Linear manifold topographic map formation based on an energy function with on-line adaptation rules

Authors:
Peyman Adibi;Reza Safabakhsh
Affiliations:
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
Venue:
Neurocomputing
Year:
2009

Citing 20
Cited 3

Original Contribution: Least mean square error reconstruction principle for self-organizing neural-nets

Neural Networks
Self-organization as an iterative kernel smoothing process

Neural Computation
Principal component neural networks: theory and applications

Principal component neural networks: theory and applications
Local models and Gaussian mixture models for statistical data processing

Local models and Gaussian mixture models for statistical data processing
Self-organized formation of various invariant-feature filters in the adaptive-subspace SOM

Neural Computation
Dimension reduction by local principal component analysis

Neural Computation
A Hierarchical Latent Variable Model for Data Visualization

IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear component analysis as a kernel eigenvalue problem

Neural Computation
A view of the EM algorithm that justifies incremental, sparse, and other variants

Learning in graphical models
Mixtures of probabilistic principal component analyzers

Neural Computation
Hierarchical GTM: Constructing Localized Nonlinear Projection Manifolds in a Principled Way

IEEE Transactions on Pattern Analysis and Machine Intelligence
Self-Organizing Maps

Self-Organizing Maps
Laplacian Eigenmaps for dimensionality reduction and data representation

Neural Computation
Principal components analysis competitive learning

Neural Computation
Maximum Likelihood Topographic Map Formation

Neural Computation
On convergence properties of the em algorithm for gaussian mixtures

Neural Computation
Optimally adaptive transform coding

IEEE Transactions on Image Processing
Modeling the manifolds of images of handwritten digits

IEEE Transactions on Neural Networks
Handwritten digit recognition by adaptive-subspace self-organizing map (ASSOM)

IEEE Transactions on Neural Networks
Self-organizing maps, vector quantization, and mixture modeling

IEEE Transactions on Neural Networks

Information Maximization in a Linear Manifold Topographic Map

Neural Processing Letters
Batch linear manifold topographic map with regional dimensionality estimation

IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Invariant feature set generation with the linear manifold self-organizing map

ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part IV

Quantified Score

Hi-index	0.01

Visualization

Abstract

The lack of an energy function is an important problem in many topographic map formation methods. This paper describes formation of a map, called linear manifold topographic map, based on minimization of an energy function. Using multiple low-dimensional linear manifolds as data representation elements, the data distributions of many problems with high-dimensional data spaces can be simply and parsimoniously modeled. Two sets of on-line adaptation rules are obtained based on stochastic gradient descent on the energy functions devised for a soft and a hard data assignment. Experimental results show good performance of the map in comparison to other relevant techniques.