Description
This assignment is designed to give you practical programming experience with radial basis functions and the K-means algorithm. Many aspects of this class can be fully understood only with
computer simulations. Programming assignments help you gain first-hand experience with the algorithms introduced in the class. Please use Python for the implementation, but you CANNOT
use any library that implements the solution for you (e.g., for K-Means or RBF). Message the
TA/instructor in Slack if you are unsure. If you are unfamiliar with Python, please reach out to
the instructor and grader as soon as possible.
Please carefully read all instructions below and also periodically check Slack for updates. Any questions that you post to the public Slack channels should NOT contain
any portion of your solution. If you need specific help with your solution, you can
send private messages to the instructor or grader. Post general questions to the
programming-2 Slack channel.
This is an individual assignment, so you must submit your own work. You also cannot use other
resources (e.g., web sites, books, blogs, research papers, other people, etc.) to solve the problems.
Your assignment must be submitted by committing your code to your Github repository before the deadline. Please create a folder called ‘pa2’ (without quotes) and
commit all files for this assignment to this folder. You are strongly encouraged to submit
early and often to avoid any last minute issues and to confirm that you are committing your work
correctly. The submission should be in the form of a Python 3 Jupyter Notebook file. Be sure to
run the file before committing, so that we can directly see your results. Programs that
were not run before submitting will result in a zero.
This assignment must be submitted on time to receive full credit. Late submissions will
result in a 10% penalty each calendar day it is late, but it cannot be submitted more than 3 days
late. Your grade will partially depend on completeness, correctness, code efficiency
(e.g., using linear algebra whenever possible), and code readability (e.g., comments).
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Spring 2023 CSE 5526: Intro to Neural Networks
Question 1. [100 points]
Implement an RBF network for a one-dimensional input variable, one-dimensional output variable,
and Gaussian basis functions. Generate a set of 75 data points by sampling the function h(x) =
0.5 + 0.4sin(2πx) with added uniform noise in the interval [-0.1, 0.1] and with x values taken
randomly from a uniform distribution in the interval [0.0, 1.0]. Determine the Gaussian centers by
the K-means algorithm, and set the variance of each cluster accordingly. If a cluster contains only
one sample point, use as its variance the mean variance of all the other clusters. Use the LMS rule
for weight update (note a bias term is needed). Perform the following:
• Vary the number of bases in the range of 2, 4, 7, 11, and 16.
• Use two values of η: 0.01 and 0.02.
For each of the above 10 cases, stop training after 100 epochs. Plot for each case a graph that shows
the data points, the original function where the data points are sampled from, and the function
generated by the RBF network.
Comment on the dependence of the network performance on the number of bases. Also comment
on the choice of η.
In addition, repeat the above implementation but use the same variance for all clusters as described
in the lectures. Comment on the comparative advantages of the two methods of determining cluster
variance.
What you need to turn in:
1. A summary report that is at least two-pages long, which contains your test results, along
with a description and explanation of those results.
2. Your Jupyter notebook that contains your code and results.
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