By Theodoridis S., et al.
An accompanying guide to Theodoridis/Koutroumbas, development popularity, that comes with Matlab code of the commonest tools and algorithms within the publication, including a descriptive precis and solved examples, and together with real-life facts units in imaging and audio acceptance. *Matlab code and descriptive precis of the most typical tools and algorithms in Theodoridis/Koutroumbas, trend reputation 4e.*Solved examples in Matlab, together with real-life facts 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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Additional info for An introduction to pattern recognition: A MATLAB approach
14) i=1 From the previous relation, it becomes clear that the explicit form of the mapping function φ(·) is not required; all we have to know is the kernel function since data appear only in inner products. Observe that the resulting discriminant function, g(x), is nonlinear because of the nonlinearity of the kernel function. 4, may be used. The input argument kernel takes the values poly for the polynomial kernel or rbf for the RBF kernel. In the former case, kpar1 and kpar2 correspond to the β and n parameters, respectively; in the latter case, kpar1 corresponds to the σ parameter.
Note that this is very low, indicating a good estimate. Step 3. 4 Support Vector Machines: The Linear Case 43 Alternatively, use the bayes_classifier MATLAB function. 82% (estimated based on X2 ). Some comments are in order. First, it is easy to check that the probability estimates may be greater than 1 or less than 0. , nonnegativity and sum to 1). However, the sum of the estimates of the a posteriori probabilities for a given vector is very close to 1. 1 1. 3 where now the means of the three classes ω1 , ω2 , and ω3 are m1 = [0, 0, 0]T , m2 = [1, 2, 2]T , and m3 = [3, 3, 4]T , respectively.
Repeat the previous steps, first with X2 replaced by a set X3 containing N3 = 10,000 data vectors and then with a set X4 containing N4 = 100,000 data vectors. Both X3 and X4 are generated using the prescription adopted for X1 . Comment on the results. Solution. Do the following: Step 1. To ensure reproducibility of the results, set seed = 0 for the randn MATLAB function for the generation of X1 ; for the generation of X2 , X3 , and X4 set seed = 100. 75]; P=[1/2 1/2]; To generate X1 and the required class labels (1 for ω1 , 2 for ω2 ), type N1=200; randn('seed',0) X1=[mvnrnd(m(:,1),S,fix(N1/2)); mvnrnd(m(:,2),S,N1-fix(N1/2))]'; z1=[ones(1,fix(N1/2)) 2*ones(1,N1-fix(N1/2))]; X2 is generated in a similar fashion.