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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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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Abstract	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.
AbstractList	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. 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. 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.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.
Author	Schneider, Petra Schleif, Frank-Michael Hammer, Barbara Biehl, Michael Villmann, Thomas Bunte, Kerstin
Author_xml	– sequence: 1 givenname: Kerstin surname: Bunte fullname: Bunte, Kerstin email: k.bunte@rug.nl organization: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science, The Netherlands – sequence: 2 givenname: Petra surname: Schneider fullname: Schneider, Petra organization: University of Birmingham, School of Clinical and Experimental Medicine, United Kingdom – sequence: 3 givenname: Barbara surname: Hammer fullname: Hammer, Barbara organization: Bielefeld University, Center of Excellence-Cognitive Interaction Technology CITEC, Germany – sequence: 4 givenname: Frank-Michael surname: Schleif fullname: Schleif, Frank-Michael organization: Bielefeld University, Center of Excellence-Cognitive Interaction Technology CITEC, Germany – sequence: 5 givenname: Thomas surname: Villmann fullname: Villmann, Thomas organization: University of Applied Sciences Mittweida, Department of MPI, Germany – sequence: 6 givenname: Michael surname: Biehl fullname: Biehl, Michael organization: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science, The Netherlands
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Keywords	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
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Snippet	We present an extension of the recently introduced Generalized Matrix Learning Vector Quantization algorithm. In the original scheme, adaptive square matrices...
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SubjectTerms	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
Title	Limited Rank Matrix Learning, discriminative dimension reduction and visualization
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