辅导MATH 189讲解数据结构语言

MATH 189 Final Project 

Due June 9th 2020 

Spam Classification 

Consider the email spam data set, which is available on Canvas. 

This consists of 4601 email messages, from which 57 features 

have been extracted. These features are described as follows: 

• 48 features giving the percentage of certain words (e.g., 

"business", "free", "george") in a given message 

• 6 features giving the percentage of certain characters (; 

( [ ! $ #) 

• feature 55: the average length of an uninterrupted 

sequence of capital letters 

• feature 56: the length of the longest uninterrupted 

sequence of capital letters 

• feature 57: the sum of the lengths of uninterrupted 

sequences of capital letters 

The data set contains a training set of size 3065, and a test set 

of size 1536. One can imagine performing several kinds of 

preprocessing to this data. Try each of the following separately: 

1) Standardize the columns so that they all have zero mean and 

unit variance; 

2) Transform the features using ; 

3) Discretize each feature using . 

log(xij + 1) 

I(xij > 0) 

(a) For each version of the data, visualize it using the tools 

introduced in the class. 

(b) For each version of the data, fit a logistic regression model. 

Interpret the results, and report the classification errors on 

both the training and test sets. Do any of the 57 features/ 

predictors appear to be statistically significant? If so, which 

ones? (Hint: consider this as a multiple testing problem). 

(c) Apply both linear and quadratic discriminant analysis 

methods to the standardized data, and the log transformed 

data. What are the classification errors (training and test)? 

(d)Apply linear and nonlinear support vector machine classifiers 

to each version of the data. What are the classification errors 

(training and test)? 

Report classification errors using different methods and 

different preprocessed data in a table, and comment on the 

different performances. 

Finally, use either a single method with properly chosen tuning 

parameter or a combination of several methods to design a 

classifier with test error rate as small as possible. Describe your 

recommended method, and report its performance.