Limited Rank Matrix Learning, discriminative dimension reduction and visualization

We present an extension of the recently introduced Generalized Matrix Learning Vector Quantization algorithm. In the original scheme, adaptive square matrices of relevance factors parameterize a discriminative distance measure. We extend the scheme to matrices of limited rank corresponding to low-di...

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Bibliographic Details
Published in:Neural networks Vol. 26; pp. 159 - 173
Main Authors: Bunte, Kerstin, Schneider, Petra, Hammer, Barbara, Schleif, Frank-Michael, Villmann, Thomas, Biehl, Michael
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.02.2012
Elsevier
Subjects:
Adaptive metrics
Algorithms
Applied sciences
Artificial Intelligence
Classification
Computer science; control theory; systems
Data processing. List processing. Character string processing
Dimension reduction
Discriminant Analysis
Exact sciences and technology
Humans
Learning
Learning Vector Quantization
Memory organisation. Data processing
Pattern Recognition, Automated
Software
Visualization
Visualization
Dimension reduction
Learning Vector Quantization
Adaptive metrics
Classification
Cluster analysis
Vector quantization
Adaptive method
Relevance
Three dimensional representation
Supervised learning
Metric
Learning algorithm
Artificial intelligence
ISSN:0893-6080, 1879-2782, 1879-2782
Online Access:Get full text
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Summary:We present an extension of the recently introduced Generalized Matrix Learning Vector Quantization algorithm. In the original scheme, adaptive square matrices of relevance factors parameterize a discriminative distance measure. We extend the scheme to matrices of limited rank corresponding to low-dimensional representations of the data. This allows to incorporate prior knowledge of the intrinsic dimension and to reduce the number of adaptive parameters efficiently. In particular, for very large dimensional data, the limitation of the rank can reduce computation time and memory requirements significantly. Furthermore, two- or three-dimensional representations constitute an efficient visualization method for labeled data sets. The identification of a suitable projection is not treated as a pre-processing step but as an integral part of the supervised training. Several real world data sets serve as an illustration and demonstrate the usefulness of the suggested method.
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ISSN:0893-6080
1879-2782
1879-2782
DOI:10.1016/j.neunet.2011.10.001