What is Projection Pursuit?

Jones, M. C.; Sibson, Robin

doi:10.2307/2981662

Cited by 445 publications

(262 citation statements)

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“…Early approaches in this respect were based on the gradient techniques [30,29] and Newton-Raphson [31,37,14,13], where the projections are performed in at most three dimensions for visual exploratory tasks, the so-called exploratory projection pursuit (EPP). Further developments focused on developing more global methods for PP optimization, such as random search [38,39,29], genetic algorithm (GA) [32], random scan sampling algorithm (RSSA) [34], simulated annealing (SA) [21], particle swarm optimization (PSO) [35] and tribes [40].…”

Section: Pp Optimizationmentioning

confidence: 99%

“…A great deal of research in the PP community has been centered on the construction of meaningful PP indexes for different purposes. It is possible to find PP indexes for clustering analysis [42,19,38,39,43,30,13], for supervised analysis [44,45,21,5] and for regression analysis [46,47]. Given that this paper is targeted to supervised analysis, we briefly describe some relevant supervised PP indexes included in the experimental evaluation of the paper.…”

Section: Projection Pursuit Indicesmentioning

confidence: 99%

“…Evidently, the problem worsens as p or m increase. Traditional PP optimizers based on the gradients or Newton methods [29][30][31]19] are usually inadequate for such a kind of data due to the vastness of possible projections and, thus, the high susceptibility to find poor local optima [14]. More global PP optimizers were described recently, including genetic algorithms (GA) [32,33], simulating annealing (SA) [21], random scan sampling (RSSA) [34] and particle swarm optimization (PSO) [35].…”

Section: Introductionmentioning

confidence: 99%

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A Projection Pursuit framework for supervised dimension reduction of high dimensional small sample datasets

et al. 2015

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Section: Pp Optimizationmentioning

confidence: 99%

Section: Projection Pursuit Indicesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Projection Pursuit framework for supervised dimension reduction of high dimensional small sample datasets

et al. 2015

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“…they can be used for the projection index. Jones and Sibson (1987) proposed a one-dimensional projection index named the "moment index," with the third cumulant k 3 = µ 3 and the fourth cumulant k 4 = µ 4 − 3:…”

Section: Moment Indexmentioning

confidence: 99%

Dimension Reduction Methods

Mizuta

2011

Handbook of Computational Statistics

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“…There are in fact an infinite number of possible projections to choose from, so which one should be used? Projection pursuit (Jones and Sibson, 1987} is concerned with resolving this kind of problem.…”

Section: Contextmentioning

confidence: 99%

Editorial introduction

Blomquist¹,

Gordon²

2007

Journal of Public Economics

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The date used by social scientists are frequently multivariate. In part, this is a consequence of a need to characterise objects of interest, such as people, houses and so on, as fully as possible, but it is also often a result of a desire to capture concepts such as social class or intelligence and overcrowding that do not permit easy measurement along one axis of variation. In consequence, quantitative social science has a long history of using statistical and mathematical transforms of data matrices such as factor and principal component analysis to reduce the dimensionality of these data and perhaps suggest appropriate constructs that might also be used to describe individuals.These techniques are not intrinsically visual, although the reprojection of individual cases onto axes that define these constructs (for examples as component scores) may well create data that can be visualized by any of the standard techniques. There remains a need to develop appropriate alternative visualizations for multidimensional data that are efficient in allowing the detection of patterns in the multivariate data space. In this Case Study, Chris Brunsdon, Stweart Fotheringham and Martin Charlton develop and illustrate three alternative projections that can be applied to multivariate data.It is interresting to note that although the static displays produces are in themselves useful, they gain maximum utility when visualized in an interactive environment. An Investigation of Methods for AbstractAlthough visualisation has become a 'hot topic' in the social sciences, the majority of visualisation studies and techniques apply only to one or two dimensional datasets. Relatively little headway has been made into visualising higher dimensional data although, paradoxically, most social science datasets are highly multivariate. Investigating multivariate data, whether it be done visually or not, in just one or two dimensions can be highly misleading. Two well-known examples of this are the use of a correlation coefficient instead of a regression parameter as an indicator of the relationship between two variables and the use of scatterplots instead of leverage plots as indicators of relationships.This project has therefore investigated several methods for visualising aspects of higher dimensional (i.e. multivariate) datasets. Although some techniques are quite well-established for this purpose, such as Andrews Plots and Chernov Faces, we have ignored these because of their well-know problems. In the case of Andrews plots the functions used are subjective and the plots become very difficult to read when the number of observations rises beyond 30. In the case of Chernov faces, variables which are attached to certain attributes of the face, for example, the eyes, receive more weight in the subjective determination of 'unusual' cases.Instead we have examined the use of four newer techniques for visualising aspects of higher dimensional data sets: projection pursuit; Geographically Weighted Regression; RADVIZ; and Parallel Co-ordinates. In pr...

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What is Projection Pursuit?

Cited by 445 publications

References 12 publications

A Projection Pursuit framework for supervised dimension reduction of high dimensional small sample datasets

A Projection Pursuit framework for supervised dimension reduction of high dimensional small sample datasets

Dimension Reduction Methods

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