By Gustavo Deco, Dragan Obradovic
Neural networks offer a robust new expertise to version and keep an eye on nonlinear and complicated platforms. during this ebook, the authors current a close formula of neural networks from the information-theoretic point of view. They convey how this angle presents new insights into the layout concept of neural networks. particularly they exhibit how those equipment can be utilized to the themes of supervised and unsupervised studying together with function extraction, linear and non-linear self sustaining part research, and Boltzmann machines. Readers are assumed to have a uncomplicated knowing of neural networks, yet all of the suitable strategies from info conception are conscientiously brought and defined. as a result, readers from numerous diverse medical disciplines, significantly cognitive scientists, engineers, physicists, statisticians, and desktop scientists, will locate this to be a really invaluable creation to this topic.
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Extra info for An Information-Theoretic Approach to Neural Computing
The next section presents an alternative derivation of PC A as the optimal linear compression method. 2 peA and Optimal Reconstruction This section focuses on reconstruction properties of PCA. 13) x where W is a M x N full-row-rank matrix and and y are the Nand M dimensional vectors respectively with N;Z M. Furthermore, let us assume that the covariance matrix of y is nonsingular. The problem is to find a N x M dimensional reconstruction matrix U which minimizes the Least Mean Square Reconstruction Error (LSE).
The information theory based approaches can be formulated in two different ways by modeling one of the two tasks associated with PCA: optimal compression or decorrelation of the output components. 10)) is based on the Infomax principle. The Infomax principle and its neural network implementation are discussed in details in this chapter. e. data compression, corresponds to maximizing the transmission of information between the input and output of the transformation. 12)), is based on redundancy reduction of the output components and is discussed in Chapter 4.
Its first M rows form an upper triangular matrix above the main diagonal while its remaining N - M rows contain elements equal to zero. e. 25) is a N x N -matrix with k = N - I if M = N or k = M if M < N. The rotation matrix KT. 26) M S .. 27) Sjj+Sij (K i , J')'. 28) (Ki'JJ J')'. 31) with P being a N x M -matrix built with columns identical to the first M columns of K and R being the upper triangular part of R. The matrix R is a M x M -matrix of rankeR) = M and thus is invertible. 23) follow immediately.
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