Page 268 - Introduction to Statistical Pattern Recognition

250 Introduction to Statistical Pattern Recognition

Computer Projects

1. Repeat Experiment 1.

2. Repeat Experiment 4. Also, estimate the asymptotic error for each n by
using the line fitting procedure.

3. Repeat Experiment 5. Also, estimate the asymptotic error for each n by
using the line fitting procedure.
4. Repeat Experiment 6.

5. Repeat Experiment 9.

6. Repeat Experiment 10.

Problems

1. The Fisher criterion, f = (m2-m l)2/(o:+o:), measures the class separa-
bility between two one-dimensional distributions. Compute the bias and
variance of f when these parameters are estimated by using N samples
from N-,(O, 1) for o1 and N samples from N,( 1.4) for 02.
,.
2. Let f (m) be a function of m, where m is the expected value of a one-
dimensional normal distribution and is estimated by the sample mean m
..
using N samples. Expand f (m) around f (m) up to the fourth order
term, and confirm that E { 0'3' I = 0 and E { 0'4' )-lIN2.
,.
A A
3. Compute the bias and variance of p (not pI and p2 separately) for nor-
mal distributions.

01
4. In order for a linear classifier h (X) = VTX + v0 >< 0 to be optimum by
02
minimizing the error of (5.37), prove that V and \io must satisfy