Otsu, N., "Nonlinear discriminant analysis as a natural extension of the linear case," Behaviormetrika, 2, 45-59 (1975). Home/Search Document Not in Database Summary Related Articles Check |
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Learning from Examples, Agent Teams and the Concept of Reflection - Beyer, Smieja (1993) (2 citations) (Correct)
....s 5 s 6 y = s 1 s 2 s 3 s 4 s 5 s 6 ) hidden units Figure 6: Operation of a feed forward neural network. 8 Beyer and Smieja 4.3. 2 Example 2: Feed forward neural network A feed forward neural network with real output nodes naturally produces confidences for a classification task [7, 16]. The confidence is simply formed by extending the discrete class answer to a set of relative probabilities between classes. Thus if a neural network agent produces an output vector s(x) see Figure 6) the confidence c k (x) for the class k is given by: c k (x) s k (x) P i s i (x) 12) For ....
N. Otsu. Nonlinear discriminant analysis as a natural extension of the linear case. Behaviormetrika, (2):24--59, 1975.
Toward Flexible Information Processing in the Real World - Nobuyuki Otsu.. (1994) (1 citation) Self-citation (Otsu) (Correct)
....denotes the transpose) is given by the eigenvectors of the matrix W Gamma1 X BX of x. This is the result of the ordinary discriminant analysis. On the other hand, the optimum nonlinear discriminant feature extraction Psi N is obtained by the variational calculus as the same form as in Eq. 4)[5], but in this the class representative vectors fe j g are obtained from the eigenvectors of the following K by K stochastic matrix S which summarizes the between class probabilistic relations. S = s ij ] s ij = Z P (C j jx)p(xjC i ) dx (10) It is noted that s ij can be rewritten as follows ....
Otsu, N., "Nonlinear discriminant analysis as a natural extension of the linear case," Behaviormetrika, 2, 45-59 (1975).
Nonlinear Discriminant Features Constructed by Using.. - Kurita, Asoh, Otsu (1994) (1 citation) Self-citation (Otsu) (Correct)
....relative to the between class scatter. LDA is useful for linear separable problems, but for more complicated problems, it is necessary to extend it to nonlinear. Otsu has already showed Nonlinear Discriminant Analysis (NDA) can be solved if we can estimate Bayesian a posteriori probabilities[9, 10]. The optimal nonlinear discriminant mapping has close relationship to Bayes s decision theory. The theory was extended to Nonlinear Canonical Correlation Analysis [12] 1 Proc. of ISSIPNN 94: 1994 International Symposium on Speech, Image Processing Neural Networks, 13 16 April 1994, Hong Kong, ....
....of each elements of the new features y are evaluated by the corresponding eigenvalues. The maximum number M is bounded by min(K 0 1; N ) 2. 2 Nonlinear Discriminant Analysis Otsu showed that LDA can be extended to nonlinear if we can know or estimate Bayesian a posteriori probabilities [9]. Nonlinear Discriminant Analysis (NDA) constructs a dimension reduction nonlinear mapping which maximizes the discriminant criterion J . The optimal nonlinear discriminant mapping is given by y = K X k=1 p(C k jx)u k (5) where x is input feature vector, p(C i jx) is the Bayesian a posteriori ....
N. Otsu, (1975). Nonlinear discriminant analysis as a natural extension of the linear case. Behavior Metrica, 2:45--59.
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