NDLI: High Dimensional Matrix Relevance Learning

Content Provider	IEEE Xplore Digital Library
Author	Schleif, Frank-Michael Villmann, Thomas Zhu, Xibin
Copyright Year	2014
Abstract	In supervised learning the parameters of a parametric Euclidean distance or mahalanobis distance can be effectively learned by so called Matrix Relevance Learning. This adaptation is not only useful to improve the discrimination capabilities of the model, but also to identify relevant features or relevant correlated features in the input data. Classical Matrix Relevance Learning scales quadratic with the number of input dimensions M and becomes prohibitive if M exceeds some thousand input features. We address Matrix Relevance Learning for data with a very large number of input dimensions. Such high dimensional data occur frequently in the life sciences domain e.g. For microarray or spectral data. We derive two respective approximation schemes and show exemplarily the implementation in Generalized Matrix Relevance Learning (GMLVQ) for classification problems. The first approximation scheme is based on Limited Rank Matrix Approximation (LiRaM) LiRaM is a random subspace projection technique which was formerly mainly considered for visualization purposes. The second novel approximation scheme is based on the Nystroem approximation and is exact if the number of Eigen values equals the rank of the Relevance Matrix. Using multiple benchmark problems, we demonstrate that the training process yields fast low rank approximations of the relevance matrices without harming the generalization ability. The approaches can be used to identify discriminative features for high dimensional data sets.
Starting Page	661
Ending Page	667
File Size	477207
Page Count	7
File Format	PDF
e-ISBN	9781479942749
DOI	10.1109/ICDMW.2014.15
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-12-14
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Training high dimensional Prototypes low rank approximation discriminative embedding Eigenvalues and eigenfunctions feature reduction Complexity theory Approximation methods Matrix decomposition Kernel relevance learning
Content Type	Text
Resource Type	Article

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