2012
Leiva-Murillo, Jose M; Artés-Rodríguez, Antonio
Algorithms for Maximum-Likelihood Bandwidth Selection in Kernel Density Estimators Artículo de revista
En: Pattern Recognition Letters, vol. 33, no 13, pp. 1717–1724, 2012, ISSN: 01678655.
Resumen | Enlaces | BibTeX | Etiquetas: Kernel density estimation, Multivariate density modeling, Pattern recognition
@article{Leiva-Murillo2012,
title = {Algorithms for Maximum-Likelihood Bandwidth Selection in Kernel Density Estimators},
author = {Jose M Leiva-Murillo and Antonio Art\'{e}s-Rodr\'{i}guez},
url = {http://www.tsc.uc3m.es/~antonio/papers/P45_2012_Algorithms for Maximum Likelihood Bandwidth Selection in Kernel Density Estimators.pdf
http://www.sciencedirect.com/science/article/pii/S0167865512001948},
issn = {01678655},
year = {2012},
date = {2012-01-01},
journal = {Pattern Recognition Letters},
volume = {33},
number = {13},
pages = {1717--1724},
publisher = {Elsevier Science Inc.},
abstract = {In machine learning and statistics, kernel density estimators are rarely used on multivariate data due to the difficulty of finding an appropriate kernel bandwidth to overcome overfitting. However, the recent advances on information-theoretic learning have revived the interest on these models. With this motivation, in this paper we revisit the classical statistical problem of data-driven bandwidth selection by cross-validation maximum likelihood for Gaussian kernels. We find a solution to the optimization problem under both the spherical and the general case where a full covariance matrix is considered for the kernel. The fixed-point algorithms proposed in this paper obtain the maximum likelihood bandwidth in few iterations, without performing an exhaustive bandwidth search, which is unfeasible in the multivariate case. The convergence of the methods proposed is proved. A set of classification experiments are performed to prove the usefulness of the obtained models in pattern recognition.},
keywords = {Kernel density estimation, Multivariate density modeling, Pattern recognition},
pubstate = {published},
tppubtype = {article}
}
Leiva-Murillo, Jose M; Artés-Rodríguez, Antonio
Information-Theoretic Linear Feature Extraction Based on Kernel Density Estimators: A Review Artículo de revista
En: IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), vol. 42, no 6, pp. 1180–1189, 2012, ISSN: 1094-6977.
Resumen | Enlaces | BibTeX | Etiquetas: Bandwidth, Density, detection theory, Entropy, Estimation, Feature extraction, Feature extraction (FE), information theoretic linear feature extraction, information theory, information-theoretic learning (ITL), Kernel, Kernel density estimation, kernel density estimators, Machine learning
@article{Leiva-Murillo2012a,
title = {Information-Theoretic Linear Feature Extraction Based on Kernel Density Estimators: A Review},
author = {Jose M Leiva-Murillo and Antonio Art\'{e}s-Rodr\'{i}guez},
url = {http://www.tsc.uc3m.es/~antonio/papers/P44_2012_Information Theoretic Linear Feature Extraction Based on Kernel Density Estimators A Review.pdf http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6185689},
issn = {1094-6977},
year = {2012},
date = {2012-01-01},
journal = {IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews)},
volume = {42},
number = {6},
pages = {1180--1189},
abstract = {In this paper, we provide a unified study of the application of kernel density estimators to supervised linear feature extraction by means of criteria inspired by information and detection theory. We enrich this study by the incorporation of two novel criteria to the study, i.e., the mutual information and the likelihood ratio test, and perform both a theoretical and an experimental comparison between the new methods and other ones previously described in the literature. The impact of the bandwidth selection of the density estimator in the classification performance is discussed. Some theoretical results that bound classification performance as a function or mutual information are also compiled. A set of experiments on different real-world datasets allows us to perform an empirical comparison of the methods, in terms of both accuracy and computational complexity. We show the suitability of these methods to determine the dimension of the subspace that contains the discriminative information.},
keywords = {Bandwidth, Density, detection theory, Entropy, Estimation, Feature extraction, Feature extraction (FE), information theoretic linear feature extraction, information theory, information-theoretic learning (ITL), Kernel, Kernel density estimation, kernel density estimators, Machine learning},
pubstate = {published},
tppubtype = {article}
}