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Homework 3 Binary classifications of facial expressions

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CSCI 631 Homework 3
Introduction
For this assignment, we will perform binary classifications of facial expressions using a logistic
regressor, a 1-layer neural network, and the SVM classifier. The main goal is to successfully
write the predict and train functions for both classifiers and compare these with values
obtained from other classifiers. The dataset we are using is quite noisy and was obtained
from the very 2013 Kaggle facial expression classification competition1
. Although the original
dataset contained 7 emotional classes (six of which are shown in Figure 1), we will only use
two of them (happy and sad) for this assignment.
Download the homework3.zip file from myCourses Contents→Programming assignments→Homework3;
this contains the instructions, starter code and image data needed for the assignment.
Figure 1: The top row shows three examples of correctly labeled faces from the Kaggle challenge; left to
right – angry, disgust and fear. The bottom row shows three incorrectly labeled faces; left to right – happy,
sad and surprise. Neutral face is not shown.
Requirements
You should perform this assignment using Python along with any image library of your
choice, and it is due on Sunday November 3rd by 11:59pm. You are required to submit
your code in a Jupyter notebook along with a brief report containing short write-ups based
on the question(s) in the assignment. Your solutions should be zipped and uploaded to
myCourses via Assignments (formerly known as Dropbox) before the due date.
Your submitted zipped file for this assignment should be named LastnameFirstname hw3.zip
and should contain at least two files – LastnameFirstname hw3.pdf and LastnameFirstname hw3.ipynb. Feel free to submit any other auxiliary files required to run your code.
We should be able to execute your code for the assignment from your submitted Jupyter
notebbok. Include a Readme file if necessary (especially if using external libraries other than
those used in the starter code).
1https://www.kaggle.com/c/challenges-in-representation-learning-facial-expression-recognition-\
\challenge/data
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CSCI 631 Homework 3 October 22, 2019
The Data Files
You are provided with two data files, where the first file fer3and4train.csv contains the
training data with 12,066 data samples and the second file fer3and4test.csv contains the
data that you will be testing your classifier on. Results should be reported on the test dataset
which contains 2000 data samples. The files were created using fer2013.csv from Kaggle
but have been shuffled and augmented to avoid the class imbalance problem.
All the files are stored as comma separated files with three columns each. The first column
contains the label of the emotional expression, where 3=happy and 4=sad; the second column
contains 2304 integer values (between 0 and 255) obtained by vectorizing 48 × 48 grayscale
images of faces; and the last column states in which part of the development process the
data should be used (i.e training or testing).
Problem 1. The logistic regression classifier (Total 30 points)
Figure 2: The logistic regression classifier
The file LRClass.py contains the skeleton code for your logistic regression module. This
is accompanied by an auxiliary file called helper.py containing the names of some helper
functions needed for your module to run. In the provided Jupyter notebook, different parts of
the code have been marked for your implementation. First load the the training data samples
X and their corresponding class labels Y using the helper function getBinaryfer13Data.
Then use the class object to train the data. Call the train function to learn the weights
and bias of the unit. The following occur within the train function:
i Initialize the weights W to small random numbers (variance – zero); also initialize the
bias b to zero. The function init weight and bias is provided to aid in this.
ii Create a loop over the number of epochs specified. Within the loop, the following
occur:
iii Call a forward function to calculate the predictions P(Y |X) also known as pY . The
forward function implements σ(X ·W+b). The argument of this equation can be implemented in numpy as σ(np.dot(X, W)+b) where σ is the sigmoid activation function;
this is provided also as a helper function.
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CSCI 631 Homework 3 October 22, 2019
iv Next, learn the weights via back-propagation, by performing gradient descent using
the equations below:
W = W − η
∂J
∂W ; W = W − η · (X · (pY − Y )) (1)
Note: When doing matrix computations, the product of the vectors XY can be
written as np.dot(X.T, Y); Also,
b = b − η
∂J
∂b ; b = b − η · (pY − Y ) (2)
v Apply the forward algorithm to predict the new labels for both the training and validation data. Compute the training cost and validation cost at each epoch and append
to a growing array (one training, the other validation). Keep note of the best error
value on the validation data.
vi Print out the best error value on the validation data. Provide this value in your final
report.
vii Plot your training and validation costs to show how the errors are changing over time.
See Figure 4. Dispaly this in your report.
viii Lastly load a new dataset, your test data from the file fer3and4test.csv. Compute
and print the accuracy (or classification rate) for predicting this new dataset from your
trained network. Provide this information in your report.
Figure 3: An example of the loss curves from the logistic regressor after 1000 epochs
Problem 2. The neural network classifier (Total 45 points)
Similar to the previous exercise, the class NNclass in the Jupyter notebook contains the
skeleton code for your neural network module. Again there are some helper functions in
helper.py. Load the training data samples X and their corresponding class labels Y using
the helper function getBinaryfer13Data. Call the train function to learn the weights and
bias of the unit. The following occur within the train function.
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CSCI 631 Homework 3 October 22, 2019
Figure 4: The single hidden layer neural network with two softmax output nodes
i Initialize the weights W1, W2 to small random numbers (variance – zero); also initialize
the bias b to zero. The function init weight and bias NN is provided to aid in this.
Remember, this time you need to set the number of hidden units in layer 1. This is
your design choice.
Note: The dimensions of these parameters here are different from those in the LRClass.
W1 is D × M1, where M1 is the number of hidden nodes and the dimension of W2 is
M1 × K, where K is the number of output classes.
ii Create a loop over the number of epochs specified. Within the loop, the following
occur:
iii Call a forward function twice to calculate P(Y train|X) also known as pY and Ztrain
(activations at hidden layer); and the other to calculate P(Y valid|Xvalid) and Zvalid
on the validation data. This implies that your forward function needs to return two
values (i) pY , the output of the softmax classifier and (ii) the hidden activations Z,
based on which activation function you choose (tanh, sigmoid, or ReLU ).
iv Now we do a first round of back propagation by first performing gradient descent using
equations (3) and (4) below;
W2 = W2 − η
∂J
∂W2
; W2 = W2 − η · (Z
· (pY − Y )) (3)
b2 = b2 − η
∂J
∂b2
; b2 = b2 − η · (pY − Y ) (4)
v Then we propagate the errors we got from the previous layer W2 to update W1 and b1
via equations (5)-(7):
∂J
∂Z = (pY − Y ) · W2

· (1 − Z
2
) (5)
W1 = W1 − η · X ·
∂J
∂Z (6)
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CSCI 631 Homework 3 October 22, 2019
b1 = b1 − η ·
∂J
∂Z (7)
Matrix multiplications in numpy will be sufficient to complete the processes.
Note: Only the training data is used for updating weights in gradient descent.
vi Apply the forward algorithm to predict the new labels for the training and validation
data and also compute the sigmoid costs of predicting them compared with the true
labels. Append the resulting cost to the growing arrays.
vii Keep note of the best error value on the validation data. Also compute and print
out the training and validation classification rates. This should be given in your final
report.
viii Display the graphs of both your training and validation errors (created from the above
process) to show how the errors change with time. Display these in your report.
ix Lastly load a new dataset, your test data from the file fer3and4test.csv. Compute
and display the accuracy (or classification rate) for predicting this new dataset from
your trained network. This value should be shown in your final report.
Figure 5: An example of the loss curves from the logistic regressor after 1000 epochs
Problem 3. Adding regularizers (Total 10 points)
After the initial training and testing, go back and add a regularizer to the cost function of
the neural network and retrain. Now report your new error rates and accuracies.
(a) Add the L1, L2 or ElasticNet regularizer using the formula provided in the slides from
class
(b) Print out your new classification rates, both for the training and validation datasets,
as well as the test dataset.
(c) Discuss your observations in working with a regularizer (in your report).
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CSCI 631 Homework 3 October 22, 2019
Problem 4. Training with SVM (Total 15 points)
Now go back and we will train with SVM. Scitkit-learns is a good machine learning library
with an easy-to-use SVM interface. Similar to the previous problems, train an SVM on a
portion of the training data, test out your results on a validation set and finally run the true
tests on the test data set. Report your results including the accuracies when using :
(a) A linear kernel
(b) A radial-basis-function (RBF) kernel
(c) A polynomial kernel. Play around with the orders of the polynomial to determine
which one gives the best result.
(d) Discuss your results in working with the 3 different kernels in your report
Note: Training an SVM with over 11,000 data samples of dimension 2034 will take a very
long time.
BONUS: (Total 10 points) Use a different activation function for the neural network to
see if the results will improve. Don’t forget to change your derivatives based on the new
activation function you choose. There are some functions to help with this in helper.py.
Add the code into your ipython notebook and discuss your findings in your report.
You should turn in both your code and report in the zipped file to get full credit.
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