The data for this problem is based on the revision history of the page Language. Wikipedia provides a history for each page that consists of the state of the page at each revision. Rather than manually considering each revision, a script was run that checked whether edits stayed or were reverted. If a change was eventually reverted then that revision is marked as vandalism. This may result in some misclassifications, but the script performs well enough for our needs.
As a result of this preprocessing, some common processing tasks have already been done, including lower-casing and punctuation removal. The columns in the dataset are:
Problem 1 - Bags of Words
1.1 The data set
wiki = read.csv("data/wiki.csv", stringsAsFactors = F)
wiki$Vandal = factor(wiki$Vandal)
table(wiki$Vandal)
0 1
2061 1815
【P1.1】How many cases of vandalism were detected in the history of this page?
1.2 DTM, The Added Words
library(tm)
library(SnowballC)
# Create corpus for Added Words
txt = iconv(wiki$Added, to = "utf-8", sub="")
corpus = Corpus(VectorSource(txt))
corpus = tm_map(corpus, removeWords, stopwords("english"))
transformation drops documents
corpus = tm_map(corpus, stemDocument)
transformation drops documents
dtm = DocumentTermMatrix(corpus)
dtm
<<DocumentTermMatrix (documents: 3876, terms: 6674)>>
Non-/sparse entries: 15367/25853057
Sparsity : 100%
Maximal term length: 784
Weighting : term frequency (tf)
【P1.2】How many terms appear in dtmAdded?
1.3 Handle Sparsity
Filter out sparse terms by keeping only terms that appear in 0.3% or more of the revisions, and call the new matrix sparseAdded.
nwAdded = rowSums(as.matrix(dtm)) # no. word added in each edit
dtm = removeSparseTerms(dtm, 0.997)
dtm
<<DocumentTermMatrix (documents: 3876, terms: 166)>>
Non-/sparse entries: 2681/640735
Sparsity : 100%
Maximal term length: 28
Weighting : term frequency (tf)
【P1.3】How many terms appear in sparseAdded?
1.4 Create Data Frames, wordAdded & wordRemoved
Convert sparseAdded to a data frame called wordsAdded, and then prepend all the words with the letter A, by using the command:
wordsAdded = as.data.frame(as.matrix(dtm))
colnames(wordsAdded) = paste("A", colnames(wordsAdded)) # for proper column names
Now repeat all of the steps we’ve done so far to create a Removed bag-of-words dataframe, called wordsRemoved, except this time, prepend all of the words with the letter R:
# Create corpus
txt = iconv(wiki$Removed, to = "utf-8", sub="")
corpus = Corpus(VectorSource(txt))
corpus = tm_map(corpus, removeWords, stopwords("english"))
transformation drops documents
corpus = tm_map(corpus, stemDocument)
transformation drops documents
dtm = DocumentTermMatrix(corpus)
dtm
<<DocumentTermMatrix (documents: 3876, terms: 5403)>>
Non-/sparse entries: 13293/20928735
Sparsity : 100%
Maximal term length: 784
Weighting : term frequency (tf)
nwRemoved = rowSums(as.matrix(dtm))
dtm = removeSparseTerms(dtm, 0.997)
dtm
<<DocumentTermMatrix (documents: 3876, terms: 162)>>
Non-/sparse entries: 2552/625360
Sparsity : 100%
Maximal term length: 28
Weighting : term frequency (tf)
wordsRemoved = as.data.frame(as.matrix(dtm))
colnames(wordsRemoved) = paste("R", colnames(wordsRemoved))
【P1.4】How many words are in the wordsRemoved data frame?
1.5 Prepare the Data Frame
Combine the Data Frames wordsAdded & wordsRemoved with the Target Variable wiki$Vandal
wikiWords = cbind(wordsAdded, wordsRemoved)
wikiWords$Vandal = wiki$Vandal
Split the data frame for train and test data
library(caTools)
set.seed(123)
spl = sample.split(wikiWords$Vandal, 0.7)
train = subset(wikiWords, spl == TRUE)
test = subset(wikiWords, spl == FALSE)
table(test$Vandal) %>% prop.table
0 1
0.53138 0.46862
【P1.5】What is the accuracy on the test set of a baseline method that always predicts “not vandalism”?
1.6 CART Model
library(rpart)
library(rpart.plot)
cart = rpart(Vandal~., train, method="class")
pred = predict(cart,test,type='class')
table(test$Vandal, pred) %>% {sum(diag(.)) / sum(.)} # 0.54428
[1] 0.54428
【P1.6】What is the accuracy of the model on the test set, using a threshold of 0.5?
1.7 Plot the Decision Tree
prp(cart)

【P1.7】How many word stems does the CART model use?
1.8 Predictability of the CART model
【P1.8】Given the performance of the CART model relative to the baseline, what is the best explanation of these results?
- Although it beats the baseline, bag of words is not very predictive for this problem.
Problem 2 - Add Features with Problem-specific Knowledge
2.1 Add HTTP column
Add a new column based on whether "http" is added
wiki2 = wikiWords
wiki2$HTTP = ifelse( grepl("http",wiki$Added,fixed=TRUE) , 1, 0)
table(wiki2$HTTP) # 217
0 1
3659 217
【P2.1】Based on this new column, how many revisions added a link?
2.2 Check accuracy again
train2 = subset(wiki2, spl==T)
test2 = subset(wiki2, spl==F)
cart2 = rpart(Vandal~., train2, method="class")
pred2 = predict(cart2,test2,type='class')
table(test2$Vandal, pred2) %>% {sum(diag(.)) / sum(.)} # 0.57524
[1] 0.57524
【P2.2】What is the new accuracy of the CART model on the test set, using a threshold of 0.5?
2.3 Total numbers of words added and removed
wiki2$nwAdded = nwAdded
wiki2$nwRemoved = nwRemoved
mean(nwAdded) # 4.0501
[1] 4.0498
【P2.3】What is the average number of words added?
2.4 Check accuracy again
train = subset(wiki2, spl)
test = subset(wiki2, !spl)
cart = rpart(Vandal~., train, method="class")
pred = predict(cart,test,type='class')
table(test$Vandal, pred) %>% {sum(diag(.)) / sum(.)} # 0.6552
[1] 0.6552
【P2.4】What is the new accuracy of the CART model on the test set?
Problem 3 - Using Non-Textual Data
原始資料之中還有一些之前沒有用到的欄位,我們把它們也加進來
wiki3 = wiki2
wiki3$Minor = wiki$Minor
wiki3$Loggedin = wiki$Loggedin
3.1 Check accuracy again
train = subset(wiki3, spl=T)
test = subset(wiki3, spl=F)
cart = rpart(Vandal~., train, method="class")
pred = predict(cart,test,type='class')
table(test$Vandal, pred) %>% {sum(diag(.)) / sum(.)} # .72472
[1] 0.72472
【P3.1】What is the accuracy of the model on the test set?
3.2 The Decision Tree
prp(cart)

【P3.2】How many splits are there in the tree?
討論議題:
■ 請舉出一些可以繼續提高模型準確率的方法,方法越多越好:
● 利用原始資料去計算出新的變數。
● 將多個模型混合成混合模型。
●
●
●
---
title: "AS10-1：誰是來亂的？"
author: "林嘉羽 M064111038"
date: "`r Sys.time()`"
output: 
  html_notebook
---

The data for this problem is based on the revision history of the page Language. Wikipedia provides a history for each page that consists of the state of the page at each revision. Rather than manually considering each revision, a script was run that checked whether edits stayed or were reverted. If a change was eventually reverted then that revision is marked as vandalism. This may result in some misclassifications, but the script performs well enough for our needs.

As a result of this preprocessing, some common processing tasks have already been done, including lower-casing and punctuation removal. The columns in the dataset are:

+ Vandal = 1 if this edit was vandalism, 0 if not.
+ Minor = 1 if the user marked this edit as a "minor edit", 0 if not.
+ Loggedin = 1 if the user made this edit while using a Wikipedia account, 0 if they did not.
+ Added = The unique words added.
+ Removed = The unique words removed.

<br><hr>

```{r}
packages = c(
  "dplyr","ggplot2","caTools","tm","SnowballC","ROCR","rpart","rpart.plot","randomForest")
existing = as.character(installed.packages()[,1])
for(pkg in packages[!(packages %in% existing)]) install.packages(pkg)
```

```{r warning=F, message=F, cache=F, error=F}
rm(list=ls(all=TRUE))
Sys.setlocale("LC_ALL","C")
options(digits=5, scipen=10)

library(dplyr)
library(tm)
library(SnowballC)
library(ROCR)
library(caTools)
library(rpart)
library(rpart.plot)
library(randomForest)
```
<br>

### Problem 1 - Bags of Words

##### 1.1 The data set

```{r}
wiki = read.csv("data/wiki.csv", stringsAsFactors = F)
wiki$Vandal = factor(wiki$Vandal)
table(wiki$Vandal)
```

【P1.1】__How many cases of vandalism were detected in the history of this page?__

+ 1815
+

##### 1.2 DTM, The Added Words
```{r}
library(tm)
library(SnowballC)

# Create corpus for Added Words
txt = iconv(wiki$Added, to = "utf-8", sub="")
corpus = Corpus(VectorSource(txt))
corpus = tm_map(corpus, removeWords, stopwords("english"))
corpus = tm_map(corpus, stemDocument)
dtm = DocumentTermMatrix(corpus)
dtm
```
【P1.2】__How many terms appear in `dtmAdded`?__

+ 6675
+

##### 1.3 Handle Sparsity
Filter out sparse terms by keeping only terms that appear in 0.3% or more of the revisions, and call the new matrix sparseAdded. 
```{r}
nwAdded = rowSums(as.matrix(dtm))     # no. word added in each edit
dtm = removeSparseTerms(dtm, 0.997)
dtm
```
【P1.3】__How many terms appear in `sparseAdded`?__

+ 166
+

##### 1.4 Create Data Frames, `wordAdded` & `wordRemoved`
Convert sparseAdded to a data frame called `wordsAdded`, and then prepend all the words with the letter A, by using the command:
```{r}
wordsAdded = as.data.frame(as.matrix(dtm))
colnames(wordsAdded) = paste("A", colnames(wordsAdded))  # for proper column names
```

Now repeat all of the steps we've done so far to create a Removed bag-of-words dataframe, called `wordsRemoved`, except this time, prepend all of the words with the letter R:

```{r}
# Create corpus
txt = iconv(wiki$Removed, to = "utf-8", sub="")
corpus = Corpus(VectorSource(txt))
corpus = tm_map(corpus, removeWords, stopwords("english"))
corpus = tm_map(corpus, stemDocument)
dtm = DocumentTermMatrix(corpus)
dtm
nwRemoved = rowSums(as.matrix(dtm))
dtm = removeSparseTerms(dtm, 0.997)
dtm
wordsRemoved = as.data.frame(as.matrix(dtm))
colnames(wordsRemoved) = paste("R", colnames(wordsRemoved))
```
【P1.4】__How many words are in the `wordsRemoved` data frame?__

+ 162
+

##### 1.5 Prepare the Data Frame
Combine the Data Frames `wordsAdded` & `wordsRemoved` with the Target Variable `wiki$Vandal`
```{r}
wikiWords = cbind(wordsAdded, wordsRemoved)
wikiWords$Vandal = wiki$Vandal
```

Split the data frame for train and test data
```{r}
library(caTools)
set.seed(123)
spl = sample.split(wikiWords$Vandal, 0.7)
train = subset(wikiWords, spl == TRUE)
test = subset(wikiWords, spl == FALSE)
table(test$Vandal) %>% prop.table
```
【P1.5】__What is the accuracy on the test set of a baseline method that always predicts "not vandalism"?__

+ 0.53138
+

##### 1.6 CART Model
```{r}
library(rpart)
library(rpart.plot)
cart = rpart(Vandal~., train, method="class")
pred = predict(cart,test,type='class')
table(test$Vandal, pred) %>% {sum(diag(.)) / sum(.)} # 0.54428
```
【P1.6】__What is the accuracy of the model on the test set, using a threshold of 0.5?__

+ 0.54428
+


##### 1.7 Plot the Decision Tree
```{r fig.height=3.6}
prp(cart)
```
【P1.7】__How many word stems does the CART model use?__

+ 3
+

##### 1.8 Predictability of the CART model
【P1.8】__Given the performance of the CART model relative to the baseline, what is the best explanation of these results?__

+ Although it beats the baseline, bag of words is not very predictive for this problem.
+

<br><hr>

### Problem 2 - Add Features with Problem-specific Knowledge

##### 2.1 Add `HTTP` column
Add a new column based on whether `"http"` is added 
```{r}
wiki2 = wikiWords
wiki2$HTTP = ifelse( grepl("http",wiki$Added,fixed=TRUE) , 1, 0)
table(wiki2$HTTP) # 217
```
【P2.1】__Based on this new column, how many revisions added a link?__

+ 217
+

##### 2.2 Check accuracy again
```{r}
train2 = subset(wiki2, spl==T)
test2 = subset(wiki2, spl==F)
cart2 = rpart(Vandal~., train2, method="class")
pred2 = predict(cart2,test2,type='class')
table(test2$Vandal, pred2) %>% {sum(diag(.)) / sum(.)} # 0.57524
```
【P2.2】__What is the new accuracy of the CART model on the test set, using a threshold of 0.5?__

+ 0.57524
+

##### 2.3 Total numbers of words added and removed
```{r}
wiki2$nwAdded = nwAdded
wiki2$nwRemoved = nwRemoved
mean(nwAdded) # 4.0501
```
【P2.3】__What is the average number of words added?__

+ 4.0501
+

##### 2.4 Check accuracy again
```{r}
train = subset(wiki2, spl)
test = subset(wiki2, !spl)
cart = rpart(Vandal~., train, method="class")
pred = predict(cart,test,type='class')
table(test$Vandal, pred) %>% {sum(diag(.)) / sum(.)} # 0.6552
```
【P2.4】__What is the new accuracy of the CART model on the test set?__

+ 
+

<br><hr>

### Problem 3 - Using Non-Textual Data

原始資料之中還有一些之前沒有用到的欄位，我們把它們也加進來
```{r}
wiki3 = wiki2
wiki3$Minor = wiki$Minor
wiki3$Loggedin = wiki$Loggedin
```

##### 3.1 Check accuracy again
```{r}
train = subset(wiki3, spl=T)
test = subset(wiki3, spl=F)
cart = rpart(Vandal~., train, method="class")
pred = predict(cart,test,type='class')
table(test$Vandal, pred) %>% {sum(diag(.)) / sum(.)} # .72472
```
【P3.1】__What is the accuracy of the model on the test set?__

+ 0.72472
+

##### 3.2 The Decision Tree
```{r  fig.height=3.6}
prp(cart)
```

【P3.2】__How many splits are there in the tree?__

+ 3
+
  
<br><hr>

<p class="qiz">
討論議題：<br>
&emsp; ■ 請舉出一些可以繼續提高模型準確率的方法，方法越多越好： <br>
&emsp; &emsp; ●  利用原始資料去計算出新的變數。<br>
&emsp; &emsp; ●  將多個模型混合成混合模型。<br>
&emsp; &emsp; ●  <br>
&emsp; &emsp; ●  <br>
&emsp; &emsp; ●  <br>
<br>
</p>

<br><br><br><br>





