Page 65 - Introduction to Statistical Pattern Recognition

2 Random Vectors and their Properties 47

clusions obtained using low-dimensional data cannot be extended to high-
dimensional cases. However, running experiments with high-dimensional data
requires a large amount of memory and frequently consumes a lot of computer
time. The dimensionality of 8 is a compromise; high-dimensional phenomena can
be observed with relatively inexpensive data-handling costs.
Experimental procedure: When an experiment is called for, a number of
samples, Nj (i = 1,2), are generated according to the specified parameters. Nor-
mally Ni = 100 is selected for n=8, unless specified otherwise. Using these Nj
samples per class, the planned experiment is conducted. This process is repeated T
times. For each trial, Nj samples per class must be generated independently. Nor-
mally T=IO is used in this book, unless specified otherwise. Then, the z experi-
mental results are averaged and the standard deviation is computed.

Data RADAR: In addition to the three standard data sets mentioned above,
a set of millimeter-wave radar data is used in this book in order to test algorithms
on high-dimensional real data. Each sample is a range profile of a target observed
using a high resolution millimeter-wave radar. The samples were collected by
rotating a Chevrolet Camaro and a Dodge Van on a turntable, taking approxi-
mately 8,800 readings over a complete revolution. The magnitude of each range
profile was time-sampled at 66 positions (range bins), and the resulting 66-
dimensional vector was normalized by energy. Furthermore, each normalized
11.4
time-sampled value, xi, was transformed to yi by yj =xi (i = 1, . . . ,66). The
justification of this transformation will be discussed in Chapter 3. The vectors
were then selected at each half-degree of revolution to form 720 sample sets.
These sets (720 samples from each class) are referred to in this book as Data
RADAR. When a large number of samples is needed, 8,800 samples per class will
be used.

Computer Projects

1. Generate samples from a normal distribution specified by
n=2, N=100, .=E], and .=I;].

2. Plot the generated samples.