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A constructive algorithm to solve "convex recursive deletion" (CoRD) classification problems via two-layer perceptron
C Cabrelli1, U Molter, R Shonkwiler
1Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, 1428 Argentina.
IEEE Transactions on Neural Networks
|February 6, 2008
Summary
This study identifies convex recursive deletion (CoRD) regions as classifiable by two-layer neural networks. A simple algorithm is presented for constructing these networks, offering an alternative to backpropagation for specific decision regions.
Area of Science:
- Computational Mathematics
- Artificial Intelligence
- Machine Learning
Background:
- Two-layer feedforward neural networks, or two-layer perceptrons, classify regions using threshold activation functions.
- Understanding the geometric properties of these decision regions is crucial for network design and analysis.
Purpose of the Study:
- To establish a sufficient condition for region classifiability by two-layer perceptrons.
- To develop a direct algorithm for constructing such perceptrons.
- To explore the implications for three-layer networks and the efficiency of training.
Main Methods:
- Definition of convex recursive deletion (CoRD) regions.
- Development of a direct algorithm to compute weights and thresholds for a two-layer perceptron implementing a CoRD region.
- Extension of the construction to disjoint unions of CoRD regions for three-layer networks.
Main Results:
- Identified convex polytopes and their complements' intersections as classifiable by two-layer perceptrons (CoRD regions).
- Presented a simple algorithm for direct construction of weights and thresholds.
- Demonstrated that disjoint unions of CoRD regions can be implemented by three-layer networks.
Conclusions:
- The geometric characterization of decision regions provides insights into perceptron capabilities.
- The direct construction algorithm offers a rapid, non-iterative method for designing perceptrons for CoRD regions, bypassing extensive backpropagation.
- This work informs the understanding of network architecture and neuron requirements in deeper networks.
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