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Axrl (or AX ) to obtain a probability. In pattern recognition, we deal with random vectors drawn from different classes (or categories), each of which is characterized by its own density function. This density function is called the class i density or conditional density of class i , and is expressed as p(X I 0 , ) or p,(X) ( i = l , . 6) where 0, indicates class i and L is the number of classes. The unconditional density function of X, which is sometimes called the mixture densiry function, is given by where Pi is a priori probability of class i.

40) E ( m , . }= E { y ) f pippi. 40). 38) which we want to estimate. 42) Then h Thus, taking the expectation of C E {i]= c - E { (M - M ) ( M - M ) T ) 1 =I:--E=N N-1 N c. 44) shows that C is a hiased estimate of C . emuriiu. 45) as the estimate of a covariance matrix unless otherwise stated, because of its unbiasedness. When N is large, both are practically the same. Introduction to Statistical Pattern Recognition 22 ,. Variances and covariances of cij: The variances and covariances of cij (the i, j component of are hard to commte exactly.

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 approximately 8,800 readings over a complete revolution. The magnitude of each range profile was time-sampled at 66 positions (range bins), and the resulting 66dimensional vector was normalized by energy. 4 time-sampled value, x i , was transformed to yi by y j = x i (i = 1, . . ,66). The justification of this transformation will be discussed in Chapter 3.