Download An introduction to pattern recognition: A MATLAB approach by Theodoridis S., et al. PDF

By Theodoridis S., et al.

An accompanying guide to Theodoridis/Koutroumbas, development popularity, that incorporates Matlab code of the most typical equipment and algorithms within the e-book, including a descriptive precis and solved examples, and together with real-life info units in imaging and audio acceptance. *Matlab code and descriptive precis of the commonest equipment and algorithms in Theodoridis/Koutroumbas, trend acceptance 4e.*Solved examples in Matlab, together with real-life info units in imaging and audio recognition*Available individually or at a different package deal cost with the most textual content (ISBN for package deal: 978-0-12-374491-3)

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Example text

2 THE PERCEPTRON ALGORITHM The perceptron algorithm is appropriate for the 2-class problem and for classes that are linearly separable. 1(b,c) shows two cases of classes that are not linearly separable. The perceptron algorithm computes the values of the weights w of a linear classifier, which separates the two classes. The algorithm is iterative. It starts with an initial estimate in the extended (l + 1)-dimensional space and converges to a solution in a finite number of iteration steps. The solution w correctly classifies all the training points (assuming, of course, that they stem from linearly separable classes).

3 Line and its margin of size 2d. 4 Two linear classifiers and the associated margin lines for a 2-class classification problem (filled circles correspond to class +1; empty circles correspond to class −1). hyperplanes do not change. The same applies to the hyperplane described by Eq. 6). Normalization by a constant value d has no effect on the points that lie on (and define) a hyperplane. So far, we have considered that an error is “committed” by a point if it is on the wrong side of the decision surface formed by the respective classifier.

2) i=1 where yi is the known class label of xi , i = 1, 2, . , N ; and N is the number of training points. Define ⎡ T⎤ ⎡ ⎤ x1 y1 ⎢ T⎥ ⎢ y2 ⎥ ⎢x2 ⎥ ⎢ ⎥ ⎥ X =⎢ . ⎥ ⎢.. ⎥, y = ⎢ ⎣ .. ⎦ ⎣. 3]. A significant advantage of the LS method is that it has a single solution (corresponding to the single minimum of J(w)). In addition, this is obtained by solving a linear system of equations (Eq. 3)). In practice, the inversion of the (l + 1) × (l + 1) matrix, X T X, may pose some numerical difficulties, especially in high-dimensional spaces.

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