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- W3122936144 abstract "The similarity between objects is a fundamental element of many learning algorithms. Most non-parametric methods take this similarity to be fixed, but much recent work has shown the advantages of learning it, in particular to exploit the local invariances in the data or to capture the possibly non-linear manifold on which most of the data lies. We propose a new non-parametric kernel density estimation method which captures the local structure of an underlying manifold through the leading eigenvectors of regularized local covariance matrices. Experiments in density estimation show significant improvements with respect to Parzen density estimators. The density estimators can also be used within Bayes classifiers, yielding classification rates similar to SVMs and much superior to the Parzen classifier. La similarite entre objets est un element fondamental de plusieurs algorithmes d'apprentissage. La plupart des methodes non parametriques supposent cette similarite constante, mais des travaux recents ont montre les avantages de les apprendre, en particulier pour exploiter les invariances locales dans les donnees ou pour capturer la variete possiblement non lineaire sur laquelle reposent la plupart des donnees. Nous proposons une nouvelle methode d'estimation de densite a noyau non parametrique qui capture la structure locale d'une variete sous-jacente en utilisant les vecteurs propres principaux de matrices de covariance locales regularisees. Les experiences d'estimation de densite montrent une amelioration significative sur les estimateurs de densite de Parzen. Les estimateurs de densite peuvent aussi etre utilises a l'interieur de classificateurs de Bayes, menant a des taux de classification similaires a ceux des SVMs, et tres superieurs au classificateur de Parzen." @default.
- W3122936144 created "2021-02-01" @default.
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- W3122936144 date "2004-05-01" @default.
- W3122936144 modified "2023-09-27" @default.
- W3122936144 title "Manifold Parzen Windows" @default.
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