Page 353 - Introduction to Statistical Pattern Recognition

7 Nonparametric Classification and Error Estimation 335

Experiment 7: Estimation of the Parzen error, L and R
Data: p (X) = 0.5Nx(M1 ,I)+0.5Nx(M2,1)
p 2 (X) = OSNx(M3 J)+0.5Nx(M4 ,I)
MI = [OO. . . OlT, M2 = [6.58 0. . . 0IT
M3 = I3.29 0. . . O]*, M4 = (9.87 0. . . OI7
n = 8, E~ = 7.5%
Sample size: N, = N, = 100
No. of trials: T = 10
Kernel: Normal with A I = A2 = I
Kernel size: 0.6-6.0
Threshold: Option 4
Results: Fig. 7-10 [I21

30.

20.

IO.

1.0 2.0 3.0 4.0 5.0 6.0
Fig. 7-10 Parzen error for a non-normal test set.

Figure 7-10 shows the results for this experiment. With a moderate
value of 1', the Bayes error of 7.5% is bounded properly, when the Parzen den-
sity estimate for each class represents the given two-modal distribution. On
the other hand, as I' grows, the density estimate converges to the kernel func-
tion itself. Thus, with normal kernels, the likelihood ratio of the estimated