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184                                                         Appendix

           Figure 1-21  Relationship between the crisp value and fuzzy membership

                       for   the  input   variable   Y in the example
           Figure 1-22  Relationship between the crisp value and fuzzy membership
                       for   the  input   variable  Z in the example

           Figure 1-23  Defuzzification in the example
           Figure 1-24  Illustration of Ant colony
           Figure 1-25  Matrix A (Ant colony)
           Figure 1-26  Matrix B (Ant colony)
           Figure 1-27  Iteration (vs)  Best cost selected by the 4 ants
           Figure 2-1  Clustering example with four clusters
           Figure 2-2  Illustration of K-means algorithm
           Figure 2-3  Data along with the final centroids obtained by k-means
                       algorithm
           Figure 2-4  Illustration of Fuzzy k-means algorithm
           Figure 2-5  Data and the final centroids obtained using Fuzzy k-means
                       algorithm
           Figure 2-6  Illustration of change in the membership value in every
                       iteration
           Figure 2-7  Illustration of Mean and Variance Normalization of the
                       speech signal

           Figure 3-1  Hotelling transformation for binary image rotation
           Figure 3-2  Vector space along with Eigen vectors
           Figure 3-3  Vector space after KLT and the corresponding eigen vectors
           Figure 3-4  Projection Illustration
           Figure 3-5  Projection of the vector on the plane
           Figure 3-6  Gram-Schmidt Orthogonalization procedure
           Figure 3-7  Original signal used for Haar decomposition
           Figure 3-8  Approximation co-efficients obtained using Haar
                       transformation
           Figure 3-9  Detail co-efficients obtained using Haar transformation
           Figure 3-10  Illustration of Inverse Haar  transformation
           Figure 3-11  Original signal used for Daubechies 4 wavelet
                       decomposition
           Figure 3-12  Approximation co-efficients at different levels
           Figure 3-13  Detail co-efficients at different levels
           Figure 3-14  Illustration of Inverse Daubechies 4 transformation
           Figure 4-1  Sample Ear images before and after
                       normalization
           Figure 4-2  Eigen Ears corresponding to the largest
                       Eigen values
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