Please submit your solutions in a pdf  le to Moodle by 5pm (UK time) on Wednesday, 14 December. Late sub- mission entails penalties: 5 marks (out of maximum 100) will be deducted for every half-day (12 hours) within the   rst 24 hours after the deadline, and 5 marks will be deducted for each further 24 hours.  Submissions are not accepted after 5pm on Monday , 19 December.

You should only submit your own work, and cannot use materials from the past and/or your classmates. Plagiarism is a very serious ofense that is quite easy to detect. It will result in instant failure (mark 0).

This exercise is on credit card fraud detection based on a data set downloaded from Kaggle Datasets at https://www.kaggle.com/mlg-ulb/creditcardfraud

Background information on the data is available at

https://www.kaggle.com/mlg-ulb/creditcardfraud/home

Previous attempts can be found at

https://www.kaggle.com/janiobachmann/credit-fraud-dealing-with-imbalanced-datasets/versions (All those analysis was done using Python.  But you should be able to follow the ideas, understand most the results. Especially some initial data exploration is easy to follow.)

The dataset contains 284,807 credit card transactions in two days in September 2013 by European card- holders, of which 492 are frauds. So the data is highly unbalanced: the positive cases (i.e. frauds) account for merely 0.172% of all transactions.

Due to the conidentiality issues, the original features for each transaction are masked via a linear transfor- mation.  The 28 transformed features are presented as V1, V2, · · · , V28.  According to the above webpage, those 28 features are the principal components of the original features. No further information on those features is provided. In addition to those 28 variables, there are 3 untransformed variables:

• Time: number of seconds elapsed between each transaction and the irst transaction in the dataset

• Amount: the amount of the transaction

• Class: binary label with value 1 for‘fraud’and 0 otherwise.

The whole dataset has 284,807 rows and 31 columns. The task is to build up efective algorithms for detecting fraudulent credit card transactions.

The data is extremely imbalanced with only 0.172%‘positives’(i.e.  frauds).  Hence the information on frauds is overwhelmed by that on true and genuine transactions. This imbalance leads the itted models using the whole data predominately led by the information on‘negatives’, and the signal on‘positives’is too weak to be picked up. To balance the information used in building classiiers, we have created a more balanced but, unfortunately, much smaller training data with 24.62% positive cases, and also a testing data set which is about equally imbalanced as the whole data set.

•  creditCardTrain.csv: of size 1592 31, consisting of 1200 randomly selected non-fraudulent transactions plus 392 randomly selected fraud transactions. The true positive rate is about 24.62%.

•  creditCardTest.csv: of size 57889  31, consisting of 57789 randomly selected non-fraudulent transac- tions plus 100 remaining fraud transactions.  It has no overlaps with creditCardTrain.csv.  The true positive rate is 0.173%.

The two data sets are placed on the course Moodle page.  For your information, I attach below the codes for constructing those two data sets.

> library(readr); library(dplyr)

> CC=read_csv("creditcard.csv") # read_csv is a much faster version of read.csv

> CC1=CC[CC$Class==1,] # extract all frauds

> dim(CC1)

[1] 492 31

> train1=sample(1:492, 392)

> CC1train=CC1[train1,]

> CC1test=CC1[-train1,]

> CC0=CC[CC$Class==0,] # extract all genuine transactions

> dim(CC0)

[1] 284315    31

> train0=sample(1:284315, 58988)

> Dtrain=bind_rows(CC1train, CC0[train0[1:1200],]) # bind the rows from two data together

> dim(Dtrain)

[1] 1592  31

> Dtrain=arrange(Dtrain, Time) # re-arrange rows according to ascending order of Time

> write.csv(Dtrain, row.names=F, "creditCardTrain.csv")

> Dtest=bind_rows(CC1test, CC0[train0[1200:58988],])

> dim(Dtest)

[1] 57889   31

> Dtest=arrange(Dtest, Time)

> write.csv(Dtest, row.names=F, "creditCardTest.csv")

> rm(CC, CC0, CC1, CC1test, CC1train, Dtest, Dtrain, train0, train1) # remove those objects

Your analysis should be based on creditCardTrain.csv. creditCardTest.csv represents the true reality, and should be used only to test the performance of your models.

1. Carry out some exploratory data analysis irst. You may like to address the issues such as

• are there any missing values and outliers?

• should you apply any transformations to any variables, for example, log(Amount + 1)?

• is Time relevant to detecting frauds?

[5 marks] [10 marks] [5 marks]

2. Suppose that the credit card company charges 2% fees for each transaction (deducted from the payment to payee).

(a) Estimate the expected potential loss of a fraudulent transaction.

(b) Estimate the expected proit from a genuine transaction.

[5 marks] [5 marks]

(c) Test the performance of your decision tree on the testing data set, with the cutting-of probability 0.5 and  respectively. Now you should calculate the true proits or losses according to the real amount of each transaction in the testing data sets.

[10 marks]