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198
Independent Component Analysis
 Neural Computing Surveys
, 2001
"... A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the ..."
Abstract

Cited by 1492 (93 self)
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A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Wellknown linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA. 1
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 ..."
Abstract

Cited by 511 (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.
Projection Pursuit Regression
 Journal of the American Statistical Association
, 1981
"... A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures, ..."
Abstract

Cited by 401 (6 self)
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A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures, does not require the definition of a metric in the predictor space, and lends itself to graphical interpretation.
Data Exploration Using SelfOrganizing Maps
 ACTA POLYTECHNICA SCANDINAVICA: MATHEMATICS, COMPUTING AND MANAGEMENT IN ENGINEERING SERIES NO. 82
, 1997
"... Finding structures in vast multidimensional data sets, be they measurement data, statistics, or textual documents, is difficult and timeconsuming. Interesting, novel relations between the data items may be hidden in the data. The selforganizing map (SOM) algorithm of Kohonen can be used to aid the ..."
Abstract

Cited by 96 (4 self)
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Finding structures in vast multidimensional data sets, be they measurement data, statistics, or textual documents, is difficult and timeconsuming. Interesting, novel relations between the data items may be hidden in the data. The selforganizing map (SOM) algorithm of Kohonen can be used to aid the exploration: the structures in the data sets can be illustrated on special map displays. In this work, the methodology of using SOMs for exploratory data analysis or data mining is reviewed and developed further. The properties of the maps are compared with the properties of related methods intended for visualizing highdimensional multivariate data sets. In a set of case studies the SOM algorithm is applied to analyzing electroencephalograms, to illustrating structures of the standard of living in the world, and to organizing fulltext document collections. Measures are proposed for evaluating the quality of different types of maps in representing a given data set, and for measuring the robu...
Objective Function Formulation of the BCM Theory of Visual Cortical Plasticity: Statistical Connections, Stability Conditions
 NEURAL NETWORKS
, 1992
"... In this paper, we present an objective function formulation of the BCM theory of visual cortical plasticity that permits us to demonstrate the connection between the unsupervised BCM learning procedure and various statistical methods, in particular, that of Projection Pursuit. This formulation provi ..."
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Cited by 86 (37 self)
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In this paper, we present an objective function formulation of the BCM theory of visual cortical plasticity that permits us to demonstrate the connection between the unsupervised BCM learning procedure and various statistical methods, in particular, that of Projection Pursuit. This formulation provides a general method for stability analysis of the fixed points of the theory and enables us to analyze the behavior and the evolution of the network under various visual rearing conditions. It also allows comparison with many existing unsupervised methods. This model has been shown successful in various applications such as phoneme and 3D object recognition. We thus have the striking and possibly highly significant result that a biological neuron is performing a sophisticated statistical procedure.
A Hierarchical Latent Variable Model for Data Visualization
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... Visualization has proven to be a powerful and widelyapplicable tool for the analysis and interpretation of multivariate data. Most visualization algorithms aim to find a projection from the data space down to a twodimensional visualization space. However, for complex data sets living in a highdi ..."
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Cited by 86 (10 self)
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Visualization has proven to be a powerful and widelyapplicable tool for the analysis and interpretation of multivariate data. Most visualization algorithms aim to find a projection from the data space down to a twodimensional visualization space. However, for complex data sets living in a highdimensional space it is unlikely that a single twodimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and subclusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectationmaximization algorithm. We demonstrate the principle of the approach on a toy data set, and we then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multiphase flows in oil pipelines,...
Xgobi: Interactive Dynamic Graphics In The X Window System With A Link To S
, 1991
"... Data analysts perform a wide variety of computational tasks in the course of an analysis, and they should be able to do them all on the same platform. XGobi helps to make this possible by bringing stateoftheart dynamic graphic methods for the display and manipulation of scatter plots to the UNIX ..."
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Cited by 77 (32 self)
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Data analysts perform a wide variety of computational tasks in the course of an analysis, and they should be able to do them all on the same platform. XGobi helps to make this possible by bringing stateoftheart dynamic graphic methods for the display and manipulation of scatter plots to the UNIX R fl workstation, and by linking these methods to the S data analysis environment. XGobi is implemented in the X Window System TM , which offers portability across a wide variety of workstations, X terminals, and personal computers, as well as the ability to run smoothly across a network. A user can run XGobi and S simultaneously, making it possible to use each program's functions on the same data. Using a highly interactive directmanipulation design, XGobi offers an array of familiar scatterplot tools. Users can view pairwise plots, threedimensional rotations and grand tour sequences. Views of the data can be reshaped, and points can be identified or brushed. Projection coefficients a...
Visualization Techniques for Mining Large Databases: A Comparison
 IEEE Transactions on Knowledge and Data Engineering
, 1996
"... Visual data mining techniques have proven to be of high value in exploratory data analysis and they also have a high potential for mining large databases. In this article, we describe and evaluate a new visualizationbased approach to mining large databases. The basic idea of our visual data mining ..."
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Cited by 75 (1 self)
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Visual data mining techniques have proven to be of high value in exploratory data analysis and they also have a high potential for mining large databases. In this article, we describe and evaluate a new visualizationbased approach to mining large databases. The basic idea of our visual data mining techniques is to represent as many data items as possible on the screen at the same time by mapping each data value to a pixel of the screen and arranging the pixels adequately. The major goal of this article is to evaluate our visual data mining techniques and to compare them to other wellknown visualization techniques for multidimensional data: the parallel coordinate and stick figure visualization techniques. For the evaluation of visual data mining techniques, in the first place the perception of properties of the data counts, and only in the second place the CPU time and the number of secondary storage accesses are important. In addition to testing the visualization techniques using re...
Grand Tour and Projection Pursuit
 Journal of Computational and Graphical Statistics
, 1995
"... The grand tour and projection pursuit are two methods for exploring multivariate data. We show how to combine them into a dynamic graphical tool for exploratory data analysis, called a projection pursuit guided tour. This tool assists in clustering data when clusters are oddly shaped and in finding ..."
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Cited by 65 (19 self)
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The grand tour and projection pursuit are two methods for exploring multivariate data. We show how to combine them into a dynamic graphical tool for exploratory data analysis, called a projection pursuit guided tour. This tool assists in clustering data when clusters are oddly shaped and in finding general lowdimensional structure in high dimensional, and in particular, sparse data. An example shows that the method, which is projectionbased, can be quite powerful in situations which may cause methods based on kernelsmoothing grief. The projection pursuit guided tour is also useful for comparing and developing projection pursuit indices and illustrating some types of asymptotic results. 1 Introduction In this paper we show that two graphical methods for exploring high (say p) dimensional data, the grand tour (Asimov, 1985; Buja and Asimov, 1986), a dynamic tool, and projection pursuit (Kruskal, 1969; Friedman and Tukey, 1974; Huber, 1985), a static tool, naturally complement each o...