Homework 4
CS 591Q/791V - Pattern Recognition
Instructor: Dr. Arun Ross
Due Date: April 24, 2008
Note: You are permitted to discuss the following questions with others in the class.
However, you must write up your own solutions to these questions. Any indication to the
contrary will be considered an act of academic dishonesty. Code developed as part of this
assignment should be placed in a zip file and sent to arun.ross at mail.wvu.edu with the
subject line “CS 591Q/791V : Homework 4”. Also, include a hard-copy of your code when
you submit the homework.
1. [20 points] Consider two class-conditional densities N(10,5) and N(25,5). Generate 100
random training samples from each of the two distributions. Write a program that employs
the Parzen window technique with a Gaussian kernel to estimate the density using al l 200
samples. Plot the estimated density function for window widths of 0.01, 0.5, and 10.0.
Repeat the above after generating 1000 training samples from each of the two distributions.
2. [20 points] The iris (flower) dataset consists of 150 4-dimensional patterns belonging to three
classes (setosa, versicolor, and virginica). There are 50 patterns per class. The 4 features
correspond to (a) sepal length in cm, (b) sepal width in cm, (c) petal length in cm, and (d)
petal width in cm. The data can be accessed here. Note that the class labels are indicated
at the end of every pattern.
Design a K-NN classifier for this dataset. Randomly choose half the data (from each class)
for training the classifier (i.e., these are the prototypes) and the remaining half for testing
the classifier. Perform this data-partitioning exercise ten times and report the empirical
error rate each time. Also, compute the average and the variance of the error rates. In order
to study the effect of Kon the performance of the classifier, report error rate statistics for
K=1,3,5,7 and 9.