By Theodoridis S., et al.
An accompanying handbook to Theodoridis/Koutroumbas, trend attractiveness, that comes with Matlab code of the most typical tools and algorithms within the e-book, including a descriptive precis and solved examples, and together with real-life facts units in imaging and audio attractiveness. *Matlab code and descriptive precis of the commonest tools and algorithms in Theodoridis/Koutroumbas, trend acceptance 4e.*Solved examples in Matlab, together with real-life facts units in imaging and audio recognition*Available individually or at a distinct package deal rate with the most textual content (ISBN for package deal: 978-0-12-374491-3)
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Extra info for An introduction to pattern recognition: A MATLAB approach
2], it is known that the LS criterion, when used with 0, 1 as desired response values (class labels), provides the LS estimates of the posterior probabilities; that is, if wj is the LS estimate of the parameter vector of the jth linear discriminant function, then gj (x) ≡ wTj x ≈ P(ωj |x) To verify this, compute the true a posteriori probabilities P(ωj |xi ) and their LS estimates, gj (xi ), j = 1, . . , c, i = 1, . . , N2 , on the vectors of X2 (N2 is the number of vectors in X2 ). Then compute the average square error of the estimate of the P(ωj |xi )’s using the gj (xi )’s.
001; steps=100000; eps=10ˆ(-10); method=1; for i=1:c [alpha(:,i), w0(i), w(i,:), evals, stp, glob] =... SMO2(X1', z1(i,:)', kernel, kpar1, kpar2, C,... 00%. 33%. 5 SVM: THE NONLINEAR CASE To employ the SVM technique for solving a nonlinear classification task, we adopt the philosophy of mapping the feature vectors in a higher-dimensional space, where we expect, with high probability, the classes to be linearly separable. 13]. The mapping is as follows: x → φ(x) ∈ H where the dimension of H is higher than Rl and, depending on the choice of the (nonlinear) φ(·), can even be infinite.
2. Based on X1 , estimate the parameter vectors w1, w2 , w3 of the three linear discriminant functions using the first modification of Platt’s algorithm [Keer 01] (SVM classifiers). Estimate the classification error rate based on X2 . Solution. Proceed as follows: Step 1. 3. To plot X1 , type figure(1), plot3(X1(1,z1(1,:)==1),X1(2,z1(1,:)==1),... ',X1(1,z1(2,:)==1),X1(2,z1(2,:)==1),... X1(3,z1(2,:)==1),'gx',X1(1,z1(3,:)==1),X1(2,z1(3,:)==1),... X1(3,z1(3,:)==1),'bo') Step 2. 3, but now the 0 elements are replaced by −1.
An introduction to pattern recognition: A MATLAB approach by Theodoridis S., et al.