Hierarchical Polytope ARTMAP for Supervised Learning

The recent Polytope ARTMAP（PTAM） suggests that irregular polytopes are more flexible than the predefined category geometries to approximate the borders among the desired output predictions.However,category expansion and adjustment steps without statistical information make PTAM not robust to noise a...

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Bibliographic Details
Published in:Journal of computer science and technology 2010-09, Vol.25 (5), p.1071-1082
Main Author: 廖鑫鹏 吴永强 韩崇昭
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Artificial Intelligence
ARTMAP
Borders
Categories
Computer Science
Data Structures and Information Theory
Error detection
Hypotheses
Information Systems Applications (incl.Internet)
Learning
Mathematical analysis
Noise
Outliers (statistics)
Polytopes
Regular Paper
Software Engineering
Supervised learning
Theory of Computation
多面体
监督学习
结构风险最小化
调整步骤
逼近误差
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Summary:The recent Polytope ARTMAP（PTAM） suggests that irregular polytopes are more flexible than the predefined category geometries to approximate the borders among the desired output predictions.However,category expansion and adjustment steps without statistical information make PTAM not robust to noise and category overlap.In order to push the learning problem towards Structural Risk Minimization（SRM）,this paper proposes Hierarchical Polytope ARTMAP （HPTAM） to use a hierarchical structure with different levels,which are determined by the complexity of regions incorporating the input pattern.Besides,overlapping of simplexes from the same desired prediction is designed to reduce category proliferation.Although HPTAM is still inevitably sensible to noisy outliers in the presence of noise,main experimental results show that HPTAM can achieve a balance between representation error and approximation error,which ameliorates the overall generalization capabilities.
ISSN:1000-9000
1860-4749
DOI:10.1007/s11390-010-9388-z