title: LESS: a model-based classifier for sparse subspaces.
abstract: 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.
authors.affiliation: Department of Mediamatics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands. C.J.Veenman@ewi.tudelft.nl
authors.forename: Cor J
authors.initials: CJ
authors.lastname: Veenman
authors.forename: David M J
authors.initials: DM
authors.lastname: Tax
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D003198:Computer Simulation; D016247:Information Storage and Retrieval / Q000379:methods*; D015233:Models, Statistical; D010363:Pattern Recognition, Automated / Q000379:methods*