## Description

1. Generate 10,000 samples from each 2D Gaussian distribution specified by the following

parameters:

1

1

1

1

2 0

0 2

2

6

6

2

2 0

0 2

Please, note that this is not the same as sampling the functions shown above; see

“Generating Gaussian Random Numbers“ on the course’s webpage for more information

on how to generate the samples using the Box-Muller transformation. A link to C code

has been provided. Since the code generates samples for 1D distributions, you would

need to call the function twice to get a 2D sample (x, y); use the x-mean, x-variance for

the x sample and the y-mean, y-variance for the y sample.

a. Assuming P(ω1) = P(ω2)

i. Design a Bayes classifier for minimum error.

ii. Plot the Bayes decision boundary together with the generated samples to

better visualize and interpret the classification results.

iii. Report the number of misclassified samples for each class separately and

the total number of misclassified samples.

iv. Plot the Chernoff bound as a function of β and find the optimum β for the

minimum.

v. Calculate the Bhattacharyya bound.

b. Repeat part (a) for P(ω1) = 0.2 and P(ω2) = 0.8.

2. Repeat (1) using the following parameters:

1

1

1

1

2 0

0 2

2

6

6

2

4 0

0 8

3. For part 2, use the minimum-distance classifier to classify the samples and compare

your results (i.e., misclassified samples) with the Bayes classifier from part 2.

PROJECT REPORT SUBMISSION REQUIREMENTS

1. Cover Page. The cover page should contain Project title, Project number, Course

number, Student’s name, Date due, and Date handed in.

2. Technical discussion. This section should include the techniques used and the principal

equations (if any) implemented.

3. Discussion of results. A discussion of results should include major findings in terms of

the project objectives, and make clear reference to any figures generated.

4. Division of work: Include a statement that describes how the work was divided between

the two group members.

5. Program listings. Includes listings of all programs written by the student. Standard

routines and other material obtained from other sources should be acknowledged by

name, but their listings should not be included.

You need to turn in a printed copy of your report (i.e., items 1-4), in the beginning of the class on

the due date. Program listings (i.e., item 5) should be emailed to the instructor, as a zip file,

before class on the due date. Each group should submit one report only.