By Gustavo Deco, Dragan Obradovic
Neural networks supply a robust new expertise to version and keep watch over nonlinear and complicated platforms. during this ebook, the authors current an in depth formula of neural networks from the information-theoretic standpoint. They exhibit how this attitude presents new insights into the layout idea of neural networks. particularly they convey how those tools should be utilized to the subjects of supervised and unsupervised studying together with characteristic extraction, linear and non-linear autonomous part research, and Boltzmann machines. Readers are assumed to have a simple knowing of neural networks, yet all of the appropriate innovations from details thought are rigorously brought and defined. for this reason, readers from numerous assorted medical disciplines, significantly cognitive scientists, engineers, physicists, statisticians, and machine scientists, will locate this to be a truly worthwhile creation to this topic.
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Extra info for An Information-Theoretic Approach to Neural Computing
Zero-mean. The first property is the diagonalization of the covariance matrix by constructing its orthonormal basis. Hence, PCA essentially performs Singular Value Decomposition of the covariance matrix, and in the Gaussian distributed input case, linearly extracts statistically independent features. e data compression, in the least-squared-error sense is achieved by projecting on the space spanned by the appropriate number of principal components. Several neural algorithms implemented in linear single-layer feedforward networks are presented and explained herein.
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. This completes the proof. o The following theorem defines the optimal reconstruction. 2: Least-Squared-Error reconstruction The reconstruction error LSE is minimal when the rows of Ware vectors spanning the same subspace as the M eigenvectors of the input covariance matrix corresponding to the M largest eigenvalues.
16]) are added to the cost function as extra terms in order to directly penalize the network complexity. The so called "stopped training" method consists of continuously monitoring the effect of learning on a separate "validation" data set. The learning is stopped when the performance of the network on the validation data begins to deteriorate. Different statistical approaches to the problem of network complexity are discussed in chapters 7 to 10. There is an extensive literature on recurrent networks, notably on recurrent multilayer perceptrons.