A constructive algorithm to solve "Convex Recursive Deletion" (CoRD) classification problems via two-layer perceptron networks

A sufficient condition that a region be classifiable by a two-layer feedforward neural net (a two-layer perceptron) using threshold activation functions is that either it be a convex polytope or that intersected with the complement of a convex polytope in its interior, or that intersected with the c...

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Autores principales: Cabrelli, C., Molter, U., Shonkwiler, R.
Formato: JOUR
Materias:
Convex recursive deletion region
Neural network
Two-layer perceptron
Algorithms
Backpropagation
Computational geometry
Matrix algebra
Multilayer neural networks
Optimization
Theorem proving
Vectors
Two layer perceptron
Feedforward neural networks
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_10459227_v11_n3_p811_Cabrelli
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_10459227_v11_n3_p811_Cabrelli2023-10-03T15:58:24Z A constructive algorithm to solve "Convex Recursive Deletion" (CoRD) classification problems via two-layer perceptron networks Cabrelli, C. Molter, U. Shonkwiler, R. Convex recursive deletion region Neural network Two-layer perceptron Algorithms Backpropagation Computational geometry Matrix algebra Multilayer neural networks Optimization Theorem proving Vectors Convex recursive deletion region Two layer perceptron Feedforward neural networks A sufficient condition that a region be classifiable by a two-layer feedforward neural net (a two-layer perceptron) using threshold activation functions is that either it be a convex polytope or that intersected with the complement of a convex polytope in its interior, or that intersected with the complement of a convex polytope in its interior or . . . recursively. These have been called convex recursive deletion (CoRD) regions. We give a simple algorithm for finding the weights and thresholds in both layers for a feedforward net that implements such a region. The results of this work help in understanding the relationship between the decision region of a perceptron and its corresponding geometry in input space. Our construction extends in a simple way to the case that the decision region is the disjoint union of CoRD regions (requiring three layers). Therefore this work also helps in understanding how many neurons are needed in the second layer of a general three-layer network. In the event that the decision region of a network is known and is the union of CoRD regions, our results enable the calculation of the weights and thresholds of the implementing network directly and rapidly without the need for thousands of backpropagation iterations. © 2000 IEEE. Fil:Cabrelli, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Molter, U. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10459227_v11_n3_p811_Cabrelli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Convex recursive deletion region
Neural network
Two-layer perceptron
Algorithms
Backpropagation
Computational geometry
Matrix algebra
Multilayer neural networks
Optimization
Theorem proving
Vectors
Convex recursive deletion region
Two layer perceptron
Feedforward neural networks
spellingShingle Convex recursive deletion region
Neural network
Two-layer perceptron
Algorithms
Backpropagation
Computational geometry
Matrix algebra
Multilayer neural networks
Optimization
Theorem proving
Vectors
Convex recursive deletion region
Two layer perceptron
Feedforward neural networks
Cabrelli, C.
Molter, U.
Shonkwiler, R.
A constructive algorithm to solve "Convex Recursive Deletion" (CoRD) classification problems via two-layer perceptron networks
topic_facet Convex recursive deletion region
Neural network
Two-layer perceptron
Algorithms
Backpropagation
Computational geometry
Matrix algebra
Multilayer neural networks
Optimization
Theorem proving
Vectors
Convex recursive deletion region
Two layer perceptron
Feedforward neural networks
description A sufficient condition that a region be classifiable by a two-layer feedforward neural net (a two-layer perceptron) using threshold activation functions is that either it be a convex polytope or that intersected with the complement of a convex polytope in its interior, or that intersected with the complement of a convex polytope in its interior or . . . recursively. These have been called convex recursive deletion (CoRD) regions. We give a simple algorithm for finding the weights and thresholds in both layers for a feedforward net that implements such a region. The results of this work help in understanding the relationship between the decision region of a perceptron and its corresponding geometry in input space. Our construction extends in a simple way to the case that the decision region is the disjoint union of CoRD regions (requiring three layers). Therefore this work also helps in understanding how many neurons are needed in the second layer of a general three-layer network. In the event that the decision region of a network is known and is the union of CoRD regions, our results enable the calculation of the weights and thresholds of the implementing network directly and rapidly without the need for thousands of backpropagation iterations. © 2000 IEEE.
format JOUR
author Cabrelli, C.
Molter, U.
Shonkwiler, R.
author_facet Cabrelli, C.
Molter, U.
Shonkwiler, R.
author_sort Cabrelli, C.
title A constructive algorithm to solve "Convex Recursive Deletion" (CoRD) classification problems via two-layer perceptron networks
title_short A constructive algorithm to solve "Convex Recursive Deletion" (CoRD) classification problems via two-layer perceptron networks
title_full A constructive algorithm to solve "Convex Recursive Deletion" (CoRD) classification problems via two-layer perceptron networks
title_fullStr A constructive algorithm to solve "Convex Recursive Deletion" (CoRD) classification problems via two-layer perceptron networks
title_full_unstemmed A constructive algorithm to solve "Convex Recursive Deletion" (CoRD) classification problems via two-layer perceptron networks
title_sort constructive algorithm to solve "convex recursive deletion" (cord) classification problems via two-layer perceptron networks
url http://hdl.handle.net/20.500.12110/paper_10459227_v11_n3_p811_Cabrelli
work_keys_str_mv AT cabrellic aconstructivealgorithmtosolveconvexrecursivedeletioncordclassificationproblemsviatwolayerperceptronnetworks
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AT shonkwilerr aconstructivealgorithmtosolveconvexrecursivedeletioncordclassificationproblemsviatwolayerperceptronnetworks
AT cabrellic constructivealgorithmtosolveconvexrecursivedeletioncordclassificationproblemsviatwolayerperceptronnetworks
AT molteru constructivealgorithmtosolveconvexrecursivedeletioncordclassificationproblemsviatwolayerperceptronnetworks
AT shonkwilerr constructivealgorithmtosolveconvexrecursivedeletioncordclassificationproblemsviatwolayerperceptronnetworks
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