tailieunhanh - COMPUTER-AIDED INTELLIGENT RECOGNITION TECHNIQUES AND APPLICATIONS phần 5

Cả hai phương pháp thử để đảm bảo rằng các mục được chọn nằm trong các cạnh lớp học, thử nghiệm nó sẽ tự động bằng cách phân loại k-NN. Phương pháp (4) là k có nghĩa là phân nhóm [23], cũng được sử dụng rộng rãi cho LVQ khởi tạo [28,29] và có được nguyên mẫu bằng cách phân cụm dữ liệu huấn luyện của mỗi lớp | Linear Subspace Techniques 187 Figure The first six eigenfaces. Figure Recognition accuracy with PCA. where Sb is the between-class scatter matrix and Sw is the within-class scatter matrix defined as Sw pF Si Sb Y p c i - rifai - m t where c is the number of classes c 15 and P Ci is the probability of class i. Here P Ci 1 c since all classes are equally probable. 188 Pose-invariant Face Recognition Si is the class-dependent scatter matrix and is defined as Si Nt E xk - Ai Xk - Mi T i 1 . c N xkeXi One method for solving the generalized eigenproblem is to take the inverse of Sw and solve the following eigenproblem for matrix Sw 1Sb S 1SbW WA where A is the diagonal matrix containing the eigenvalues of Sw1Sb. But this problem is numerically unstable as it involves direct inversion of a very large matrix which is probably close to singular. One method for solving the generalized eigenvalue problem is to simultaneously diagonalize both Sw and Sb 21 WTSwW I WTSb W A The algorithm can be outlined as follows 1. Find the eigenvectors of PTPb corresponding to the largest K nonzero eigenvalues Vc K ej e2. . . eK where Pb of size n X c Sb PbPT . 2. Deduce the first K most significant eigenvectors and eigenvalues of Sb Y PbV Db YTSbY YTPb PbTY 3. Let Z YD-1 2 which projects Sb and Sw onto a subspace spanned by Z this results in I and ZTSwZ 4. We then diagonalize ZTSwZ which is a small matrix of size K X K UTZTSwZU Aw 5. We discard the large eigenvalues and keep the smallest r eigenvalues including the 0 s. The corresponding eigenvector matrix becomes R k X r . 6. The overall LDA transformation matrix becomes W ZR. Notice that we have diagonalized both the numerator and the denominator in the Fisher criterion. Experimental Results We have also performed a leave one out experiment on the Yale faces database 20 . The first six Fisher faces are shown in Figure . The eigenvalue spectrum of .