By Sergios Theodoridis
ISBN-10: 1597492728
ISBN-13: 9781597492720
This e-book considers classical and present idea and perform, of supervised, unsupervised and semi-supervised trend attractiveness, to construct an entire history for execs and scholars of engineering. The authors, major specialists within the box of trend reputation, have supplied an up to date, self-contained quantity encapsulating this extensive spectrum of data. The very most up-to-date tools are integrated during this version: semi-supervised studying, combining clustering algorithms, and relevance suggestions. completely built to incorporate many extra labored examples to offer better knowing of a few of the tools and methods Many extra diagrams included--now in color--to supply better perception via visible presentation Matlab code of the commonest tools are given on the finish of every bankruptcy An accompanying e-book with Matlab code of the most typical equipment and algorithms within the publication, including a descriptive precis and solved examples, and together with real-life info units in imaging and audio reputation. The significant other ebook is offered individually or at a unique packaged rate (Book ISBN: 9780123744869. package deal ISBN: 9780123744913) newest scorching issues incorporated to extra the reference price of the textual content together with non-linear dimensionality aid innovations, relevance suggestions, semi-supervised studying, spectral clustering, combining clustering algorithms options handbook, powerpoint slides, and extra assets can be found to college utilizing the textual content for his or her direction. sign up at www.textbooks.elsevier.com and seek on "Theodoridis" to entry assets for teacher.
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Extra resources for Pattern Recognition, Fourth Edition
Sample text
X N be random samples drawn from pdf p(x; ). We form the joint pdf p(X; ), where X ϭ {x 1 , . . , x N } is the set of the samples. Assuming statistical independence between the different samples, we have N p(X; ) ≡ p(x 1 , x 2 , . . 55) kϭ1 This is a function of , and it is also known as the likelihood function of with respect to X. 14 illustrates the method for the single unknown parameter case. The ML estimate corresponds to the peak of the log-likelihood function. Maximum likelihood estimation has some very desirable properties.
8 and N ϭ 20000 samples. Large values of h lead to smooth estimates, but the approximation accuracy is low (the estimate is highly biased), as one can observe by comparing (a) with (d). For small values of h, the estimate is more noisy in appearance, but it becomes smoother as the number of samples increases, (b) and (c). The smaller the h and the larger the N , the better the approximation accuracy. 5 Estimation of Unknown Probability Density Functions Remarks ■ In practice, where only a finite number of samples is possible, a compromise between h and N must be made.
Thus, the decision surface is a hyperplane passing through the point x 0 . Obviously, if P(i ) ϭ P(j ), then x 0 ϭ 12 (i ϩ j ), and the hyperplane passes through the average of i , j , that is, the middle point of the segment joining the mean values. On the other hand, if P(j ) Ͼ P(i ) (P(i ) Ͼ P(j )) the hyperplane is located closer to i (j ). In other words, the area of the region where we decide in favor of the more probable of the two classes is increased. 10 for the two-dimensional case and for two cases, that is, P(j ) ϭ P(i ) (black line) and P(j ) Ͼ P(i ) (red line).