This paper presents two methods for generating numerical codes representing clusters of R-n, while preserving various topological properties of data spaces. This is useful for networks whose input, or eventually outpu...
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This paper presents two methods for generating numerical codes representing clusters of R-n, while preserving various topological properties of data spaces. This is useful for networks whose input, or eventually output, consists of unordered sets of points. The first method is the best one from a theoretical point of view, while the second one is more usable for large clusters in practice. (C) 2001 Elsevier Science Ltd. All rights reserved.
This paper shows a method to represent a multiple-output function: Encoded characteristic function for non-zero poutputs (ECFN). The ECFN uses (n + u) binary variables to represent an n-input m-output function, where ...
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ISBN:
(纸本)0769510833
This paper shows a method to represent a multiple-output function: Encoded characteristic function for non-zero poutputs (ECFN). The ECFN uses (n + u) binary variables to represent an n-input m-output function, where u = [log(2) m]. The size of the sum-of-products expressions (SOPs) depends on the encoding method of the outputs. For some class of functions, the optimal encoding produces SOPs with O(n) products, while the worst encoding produces SOPs with O(2(n)) products. We formulate encoding problem and show a heuristic optimization method. Experimental results using standard benchmark functions show the usefulness of the method.
The encoding problem (Rumelhart and McClelland 1986) is an important canonical problem. It has been widely used as a benchmark. Here, we have analytically derived minimal-sized nets necessary and sufficient to solve e...
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The encoding problem (Rumelhart and McClelland 1986) is an important canonical problem. It has been widely used as a benchmark. Here, we have analytically derived minimal-sized nets necessary and sufficient to solve encoding problems of arbitrary size. The proofs are constructive: we construct n-2-n encoders and show that two hidden units are also necessary for n > 2. Moreover, the geometric approach employed is general and has much wider applications. For example, this method has also helped us derive lower bounds on the redundancy necessary for achieving complete fault tolerance (Phatak and Koren 1992a,b).
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