Project
CS 591Q/791V - Pattern Recognition
Instructor: Dr. Arun Ross
Due Date: May 8, 5:00pm
Note: You are permitted to discuss this project with the others in class, but the final
report should reflect your own effort. Any indication to the contrary will be considered an
act of academic dishonesty. A zipped version of your submission consisting of the code and
the report must be sent via email to arun.ross at mail.wvu.edu by 5:00pm on 5/8/2009.
1. Consider the dataset available here. It consists of two-dimensional patterns, x= [x1, x2]t,
pertaining to 3 classes (C1, C2, C3). The feature values are indicated in the first two columns
while the class labels are specified in the last column. The priors of all 3 classes are the
same. Randomly partition this dataset into a training set (70% of each class) and a test set
(30% of each class).
(a) Let
p([x1, x2]t|C1)∼N([0,0]t,4I),
p([x1, x2]t|C2)∼N([10,0]t,4I),
p([x1, x2]t|C3)∼N([5,5]t,5I),
where Iis the 2 ×2 identity matrix. What is the error rate on the test set when the
Bayesian decision rule is employed for classification?
(b) Suppose p([x1, x2]t|Ci)∼N(µi,Σi), i= 1,2,3, where the µi’s and Σi’s are unknown.
Use the training set to compute the MLE of the µi’s and the Σi’s. What is the error
rate on the test set when the Bayes decision rule using the estimated parameters is
employed for classification?
(c) Suppose the form of the distributions of p([x1x2]|Ci), i= 1,2,3 is unknown. Assume
that the training dataset can be used to estimate the density at a point using the
Parzen window technique (a spherical Gaussian kernel with h= 1). What is the error
rate on the test set when the Bayes decision rule is employed for classification?
(d) Repeat the above three classification procedures by varying the size of the training set
as follows: 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% of each class. Plot the
error rate as a function of the size of the training set for each of the 3 cases.
