Description
1) 10 points for part 1)
Create (in MATLAB) 20, 2-dimensional, normally distributed data with standard deviation 2, centered
at [0; 0] for positive class, and 10, 2-dimensional, normally distributed data with standard deviation
2, centered at [5; 5] for negative class. Data should be created with a seed = 1. Train Perceptron with
learning rate η = 0.1. Implement Perceptron update as given by Method 1 in the textbook. Initial
weight vector w = [0 0 0]’.
a) Show data and separation boundary in the first graph. How many epochs are needed?
b) What is the final weight vector w?
c) Run experiments with various learning rates η, say [1e-4 1e-3 1e-2 1e-1 1e0 1e 1e1 1e2 1e3
1e4]. Show in the second graph how number of epochs depends upon η.
d) Train linear neuron in a batch mode. Show its separation boundary in the first graph too.
Comment all the results in 1).
2) 5 points for part 2)
Create an outlier at [20, 20] which belongs to negative class.
a) Train perceptron with η = 1. Show on the first graph from 1a) both the outlier and percep-
tron’s separation boundary.
b) Train linear neuron in a batch mode again without regularization. Show its separation
boundary too.
c) Train linear neuron in a batch mode again with penalty parameter λ = 1. Now the weight
vector must be calculated as follows w = (X’X + λI)
-1X’Y. Show the new separation
boundary too.
3) 10 points for part 3)
Run 10-fold crossvalidation and find the best penalty parameter λbest.
Using the λbest design linear neuron and show its (best) separation boundary. What is the w now?
Comment all the results in 2) & 3).
Some hints:
SOFTWARE MUST BE USER FRIENDLY, so that I can run it easily too. At the top of your routine have the
commands: close all, format compact None of the calculations should be longer than 5 seconds on my laptop.
Your report should STRICTLY be (in terms of everything; starting with 2 columns format up to fonts type and
font size) in the form of IEEE journal (conference) paper. Use the template attached but don’t send to me your
Word file, send to me PDF file.
Submit both your written report and program to me by Email.
ZIP your report and programs into a single zip file (which will contain max 2 files (the report in PDF, and
the MATLAB’s m routine) name it with your family name (say, lee.zip) and send it to me. A Subject field
in your Email MUST be CMSC 678, Family name, Project 1. Don’t hesitate to contact me in the case of
need. Use my office hours –Tuesday 11am-12pm (but, you can always drop by for up to 7 minutes
questions and discussion. Just knock on my door!)
FINALLY: Any copying, “copying” or use in any form of somebody else’s code or report will be
treated as cheating and treated according to the VCU Honors Code.
My Email is: vkecman@vcu.edu.
