Biological Neural Computation
Homework problem set 2
Spring 2024
Data Assigned: 2/19/2024
Data Due: 3/08/2024
General Guidelines: The homework solutions should include figures that clearly
capture the result. The figures have to be labeled, well explained and the results
must be clearly discussed. When appropriate, it is recommended that you use
the Hypothesis – Rationale – Experiments/data – Analysis – Results –
Discussion/Conclusions – Limitation(s) framework to discuss your work.
The first sheet of the homework must certify that this is completely your
work and list the students/people you have consulted or received help from
(with your signature and date of submission). All online references used
must be listed in the reference section at the end of the homework.
Good luck,
Barani Raman
2
Points for BME 572 /BME 472 students
PointsforL415657 students
Problem 1. Implement the batch perceptron algorithm to obtain a linear discriminating
function as described in Chapter 5 of Duda et al Pattern Classification book. Create
linearly separable and non-linearly separable datasets with samples belonging to the two
classes. Apply your perceptron algorithm to discriminate. Report your observation and
analysis? Plot classification error vs. # of iterations, classification results, and the
obtained decision boundary.
[30 pts]
[50 pts]
Problem 2: Using the same datasets used in problem 1, now create a linear classifier
using Least Mean Squares (LMS) rule. Compare these results with the Perceptron
algorithm results.
[20 pts]
[50 pts]
3
For BME 572 students only
[50 pts]
Problem 3: Using back-propagation algorithm train a multilayer perceptron for the
problem of recognizing handwritten digits. A popular dataset (‘mnist_all.dat’) comprising
of training and testing samples of the different digits is provided in the homework folder.
Each sample is 28x28 gray scale 8-bit image.
Figure 1: Sample of the nine handwritten digits in the MNIST dataset.
Training:
The Matrix train0 has the training samples for digit ‘0’. Each row has 784 columns
corresponding to the 28x28 pixel (you can use reshape command to plot the digits; e.g.
imagesc(reshape(test0(1,:),28,28)') plots first training sample for digit 0’’.) Similarly,
there is one dataset corresponding to each digit. You will train your network using the
training samples only. You are free to choose a network of any size, and any non-linear
activation function. Also, you are free to use any preprocessing technique or
dimensionality reduction technique, or use only a subset of training samples, if you
would like to reduce the complexity of the neural network or the training process.
Initialize the weight vectors to a very small random number between 0 and 0.1. This will
help the network to converge better than equal weights or zero weights.
4
For non-linear activation two popular choices are the following:
Choice1: Logistic function
Choice2: Hyperbolic tangent function
[Note: a, b are constants]
Testing:
The Matrix test0 has the test samples for digit ‘0’. Similarly, there is one corresponding
to each digit. You will evaluate the performance of your network using the test samples
only.
Show the evolution of the prediction error as a function of training iteration, final
classification percentages for each digit, and the overall classification performance.
Discuss your findings.
For reference about this popular dataset take a look at: http://yann.lecun.com/exdb/mnist/
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