Page 380 - Introduction to Statistical Pattern Recognition

362 Introduction to Statistical Pattern Recognition

Fig. 7-18 A criterion to eliminate a group of samples.

experiment, the tree consists of 3 levels with each node decomposed to 3
nodes. At the bottom of the tree, there are 27 subsets containing 1000 sam-
ples. However, for an 8-dimensional uniform distribution, 45 1 distance com-
putations are needed to find the NN from 3000 samples. The tree is formed
with 4 levels and 4 decomposition, which yields 256 subsets at the bottom
housing 3000 samples. As discussed in Chapter 6, all pairwise distances
among samples become close, as the dimensionality gets high. Therefore, the
effectiveness of (7.87) to eliminate subsets diminishes, and only a smaller
number of subsets are rejected by satisfying (7.87).

Another problem of this method is how to divide samples into subsets.
We will discuss this problem, which is called clustering, in Chapter 1 1. Again,
finding clusters becomes more difficult, as the dimensionality goes up.

Computer Projects

1. Repeat Experiment 3 for Data I-A. Use (a) I and (b) (I +A)/2 as the
metric.

2. Repeat Experiment 5.

3. Repeat Experiment 6.

4. Repeat Experiment 8.

5. Repeat Experiment 9.
6. Repeat Experiment 1 1.