Local Component Analysis

Nicolas Le Roux 1, 2 Francis Bach 1, 2
1 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : Kernel density estimation, a.k.a. Parzen windows, is a popular density estimation method, which can be used for outlier detection or clustering. With multivariate data, its performance is heavily reliant on the metric used within the kernel. Most earlier work has focused on learning only the bandwidth of the kernel (i.e., a scalar multiplicative factor). In this paper, we propose to learn a full Euclidean metric through an expectation-minimization (EM) procedure, which can be seen as an unsupervised counterpart to neighbourhood component analysis (NCA). In order to avoid overfitting with a fully nonparametric density estimator in high dimensions, we also consider a semi-parametric Gaussian-Parzen density model, where some of the variables are modelled through a jointly Gaussian density, while others are modelled through Parzen windows. For these two models, EM leads to simple closed-form updates based on matrix inversions and eigenvalue decompositions. We show empirically that our method leads to density estimators with higher test-likelihoods than natural competing methods, and that the metrics may be used within most unsupervised learning techniques that rely on such metrics, such as spectral clustering or manifold learning methods. Finally, we present a stochastic approximation scheme which allows for the use of this method in a large-scale setting.
Type de document :
Communication dans un congrès
ICLR - International Conference on Learning Representations 2013, 2013, Scottsdale, United States. 2013
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Dernière modification le : vendredi 25 mai 2018 - 12:02:06
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  • HAL Id : inria-00617965, version 4
  • ARXIV : 1109.0093

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Nicolas Le Roux, Francis Bach. Local Component Analysis. ICLR - International Conference on Learning Representations 2013, 2013, Scottsdale, United States. 2013. 〈inria-00617965v4〉

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