Adaptive Relevance Matrices in Learning Vector Quantization

We propose a new matrix learning scheme to extend relevance learning vector quantization (RLVQ), an efficient prototype-based classification algorithm, toward a general adaptive metric. By introducing a full matrix of relevance factors in the distance measure, correlations between different features...

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Bibliographic Details
Published in:Neural computation 2009-12, Vol.21 (12), p.3532-3561
Main Authors: Schneider, Petra, Biehl, Michael, Hammer, Barbara
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Artificial Intelligence
Automatic Data Processing
Biological and medical sciences
Brain - physiology
Comparative analysis
Computer science
control theory
systems
Correlation analysis
Euclidean space
Exact sciences and technology
Functional analysis
Fundamental and applied biological sciences. Psychology
General aspects
Humans
Information Theory
Learning
Learning - physiology
Learning and adaptive systems
Letters
Mathematical analysis
Mathematics
Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)
Matrix
Miscellaneous
Probability Learning
Sciences and techniques of general use
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Summary:We propose a new matrix learning scheme to extend relevance learning vector quantization (RLVQ), an efficient prototype-based classification algorithm, toward a general adaptive metric. By introducing a full matrix of relevance factors in the distance measure, correlations between different features and their importance for the classification scheme can be taken into account and automated, and general metric adaptation takes place during training. In comparison to the weighted Euclidean metric used in RLVQ and its variations, a full matrix is more powerful to represent the internal structure of the data appropriately. Large margin generalization bounds can be transferred to this case, leading to bounds that are independent of the input dimensionality. This also holds for local metrics attached to each prototype, which corresponds to piecewise quadratic decision boundaries. The algorithm is tested in comparison to alternative learning vector quantization schemes using an artificial data set, a benchmark multiclass problem from the UCI repository, and a problem from bioinformatics, the recognition of splice sites for .
ISSN:0899-7667
1530-888X
DOI:10.1162/neco.2009.11-08-908