Page 313 - Introduction to Statistical Pattern Recognition

6 Nonparametric Density Estimation 295

yg = +{(2x0 - 1)(2xO - 1) + (2x1 - 1)(2xO - 1)

+ (2x0 - 1)(2x1 - 1) + (2x1 - 1)(2x1 - 1)) = 0, (6.163)

I 1
y\': = -(2xO - 1)(2x0 - 1) + -(2x1 - 1)(2XO - 1)
6 3

1 1 1
+ -(2x0 - 1)(2x1 - 1) + -(2x1 - 1)(2x1 - 1) = -- . (6.164)
3 6 3
Therefore, substituting these results into (6.157), we obtain

(6.165)

(6.166)

Computer Projects
,.
1. Estimate the mean and variance of the Parzen density estimate, p(X), as
follows:

Data: NX(OJ), n = 8
Design samples: N = 100
Test points: [e 0. . . O]', . . . ,[O. . . 0 elT
i= 1, 2, 3, 4, 5
Procedure: Parzen
Kernel: Uniform
Kernel size: Optimal I'
No. of trials: T = 10
Results: Mean and variance vs. 1.
2. Repeat Project 1 for a normal kernel.

3. Repeat Project 1 for the kNN density estimate with the optimal k.