Information Maximization in a Linear Manifold Topographic Map

Peyman Adibi; Reza Safabakhsh

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Information Maximization in a Linear Manifold Topographic Map

机译：线性流形地形图中的信息最大化

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摘要

This article addresses the problem of unsupervised learning of multiple linear manifolds in a topology preserving neural map. The model finds simple linear estimations of the regions of the unknown data manifold. Each neuron of the map corresponds to a linear manifold whose basis and mean vectors and on- and off-manifold standard deviations must be learnt. The learning rules are derived based on competition between neurons and maximizing an approximation of the mutual information between the input and the output of each neuron. Neighborhood functions are also considered in the learning rules in order to develop the topology preserving property for the map. Considering two special density models for the input data, the optimal nonlinear input/output mappings of the neurons are found. Experimental results show a good performance for the proposed method on synthesized and practical problems compared with other relevant techniques.

机译：本文解决了在拓扑保留神经图中的多个线性流形的无监督学习问题。该模型找到未知数据流形区域的简单线性估计。映射的每个神经元都对应一个线性流形，必须学习其基础向量和均值向量以及流形上和流形外的标准差。基于神经元之间的竞争并最大化每个神经元的输入和输出之间的相互信息的近似来得出学习规则。学习规则中还考虑了邻域功能，以便为地图开发拓扑保留属性。考虑输入数据的两个特殊密度模型，找到了神经元的最佳非线性输入/输出映射。实验结果表明，与其他相关技术相比，该方法在合成和实际问题上具有良好的性能。

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来源
《Neural processing letters》 |2009年第3期|155-178|共24页
作者
Peyman Adibi; Reza Safabakhsh;
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作者单位

Computational Vision/Intelligence Laboratory, Computer Engineering Department, Amirkabir University of Technology, Tehran 15914, Iran;

Computational Vision/Intelligence Laboratory, Computer Engineering Department, Amirkabir University of Technology, Tehran 15914, Iran;

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原文格式 PDF
正文语种 eng
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关键词
neural networks; unsupervised learning; linear manifold topographic map; adaptive subspace self-organizing map; principal component analysis; information maximization; entropy;

机译：神经网络;无监督学习;线性流形地形图;自适应子空间自组织图;主成分分析信息最大化熵;

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Information Maximization in a Linear Manifold Topographic Map

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