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313
Sparse coding with an overcomplete basis set: a strategy employed by V1
 Vision Research
, 1997
"... The spatial receptive fields of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive f ..."
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Cited by 954 (12 self)
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The spatial receptive fields of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive field properties may be accounted for in terms of a strategy for producing a sparse distribution of output activity in response to natural images. Here, in addition to describing this work in a more expansive fashion, we examine the neurobiological implications of sparse coding. Of particular interest is the case when the code is overcompletei.e., when the number of code elements is greater than the effective dimensionality of the input space. Because the basis functions are nonorthogonal and not linearly independent of each other, sparsifying the code will recruit only those basis functions necessary for representing a given input, and so the inputoutput function will deviate from being purely linear. These deviations from linearity provide a potential explanation for the weak forms of nonlinearity observed in the response properties of cortical simple cells, and they further make predictions about the expected interactions among units in
Fast and robust fixedpoint algorithms for independent component analysis
 IEEE TRANS. NEURAL NETW
, 1999
"... Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon’s informat ..."
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Cited by 858 (34 self)
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Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon’s informationtheoretic approach and the projection pursuit approach. Using maximum entropy approximations of differential entropy, we introduce a family of new contrast (objective) functions for ICA. These contrast functions enable both the estimation of the whole decomposition by minimizing mutual information, and estimation of individual independent components as projection pursuit directions. The statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model, and it is shown how to choose contrast functions that are robust and/or of minimum variance. Finally, we introduce simple fixedpoint algorithms for practical optimization of the contrast functions. These algorithms optimize the contrast functions very fast and reliably.
Independent component analysis: algorithms and applications
 NEURAL NETWORKS
, 2000
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Survey of clustering algorithms
 IEEE TRANSACTIONS ON NEURAL NETWORKS
, 2005
"... Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the ..."
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Cited by 483 (4 self)
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Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.
Centroidal Voronoi tessellations: Applications and algorithms
 SIAM REV
, 1999
"... A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution of res ..."
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Cited by 389 (37 self)
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A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution of resources, cellular biology, statistics, and the territorial behavior of animals. We discuss methods for computing these tessellations, provide some analyses concerning both the tessellations and the methods for their determination, and, finally, present the results of some numerical experiments.
Sliced inverse regression for dimension reduction
 J. AMER. STATIST. ASSOC
, 1991
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Flexible Discriminant Analysis by Optimal Scoring
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1993
"... Fisher's linear discriminant analysis is a valuable tool for multigroup classification. With a large number of predictors, one can nd a reduced number of discriminant coordinate functions that are "optimal" for separating the groups. With two such functions one can produce a classific ..."
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Cited by 139 (12 self)
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Fisher's linear discriminant analysis is a valuable tool for multigroup classification. With a large number of predictors, one can nd a reduced number of discriminant coordinate functions that are "optimal" for separating the groups. With two such functions one can produce a classification map that partitions the reduced space into regions that are identified with group membership, and the decision boundaries are linear. This paper is about richer nonlinear classification schemes. Linear discriminant analysis is equivalent to multiresponse linear regression using optimal scorings to represent the groups. We obtain nonparametric versions of discriminant analysis by replacing linear regression by any nonparametric regression method. In this way, any multiresponse regression technique (such as MARS or neural networks) can be postprocessed to improve their classification performence.
Feature selection for unsupervised learning
 Journal of Machine Learning Research
, 2004
"... In this paper, we identify two issues involved in developing an automated feature subset selection algorithm for unlabeled data: the need for finding the number of clusters in conjunction with feature selection, and the need for normalizing the bias of feature selection criteria with respect to dime ..."
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Cited by 139 (4 self)
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In this paper, we identify two issues involved in developing an automated feature subset selection algorithm for unlabeled data: the need for finding the number of clusters in conjunction with feature selection, and the need for normalizing the bias of feature selection criteria with respect to dimension. We explore the feature selection problem and these issues through FSSEM (Feature Subset Selection using ExpectationMaximization (EM) clustering) and through two different performance criteria for evaluating candidate feature subsets: scatter separability and maximum likelihood. We present proofs on the dimensionality biases of these feature criteria, and present a crossprojection normalization scheme that can be applied to any criterion to ameliorate these biases. Our experiments show the need for feature selection, the need for addressing these two issues, and the effectiveness of our proposed solutions.
The nonlinear statistics of highcontrast patches in natural images
 International Journal of Computer Vision
"... (Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. ..."
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Cited by 116 (3 self)
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters.