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To illustrate the general EM algorithm, let us use it to derive the algorithm given in Section 6121 for estimating the means of a mixture of k Normal distributions As discussed above, the k-means problem is to estimate the parameters 0 = ( P I p k ) that define the means of the k Normal distributions We are given the observed The hidden variables Z = { ( z i l , , z i k ) }in this case indicate data X = { ( x i ) } which of the k Normal distributions was used to generate xi To apply EM we must derive an expression for Q ( h ( h f )that applies to our k-means problem First, let us derive an expression for 1np(Y(h1) Note the ) probability p(yi (h') of a single instance yi = ( x i ,Z i l , ~ i k of the full data can be written

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click the Choose button Name the project C Main Project (Figure 2-1)

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At minimal levels of compression, around 7:1 or less for today s encoders and even less for future encoders, perceptual encoding removes only the imperceptible information and provides decoded audio that is virtually indistinguishable from the original At higher levels of compression, and depending on the nature of the audio, bit starvation may produce identifiable effects of compression These include a slightly harsh or gritty sound, poor reproduction of transients, loss of detail, and less pronounced separation and spaciousness Both Dolby Digital and MPEG-2 audio on DVD are usually compressed at a factor of about 10:1 Most tests place the quality of Dolby Digital and MPEG-2 audio neck and neck, just short of sounding as good as the original uncompressed source These tests have shown that the audio quality is completely acceptable to average listeners, many of whom are unable to tell the difference between Dolby Digital and the original uncompressed PCM source DTS on DVD is usually compressed at a factor of 6:1 or 3:1 Many listeners claim that DTS audio quality is better than Dolby Digital, but such claims are rarely based on accurate comparisons DTS tracks are usually encoded at a reference volume level that is 4 decibels higher, and most DTS soundtracks are mixed differently than their Dolby Digital counterparts, including different volume levels in the surround and LFE tracks This makes it nigh impossible to compare them objectively, even using a disc that contains a soundtrack in both formats The limited semiscientific comparisons that have been done indicate that there is little perceptible difference between the two and that any difference is noticeable only on high-end audio systems

message for you (Listing 2-1) Click Build And Go, and review the Debugger Console s logging Listing 2-1 The main method in a C program

To verify this note that only one of the zij can have the value 1, and all others must be 0 Therefore, this expression gives the probability distribution for xi generated by the selected Normal distribution Given this probability for a single instance p(yi(hl), the logarithm of the probability In P(Y(hl) for all m instances in the data is

#include <stdioh> int main (int argc, const char * argv[]) { // insert code here printf("Hello, World!\n"); return 0; }

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