 0.06 0 0 0.12 0 0.06 0.06
## 4 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
## 5 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
## 6 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
## table conference charSemicolon charRoundbracket charSquarebracket
## 1 0 0 0.00 0.000 0
## 2 0 0 0.00 0.132 0
## 3 0 0 0.01 0.143 0
## 4 0 0 0.00 0.137 0
## 5 0 0 0.00 0.135 0
## 6 0 0 0.00 0.223 0
## charExclamation charDollar charHash capitalAve capitalLong capitalTotal type
## 1 0.778 0.000 0.000 3.756 61 278 spam
## 2 0.372 0.180 0.048 5.114 101 1028 spam
## 3 0.276 0.184 0.010 9.821 485 2259 spam
## 4 0.137 0.000 0.000 3.537 40 191 spam
## 5 0.135 0.000 0.000 3.537 40 191 spam
## 6 0.000 0.000 0.000 3.000 15 54 spamplot( your, address, col = type)
SUPPORT VECTOR MACHINES
library(e1071)
SVM = svm( type ~ ., data=spam, kernel="linear" )
summary(SVM)##
## Call:
## svm(formula = type ~ ., data = spam, kernel = "linear")
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: linear
## cost: 1
##
## Number of Support Vectors: 940
##
## ( 456 484 )
##
##
## Number of Classes: 2
##
## Levels:
## nonspam spam940 support vectors (not cleanly classified) out of 4601 data points.
dim(spam)## [1] 4601 58class = predict(SVM)
table(class,type)## type
## class nonspam spam
## nonspam 2663 185
## spam 125 1628mean( class != type ) # This error rate is so far the lowest ~6.7%## [1] 0.06737666# thus we can predict the spam detection using support vectors machine algorithm reasonably.
#let us check other SVM kernels
SVMPoly = svm( type ~ ., data=spam, kernel="polynomial" )
summary(SVMPoly) ##
## Call:
## svm(formula = type ~ ., data = spam, kernel = "polynomial")
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: polynomial
## cost: 1
## degree: 3
## coef.0: 0
##
## Number of Support Vectors: 2561
##
## ( 1250 1311 )
##
##
## Number of Classes: 2
##
## Levels:
## nonspam spam2561 support vectors (not cleanly classified) out of 4601 data points.
SVMradial = svm( type ~ ., data=spam, kernel="radial" )
summary(SVMradial) ##
## Call:
## svm(formula = type ~ ., data = spam, kernel = "radial")
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: radial
## cost: 1
##
## Number of Support Vectors: 1275
##
## ( 595 680 )
##
##
## Number of Classes: 2
##
## Levels:
## nonspam spam1275 support vectors (not cleanly classified) out of 4601 data points.
SVMsigmoid = svm( type ~ ., data=spam, kernel="sigmoid" )
summary(SVMsigmoid) ##
## Call:
## svm(formula = type ~ ., data = spam, kernel = "sigmoid")
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: sigmoid
## cost: 1
## coef.0: 0
##
## Number of Support Vectors: 1038
##
## ( 517 521 )
##
##
## Number of Classes: 2
##
## Levels:
## nonspam spam1038 support vectors (not cleanly classified) out of 4601 data points.
Tuning and cross-validation
The “cost” option specifies the cost of violating the margin. We can try costs 0.001, 0.01, 0.1, 1, 10, 100, 1000:
Stuned = tune( svm,type ~ ., data=spam, kernel="linear", ranges=list(cost=10^seq(-3,3)) )
summary(Stuned)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## cost
## 10
##
## - best performance: 0.06846223
##
## - Detailed performance results:
## cost error dispersion
## 1 1e-03 0.10758512 0.01588266
## 2 1e-02 0.08215599 0.01441233
## 3 1e-01 0.07498302 0.01284616
## 4 1e+00 0.07215599 0.01277532
## 5 1e+01 0.06846223 0.01035335
## 6 1e+02 0.07063614 0.01004829
## 7 1e+03 0.08346176 0.01298136