Chapter 4: Classification using Naive Bayes
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Example: Filtering spam SMS messages
Step 1: Download the data
URL <- "http://www.sci.csueastbay.edu/~esuess/classes/Statistics_6620/Presentations/ml6/sms_spam.csv"
download.file(URL, destfile = "./sms_spam.csv", method="curl") % Total % Received % Xferd Average Speed Time Time Time Current
Dload Upload Total Spent Left Speed
0 0 0 0 0 0 0 0 --:--:-- --:--:-- --:--:-- 0
3 469k 3 18534 0 0 129k 0 0:00:03 --:--:-- 0:00:03 129k
100 469k 100 469k 0 0 1005k 0 --:--:-- --:--:-- --:--:-- 1005kStep 2: Exploring and preparing the data —-
# read the sms data into the sms data frame
sms_raw <- read.csv("sms_spam.csv", stringsAsFactors = FALSE)
# examine the structure of the sms data
str(sms_raw)'data.frame': 5559 obs. of 2 variables:
$ type: chr "ham" "ham" "ham" "spam" ...
$ text: chr "Hope you are having a good week. Just checking in" "K..give back my thanks." "Am also doing in cbe only. But have to pay." "complimentary 4 STAR Ibiza Holiday or £10,000 cash needs your URGENT collection. 09066364349 NOW from Landline "| __truncated__ ...# convert spam/ham to factor.
sms_raw$type <- factor(sms_raw$type)
# examine the type variable more carefully
str(sms_raw$type) Factor w/ 2 levels "ham","spam": 1 1 1 2 2 1 1 1 2 1 ...table(sms_raw$type)
ham spam
4812 747 # build a corpus using the text mining (tm) package
library(tm)
sms_corpus <- VCorpus(VectorSource(sms_raw$text))
# examine the sms corpus
print(sms_corpus)<<VCorpus>>
Metadata: corpus specific: 0, document level (indexed): 0
Content: documents: 5559inspect(sms_corpus[1:2])<<VCorpus>>
Metadata: corpus specific: 0, document level (indexed): 0
Content: documents: 2
[[1]]
<<PlainTextDocument>>
Metadata: 7
Content: chars: 49
[[2]]
<<PlainTextDocument>>
Metadata: 7
Content: chars: 23as.character(sms_corpus[[1]])[1] "Hope you are having a good week. Just checking in"lapply(sms_corpus[1:2], as.character)$`1`
[1] "Hope you are having a good week. Just checking in"
$`2`
[1] "K..give back my thanks."# clean up the corpus using tm_map()
sms_corpus_clean <- tm_map(sms_corpus, content_transformer(tolower))
# show the difference between sms_corpus and corpus_clean
as.character(sms_corpus[[1]])[1] "Hope you are having a good week. Just checking in"as.character(sms_corpus_clean[[1]])[1] "hope you are having a good week. just checking in"sms_corpus_clean <- tm_map(sms_corpus_clean, removeNumbers) # remove numbers
sms_corpus_clean <- tm_map(sms_corpus_clean, removeWords, stopwords()) # remove stop words
sms_corpus_clean <- tm_map(sms_corpus_clean, removePunctuation) # remove punctuation# tip: create a custom function to replace (rather than remove) punctuation
removePunctuation("hello...world")[1] "helloworld"replacePunctuation <- function(x) { gsub("[[:punct:]]+", " ", x) }
replacePunctuation("hello...world")[1] "hello world"# illustration of word stemming
library(SnowballC)
wordStem(c("learn", "learned", "learning", "learns"))[1] "learn" "learn" "learn" "learn"sms_corpus_clean <- tm_map(sms_corpus_clean, stemDocument)
sms_corpus_clean <- tm_map(sms_corpus_clean, stripWhitespace) # eliminate unneeded whitespace
# examine the final clean corpus
lapply(sms_corpus[1:3], as.character)$`1`
[1] "Hope you are having a good week. Just checking in"
$`2`
[1] "K..give back my thanks."
$`3`
[1] "Am also doing in cbe only. But have to pay."lapply(sms_corpus_clean[1:3], as.character)$`1`
[1] "hope good week just check"
$`2`
[1] "kgive back thank"
$`3`
[1] "also cbe pay"# create a document-term sparse matrix
sms_dtm <- DocumentTermMatrix(sms_corpus_clean)
# alternative solution: create a document-term sparse matrix directly from the SMS corpus
sms_dtm2 <- DocumentTermMatrix(sms_corpus, control = list(
tolower = TRUE,
removeNumbers = TRUE,
stopwords = TRUE,
removePunctuation = TRUE,
stemming = TRUE
))
# alternative solution: using custom stop words function ensures identical result
sms_dtm3 <- DocumentTermMatrix(sms_corpus, control = list(
tolower = TRUE,
removeNumbers = TRUE,
stopwords = function(x) { removeWords(x, stopwords()) },
removePunctuation = TRUE,
stemming = TRUE
))
# compare the result
sms_dtm<<DocumentTermMatrix (documents: 5559, terms: 6559)>>
Non-/sparse entries: 42147/36419334
Sparsity : 100%
Maximal term length: 40
Weighting : term frequency (tf)sms_dtm2<<DocumentTermMatrix (documents: 5559, terms: 6961)>>
Non-/sparse entries: 43221/38652978
Sparsity : 100%
Maximal term length: 40
Weighting : term frequency (tf)sms_dtm3<<DocumentTermMatrix (documents: 5559, terms: 6559)>>
Non-/sparse entries: 42147/36419334
Sparsity : 100%
Maximal term length: 40
Weighting : term frequency (tf)# creating training and test datasets
sms_dtm_train <- sms_dtm[1:4169, ]
sms_dtm_test <- sms_dtm[4170:5559, ]
# also save the labels
sms_train_labels <- sms_raw[1:4169, ]$type
sms_test_labels <- sms_raw[4170:5559, ]$type
# check that the proportion of spam is similar
prop.table(table(sms_train_labels))sms_train_labels
ham spam
0.8647158 0.1352842 prop.table(table(sms_test_labels))sms_test_labels
ham spam
0.8683453 0.1316547 # word cloud visualization
library(wordcloud)
wordcloud(sms_corpus_clean, min.freq = 50, random.order = FALSE)
# subset the training data into spam and ham groups
spam <- subset(sms_raw, type == "spam")
ham <- subset(sms_raw, type == "ham")
wordcloud(spam$text, max.words = 40, scale = c(3, 0.5))
wordcloud(ham$text, max.words = 40, scale = c(3, 0.5))
sms_dtm_freq_train <- removeSparseTerms(sms_dtm_train, 0.999)
sms_dtm_freq_train<<DocumentTermMatrix (documents: 4169, terms: 1104)>>
Non-/sparse entries: 24827/4577749
Sparsity : 99%
Maximal term length: 19
Weighting : term frequency (tf)# indicator features for frequent words
findFreqTerms(sms_dtm_train, 5) [1] "£wk" "€˜m" "€˜s" "abiola"
[5] "abl" "abt" "accept" "access"
[9] "account" "across" "act" "activ"
[13] "actual" "add" "address" "admir"
[17] "adult" "advanc" "aft" "afternoon"
[21] "age" "ago" "aha" "ahead"
[25] "aight" "aint" "air" "aiyo"
[29] "alex" "almost" "alon" "alreadi"
[33] "alright" "also" "alway" "angri"
[37] "announc" "anoth" "answer" "anymor"
[41] "anyon" "anyth" "anytim" "anyway"
[45] "apart" "app" "appli" "appreci"
[49] "arcad" "ard" "area" "argu"
[53] "argument" "armand" "around" "arrang"
[57] "arriv" "asap" "ask" "askd"
[61] "attempt" "auction" "avail" "ave"
[65] "avoid" "await" "awak" "award"
[69] "away" "awesom" "babe" "babi"
[73] "back" "bad" "bag" "bank"
[77] "bare" "basic" "bath" "batteri"
[81] "bcoz" "bday" "beauti" "becom"
[85] "bed" "bedroom" "beer" "begin"
[89] "believ" "best" "better" "bid"
[93] "big" "bill" "bird" "birthday"
[97] "bit" "black" "blank" "bless"
[101] "blue" "bluetooth" "bold" "bonus"
[105] "boo" "book" "boost" "bore"
[109] "boss" "bother" "bout" "box"
[113] "boy" "boytoy" "break" "breath"
[117] "bring" "brother" "bslvyl" "btnationalr"
[121] "buck" "bus" "busi" "buy"
[125] "cabin" "call" "caller" "callertun"
[129] "camcord" "came" "camera" "campus"
[133] "can" "cancel" "cancer" "cant"
[137] "car" "card" "care" "carlo"
[141] "case" "cash" "cashbal" "catch"
[145] "caus" "celebr" "cell" "centr"
[149] "chanc" "chang" "charg" "chat"
[153] "cheap" "cheaper" "check" "cheer"
[157] "chennai" "chikku" "childish" "children"
[161] "choic" "choos" "christma" "claim"
[165] "class" "clean" "clear" "close"
[169] "club" "code" "coffe" "cold"
[173] "colleagu" "collect" "colleg" "colour"
[177] "come" "comin" "comp" "compani"
[181] "competit" "complet" "complimentari" "comput"
[185] "condit" "confirm" "congrat" "congratul"
[189] "connect" "contact" "content" "contract"
[193] "cook" "cool" "copi" "correct"
[197] "cos" "cost" "cost£pm" "costa"
[201] "coupl" "cours" "cover" "coz"
[205] "crave" "crazi" "creat" "credit"
[209] "cri" "cross" "cuddl" "cum"
[213] "cup" "current" "custcar" "custom"
[217] "cut" "cute" "cuz" "dad"
[221] "daddi" "darl" "darlin" "darren"
[225] "dat" "date" "day" "dead"
[229] "deal" "dear" "decid" "decim"
[233] "decis" "deep" "definit" "del"
[237] "deliv" "deliveri" "den" "depend"
[241] "detail" "didnt" "die" "diet"
[245] "differ" "difficult" "digit" "din"
[249] "dinner" "direct" "dis" "discount"
[253] "discuss" "disturb" "dnt" "doc"
[257] "doctor" "doesnt" "dog" "doin"
[261] "don" "done" "dont" "door"
[265] "doubl" "download" "draw" "dream"
[269] "drink" "drive" "drop" "drug"
[273] "dude" "due" "dun" "dunno"
[277] "dvd" "earli" "earlier" "earth"
[281] "easi" "eat" "eatin" "egg"
[285] "either" "els" "email" "embarass"
[289] "end" "energi" "england" "enjoy"
[293] "enough" "enter" "entitl" "entri"
[297] "envelop" "etc" "euro" "eve"
[301] "even" "ever" "everi" "everybodi"
[305] "everyon" "everyth" "exact" "exam"
[309] "excel" "excit" "excus" "expect"
[313] "experi" "expir" "extra" "eye"
[317] "face" "facebook" "fact" "fall"
[321] "famili" "fanci" "fantasi" "fantast"
[325] "far" "fast" "fat" "father"
[329] "fault" "feb" "feel" "felt"
[333] "fetch" "fight" "figur" "file"
[337] "fill" "film" "final" "find"
[341] "fine" "finger" "finish" "first"
[345] "fix" "flag" "flat" "flight"
[349] "flower" "follow" "fone" "food"
[353] "forev" "forget" "forgot" "forward"
[357] "found" "freak" "free" "freemsg"
[361] "freephon" "fren" "fri" "friday"
[365] "friend" "friendship" "frm" "frnd"
[369] "frnds" "full" "fullonsmscom" "fun"
[373] "funni" "futur" "gal" "game"
[377] "gap" "gas" "gave" "gay"
[381] "gentl" "get" "gettin" "gift"
[385] "girl" "girlfrnd" "give" "glad"
[389] "god" "goe" "goin" "gone"
[393] "gonna" "good" "goodmorn" "goodnight"
[397] "got" "goto" "gotta" "great"
[401] "grin" "guarante" "gud" "guess"
[405] "guy" "gym" "haf" "haha"
[409] "hai" "hair" "half" "hand"
[413] "handset" "hang" "happen" "happi"
[417] "hard" "hate" "hav" "havent"
[421] "head" "hear" "heard" "heart"
[425] "heavi" "hee" "hell" "hello"
[429] "help" "hey" "hgsuiteland" "hit"
[433] "hiya" "hmm" "hmmm" "hmv"
[437] "hol" "hold" "holder" "holiday"
[441] "home" "hook" "hop" "hope"
[445] "horni" "hospit" "hot" "hotel"
[449] "hour" "hous" "how" "howev"
[453] "howz" "hrs" "httpwwwurawinnercom" "hug"
[457] "huh" "hungri" "hurri" "hurt"
[461] "ice" "idea" "identifi" "ignor"
[465] "ill" "immedi" "import" "inc"
[469] "includ" "india" "info" "inform"
[473] "insid" "instead" "interest" "invit"
[477] "ipod" "irrit" "ish" "island"
[481] "issu" "ive" "izzit" "januari"
[485] "jay" "job" "john" "join"
[489] "joke" "joy" "jst" "jus"
[493] "just" "juz" "kate" "keep"
[497] "kept" "kick" "kid" "kill"
[501] "kind" "kinda" "king" "kiss"
[505] "knew" "know" "knw" "ladi"
[509] "land" "landlin" "laptop" "lar"
[513] "last" "late" "later" "latest"
[517] "laugh" "lazi" "ldn" "lead"
[521] "learn" "least" "leav" "lect"
[525] "left" "leh" "lei" "less"
[529] "lesson" "let" "letter" "liao"
[533] "librari" "lie" "life" "lift"
[537] "light" "like" "line" "link"
[541] "list" "listen" "littl" "live"
[545] "lmao" "load" "loan" "local"
[549] "locat" "log" "lol" "london"
[553] "long" "longer" "look" "lookin"
[557] "lor" "lose" "lost" "lot"
[561] "lovabl" "love" "lover" "loyalti"
[565] "ltd" "luck" "lucki" "lunch"
[569] "luv" "mad" "made" "mah"
[573] "mail" "make" "malaria" "man"
[577] "mani" "march" "mark" "marri"
[581] "match" "mate" "matter" "maxim"
[585] "maxmin" "may" "mayb" "meal"
[589] "mean" "meant" "med" "medic"
[593] "meet" "meetin" "meh" "member"
[597] "men" "merri" "messag" "met"
[601] "mid" "midnight" "might" "min"
[605] "mind" "mine" "minut" "miracl"
[609] "miss" "mistak" "moan" "mob"
[613] "mobil" "mobileupd" "mode" "mom"
[617] "moment" "mon" "monday" "money"
[621] "month" "morn" "mother" "motorola"
[625] "move" "movi" "mrng" "mrt"
[629] "mrw" "msg" "msgs" "mths"
[633] "much" "mum" "murder" "music"
[637] "must" "muz" "nah" "nake"
[641] "name" "nation" "natur" "naughti"
[645] "near" "need" "net" "network"
[649] "neva" "never" "new" "news"
[653] "next" "nice" "nigeria" "night"
[657] "nite" "nobodi" "noe" "nokia"
[661] "noon" "nope" "normal" "normpton"
[665] "noth" "notic" "now" "num"
[669] "number" "nyt" "obvious" "offer"
[673] "offic" "offici" "okay" "oki"
[677] "old" "omg" "one" "onlin"
[681] "onto" "oop" "open" "oper"
[685] "opinion" "opt" "optout" "orang"
[689] "orchard" "order" "oredi" "oso"
[693] "other" "otherwis" "outsid" "pack"
[697] "page" "paid" "pain" "paper"
[701] "parent" "park" "part" "parti"
[705] "partner" "pass" "passion" "password"
[709] "past" "pay" "peopl" "per"
[713] "person" "pete" "phone" "photo"
[717] "pic" "pick" "pictur" "pin"
[721] "piss" "pix" "pizza" "place"
[725] "plan" "play" "player" "pleas"
[729] "pleasur" "plenti" "pls" "plus"
[733] "plz" "pmin" "pmsg" "pobox"
[737] "point" "poli" "polic" "poor"
[741] "pop" "possess" "possibl" "post"
[745] "pound" "power" "ppm" "pray"
[749] "present" "press" "pretti" "previous"
[753] "price" "princess" "privat" "prize"
[757] "prob" "probabl" "problem" "project"
[761] "promis" "pub" "put" "qualiti"
[765] "question" "quick" "quit" "quiz"
[769] "quot" "rain" "random" "rang"
[773] "rate" "rather" "rcvd" "reach"
[777] "read" "readi" "real" "reali"
[781] "realli" "reason" "receipt" "receiv"
[785] "recent" "record" "refer" "regard"
[789] "regist" "relat" "relax" "remain"
[793] "rememb" "remind" "remov" "rent"
[797] "rental" "repli" "repres" "request"
[801] "respond" "respons" "rest" "result"
[805] "return" "reveal" "review" "reward"
[809] "right" "ring" "rington" "rite"
[813] "road" "rock" "role" "room"
[817] "roommat" "rose" "round" "rowwjhl"
[821] "rpli" "rreveal" "run" "rush"
[825] "sad" "sae" "safe" "said"
[829] "sale" "sat" "saturday" "savamob"
[833] "save" "saw" "say" "sch"
[837] "school" "scream" "sea" "search"
[841] "sec" "second" "secret" "see"
[845] "seem" "seen" "select" "self"
[849] "sell" "semest" "send" "sens"
[853] "sent" "serious" "servic" "set"
[857] "settl" "sex" "sexi" "shall"
[861] "share" "shd" "ship" "shirt"
[865] "shop" "short" "show" "shower"
[869] "sick" "side" "sigh" "sight"
[873] "sign" "silent" "simpl" "sinc"
[877] "singl" "sipix" "sir" "sis"
[881] "sister" "sit" "situat" "skxh"
[885] "skype" "slave" "sleep" "slept"
[889] "slow" "slowli" "small" "smile"
[893] "smoke" "sms" "smth" "snow"
[897] "sofa" "sol" "somebodi" "someon"
[901] "someth" "sometim" "somewher" "song"
[905] "soni" "sonyericsson" "soon" "sorri"
[909] "sort" "sound" "south" "space"
[913] "speak" "special" "specialcal" "spend"
[917] "spent" "spoke" "spree" "stand"
[921] "start" "statement" "station" "stay"
[925] "std" "step" "still" "stockport"
[929] "stone" "stop" "store" "stori"
[933] "street" "student" "studi" "stuff"
[937] "stupid" "style" "sub" "subscrib"
[941] "success" "suck" "suit" "summer"
[945] "sun" "sunday" "sunshin" "sup"
[949] "support" "suppos" "sure" "surf"
[953] "surpris" "sweet" "swing" "system"
[957] "take" "talk" "tampa" "tariff"
[961] "tcs" "tea" "teach" "tear"
[965] "teas" "tel" "tell" "ten"
[969] "tenerif" "term" "test" "text"
[973] "thank" "thanx" "that" "thing"
[977] "think" "thinkin" "thk" "tho"
[981] "though" "thought" "throw" "thru"
[985] "tht" "thur" "tick" "ticket"
[989] "til" "till" "time" "tire"
[993] "titl" "tmr" "toclaim" "today"
[997] "togeth" "told" "tomo" "tomorrow"
[ reached getOption("max.print") -- omitted 139 entries ]# save frequently-appearing terms to a character vector
sms_freq_words <- findFreqTerms(sms_dtm_train, 5)
str(sms_freq_words) chr [1:1139] "£wk" "€˜m" "€˜s" "abiola" "abl" "abt" "accept" "access" "account" "across" "act" ...# create DTMs with only the frequent terms
sms_dtm_freq_train <- sms_dtm_train[ , sms_freq_words]
sms_dtm_freq_test <- sms_dtm_test[ , sms_freq_words]
# convert counts to a factor
convert_counts <- function(x) {
x <- ifelse(x > 0, "Yes", "No")
}
# apply() convert_counts() to columns of train/test data
sms_train <- apply(sms_dtm_freq_train, MARGIN = 2, convert_counts)
sms_test <- apply(sms_dtm_freq_test, MARGIN = 2, convert_counts)Step 3: Training a model on the data —-
library(e1071)
sms_classifier <- naiveBayes(sms_train, sms_train_labels)Step 4: Evaluating model performance —-
sms_test_pred <- predict(sms_classifier, sms_test)
head(sms_test_pred)[1] ham ham ham ham spam ham
Levels: ham spamlibrary(gmodels)
CrossTable(sms_test_pred, sms_test_labels,
prop.chisq = FALSE, prop.t = FALSE, prop.r = FALSE,
dnn = c('predicted', 'actual'))
Cell Contents
|-------------------------|
| N |
| N / Col Total |
|-------------------------|
Total Observations in Table: 1390
| actual
predicted | ham | spam | Row Total |
-------------|-----------|-----------|-----------|
ham | 1201 | 30 | 1231 |
| 0.995 | 0.164 | |
-------------|-----------|-----------|-----------|
spam | 6 | 153 | 159 |
| 0.005 | 0.836 | |
-------------|-----------|-----------|-----------|
Column Total | 1207 | 183 | 1390 |
| 0.868 | 0.132 | |
-------------|-----------|-----------|-----------|
Step 5: Improving model performance —-
sms_classifier2 <- naiveBayes(sms_train, sms_train_labels, laplace = 1)
sms_test_pred2 <- predict(sms_classifier2, sms_test)
CrossTable(sms_test_pred2, sms_test_labels,
prop.chisq = FALSE, prop.t = FALSE, prop.r = FALSE,
dnn = c('predicted', 'actual'))
Cell Contents
|-------------------------|
| N |
| N / Col Total |
|-------------------------|
Total Observations in Table: 1390
| actual
predicted | ham | spam | Row Total |
-------------|-----------|-----------|-----------|
ham | 1202 | 28 | 1230 |
| 0.996 | 0.153 | |
-------------|-----------|-----------|-----------|
spam | 5 | 155 | 160 |
| 0.004 | 0.847 | |
-------------|-----------|-----------|-----------|
Column Total | 1207 | 183 | 1390 |
| 0.868 | 0.132 | |
-------------|-----------|-----------|-----------|
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