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LESS: a model-based classifier for sparse subspaces

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2 Author(s)
Veenman, C.J. ; Dept. of Mediamatics, Delft Univ. of Technol., Netherlands ; Tax, D.M.J.

In this paper, we specifically focus on high-dimensional data sets for which the number of dimensions is an order of magnitude higher than the number of objects. From a classifier design standpoint, such small sample size problems have some interesting challenges. The first challenge is to find, from all hyperplanes that separate the classes, a separating hyperplane which generalizes well for future data. A second important task is to determine which features are required to distinguish the classes. To attack these problems, we propose the LESS (lowest error in a sparse subspace) classifier that efficiently finds linear discriminants in a sparse subspace. In contrast with most classifiers for high-dimensional data sets, the LESS classifier incorporates a (simple) data model. Further, by means of a regularization parameter, the classifier establishes a suitable trade-off between subspace sparseness and classification accuracy. In the experiments, we show how LESS performs on several high-dimensional data sets and compare its performance to related state-of-the-art classifiers like, among others, linear ridge regression with the LASSO and the support vector machine. It turns out that LESS performs competitively while using fewer dimensions.

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:27 ,  Issue: 9 )