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# Homework 02: Discrimination by Regression

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ENGR 421 / DASC 521
Homework 02: Discrimination by Regression

In this homework, you will implement a discrimination by regression algorithm for multiclass
classification in R, Matlab, or Python. Here are the steps you need to follow:
1. Read Section 10.8 from the textbook.
2. You are given a multivariate classification data set, which contains 1000 clothing images
of size 28 pixels × 28 pixels (i.e., 784 pixels). These images are from five distinct
classes, namely, T-shirt, trouser, dress, sneaker, and bag. The figure below shows five
sample figures from each class. You are given two data files:
a. hw02_images.csv: letter images,
b. hw02_labels.csv: corresponding image labels (1: T-shirt, 2: trouser, 3: dress,
4: sneaker, and 5: bag).
3. Divide the data set into two parts by assigning the first 500 images to the training set and
the remaining 500 images to the test set.
4. Learn a discrimination by regression algorithm using the sigmoid function for this
multiclass classification problem. You can use the following learning parameters.
eta <- 0.0001
epsilon <- 1e-3
max_iteration <- 500
You should initialize the weight parameters to the values given in initial_W.csv
and initial_w0.csv files before running your algorithm.
5. Draw the objective function values throughout the iterations. Your figure should be
similar to the following figure.
6. Calculate the confusion matrix for the data points in your training set using the
discrimination rule you will develop using the estimated parameters. Your confusion
matrix should be similar to the following matrix.
y_train
y_predicted 1 2 3 4 5
1 101 2 11 0 1
2 0 79 1 0 0
3 6 5 100 0 1
4 0 0 0 99 2
5 0 0 0 1 91
7. Calculate the confusion matrix for the data points in your test set using the parametric
discrimination rule you will develop using the estimated parameters. Your confusion
matrix should be similar to the following matrix.
y_test
y_predicted 1 2 3 4 5
1 82 1 4 0 2
2 0 87 0 0 0
3 13 3 98 0 3
4 0 0 0 103 1
5 4 0 3 0 96
What to submit: You need to submit your source code in a single file (.R file if you are using R,
.m ENGR 421 / DASC 521
Homework 02: Discrimination by Regression

In this homework, you will implement a discrimination by regression algorithm for multiclass
classification in R, Matlab, or Python. Here are the steps you need to follow:
1. Read Section 10.8 from the textbook.
2. You are given a multivariate classification data set, which contains 1000 clothing images
of size 28 pixels × 28 pixels (i.e., 784 pixels). These images are from five distinct
classes, namely, T-shirt, trouser, dress, sneaker, and bag. The figure below shows five
sample figures from each class. You are given two data files:
a. hw02_images.csv: letter images,
b. hw02_labels.csv: corresponding image labels (1: T-shirt, 2: trouser, 3: dress,
4: sneaker, and 5: bag).
3. Divide the data set into two parts by assigning the first 500 images to the training set and
the remaining 500 images to the test set.
4. Learn a discrimination by regression algorithm using the sigmoid function for this
multiclass classification problem. You can use the following learning parameters.
eta <- 0.0001
epsilon <- 1e-3
max_iteration <- 500
You should initialize the weight parameters to the values given in initial_W.csv
and initial_w0.csv files before running your algorithm.
5. Draw the objective function values throughout the iterations. Your figure should be
similar to the following figure.
6. Calculate the confusion matrix for the data points in your training set using the
discrimination rule you will develop using the estimated parameters. Your confusion
matrix should be similar to the following matrix.
y_train
y_predicted 1 2 3 4 5
1 101 2 11 0 1
2 0 79 1 0 0
3 6 5 100 0 1
4 0 0 0 99 2
5 0 0 0 1 91
7. Calculate the confusion matrix for the data points in your test set using the parametric
discrimination rule you will develop using the estimated parameters. Your confusion
matrix should be similar to the following matrix.
y_test
y_predicted 1 2 3 4 5
1 82 1 4 0 2
2 0 87 0 0 0
3 13 3 98 0 3
4 0 0 0 103 1
5 4 0 3 0 96
What to submit: You need to submit your source code in a single file (.R file if you are using R,
.m file if you are using Matlab, or .py file if you are using Python) and a short report explaining
0 100 200 300 400 500
50
100
150
200
250
300
Iteration
Error
your approach (.doc, .docx, or .pdf file). You will put these two files in a single zip file named as
STUDENTID.zip, where STUDENTID should be replaced with your 7-digit student number.
How to submit: Submit the zip file you created to Blackboard. Please follow the exact style
mentioned and do not send a zip file named as STUDENTID.zip.file if you are using Matlab, or .py file if you are using Python) and a short report explaining
0 100 200 300 400 500
50
100
150
200
250
300
Iteration
Error
your approach (.doc, .docx, or .pdf file). You will put these two files in a single zip file named as
STUDENTID.zip, where STUDENTID should be replaced with your 7-digit student number.
How to submit: Submit the zip file you created to Blackboard. Please follow the exact style
mentioned and do not send a zip file named as STUDENTID.zip.

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