## Description

In this programming assignment, you will implement techniques to learn a multi-class logistic regressor

for image digit classification on the MNIST dataset (https://en.wikipedia.org/wiki/MNIST_database).

The classifier will take an image of a hand-written numerical digit between 1 and 5 as input and classify

it into one of 5 classes corresponding to digit 1 to 5 respectively. Given the training data, you will follow

the equations in the lecture notes to train a multi-class logistic regressor using the gradient descent

method and then evaluate its performance on the given testing data. For training, you will learn the

discriminant function regression parameters Θ=(Wk,Wk,0)

t

, where k=1,2,3, 4, 5, Wk is a vector for kth

discriminant function, and Wk,0 is its bias.

Specifically, given the training data D={x[m], y[m]}, m=1,2, …, M, where x[m] is a grayscale image of

28×28 (a 784×1 vector) and y[m] is output vector that follows the 1 of K encoding, with kth element of

being 1 and the rest being 0. You will implement the following methods to learn the parameters Θ

1. For students taking this class at 4000 level, implement in Tensorflow the gradient descent method

to solve for Θ iteratively using all data in D. Initialize Θ to small values and literately update

Θ with appropriate learning rate until convergence. Save Θ and plot the (Wk) for each class

using matplotlib.pyplot functions (see below for details).

2. For students taking this class at 6000 level, implement in Tensorflow the Stochastic Gradient

Descent method with L2 regularization. Initialize Θ to small values and literately update Θ with

appropriate learning rate and regularization parameter λ until convergence. Save Θ and plot the

(Wk) for each class using matplotlib.pyplot functions (see below for details).

3. Using the given testing dataset T, evaluate the performance of your trained classifier by

computing the classification error for each digit as well as the average classification errors

for all five digits. The classification error for each digit is computed as the ratio of incorrect

classification to the total number images for that digit

Do not use Tensorflow’s existing gradient descent and stochastic gradient descent functions. Submit your

Tensorflow code via LMS, along with the required classification errors, weight plots, and the saved

weights W .

Data format

The training data D contains 25112 training images (00001.jpg – 25112.jpg) in train_data folder, and

their labels are stored in train_label.txt with each raw being the label of the corresponding image.

The testing data T contains 4982 testing images (00000.jpg – 04982.jpg) in test_data folder, and their

labels are stored in test_label.txt.

Load images and normalize

Load the images in the order

Convert it to vector and normalize it to [0,1] by dividing the intensity of each pixel by 255

The following link teaches how to load images:

http://learningtensorflow.com/lesson3/

Output

Use the code below to save the learned parameters matrix W in the following format

⎥

⎦

⎤ ⎢

⎣

⎡ = 1,0 2,0 3,0 4,0 5,0

1 2 3 4 5

W W W W W

W W W W W

W

Wk is the learnt weights for the kth digit and Wk,0 is the corresponding bias.

——————–

import pickle

filehandler = open(“multiclass_parameters.txt”,”wb”)

pickle.dump(W, filehandler)

filehandler.close()

—————–

Plot

Use the following function to plot Wk as an image for each digit:

—————–

import matplotlib.pyplot as plt

Img = W_k.reshape(28,28)

plt.imshow(img)

plt.colorbar()

plt.show()

—————–