Projection Pursuit Clustering for Exploratory Data Analysis

Bolton, Richard J.; Krzanowski, W. J.

doi:10.1198/1061860031374

Cited by 48 publications

(32 citation statements)

References 13 publications

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“…Unfortunately optimal transformations required for clustering require knowing the true cluster means. A promising approach to solving this problem is to use projection pursuit clustering (Bolton and Krzanowski, 2003).…”

Section: Discussionmentioning

confidence: 99%

“…This algorithm iterates by estimating the common hyperplane using the subspace spanned by the largest eigenvectors from the between group sums-of-squares-and-products matrix and then applying the k-means algorithm to the data projected onto this hyperplane. Bolton and Krzanowski (2003) note that Bock's algorithm tends to find groups in the direction of the data corresponding to the largest variance and they propose a slightly different projection pursuit index to avoid this problem.…”

Section: Example: An Simple Illustration Of a Canonical Transformationmentioning

confidence: 99%

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Linear Transformations and thek-Means Clustering Algorithm

Tarpey

2007

The American Statistician

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Functional data can be clustered by plugging estimated regression coefficients from individual curves into the k-means algorithm. Clustering results can differ depending on how the curves are fit to the data. Estimating curves using different sets of basis functions corresponds to different linear transformations of the data. k-means clustering is not invariant to linear transformations of the data. The optimal linear transformation for clustering will stretch the distribution so that the primary direction of variability aligns with actual differences in the clusters. It is shown that clustering the raw data will often give results similar to clustering regression coefficients obtained using an orthogonal design matrix. Clustering functional data using an L 2 metric on function space can be achieved by clustering a suitable linear transformation of the regression coefficients. An example where depressed individuals are treated with an antidepressant is used for illustration.

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Section: Discussionmentioning

confidence: 99%

Section: Example: An Simple Illustration Of a Canonical Transformationmentioning

confidence: 99%

Linear Transformations and thek-Means Clustering Algorithm

Tarpey

2007

The American Statistician

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“…However, predictive aspects have had little direct attention. Bolton and Krzanowski (2003), following some previous work by Bock (1987), used a discrimination criterion in seeking low-dimensional clusters, while Gower (1974) incorporated class prediction into the clustering criterion, but these methods focussed only on the y variables. Few papers have actually tackled the incorporation of the x variables.…”

Section: Introductionmentioning

confidence: 99%

Optimal predictive partitioning

2007

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In many situations, one wishes to group objects into well-defined classes on the basis of one set of descriptor variables, and then predict the classes of new objects from a different set of variables. For example, a bank may categorise customers into distinct financial behaviour pattern classes by observing how they have behaved over a period of years, and then seek to assign new customers to future behaviour classes using information captured when they open an account. Such situations require the striking of a compromise between the compactness and integrity of the cluster structure, and the accuracy of the predictive assignment to clusters. We describe two algorithms for achieving such a compromise, discuss some of their features, and illustrate their performance in a simulation study and in a liver transplant problem.

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“…Projection structure, optimization of method and the mathematics model are the keys to using Projection Pursuit to solve practical problem. Projection pursuit as a new method, was applied to comprehensive assessment in various research during the past decades [14][15][16][17][18][19], especially in water resources and environment [20][21][22]. However, because traditional Projection Pursuit computing technology is complicated [23], further application of traditional Projection Pursuit method is limited.…”

Section: Introductionmentioning

confidence: 99%

Genetic Projection Pursuit Interpolation Model for Social Renewability Assessment of Water Resources

Zhang

Huang

et al. 2008

2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery

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In order to resolve the non-uniformity problem of evaluation results of social renewability of water resources in cities, and to raise the evaluation result precision, a genetic projection pursuit interpolation model (GPPIM) is founded for comprehensive assessment of social renewability of water resources, which is by using Gray-encoded accelerating genetic algorithm (GAGA). Taking the 15 cities in the Yellow River basin as examples, the social renewability of water resources is assessed with 11-index system by the GPPIM, the results show that the social renewability of water resources in Xining, Baoji, Xianyang and Luoyang are weaker grade, and it is medium grade in the other cities. The levels of them are very low. And it is hard task to improve their social renewability of water resources. In addition, the GPPIM for social renewability of water resources is effective and precise, which can be used for other cluster analyses of high-dimensional data sets. Then, Grayencoded accelerating genetic algorithm is applied to optimize projection direction of the projection pursuit interpolation model and the steps of the Gray-encoded accelerating genetic algorithm are introduced in detail.

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Projection Pursuit Clustering for Exploratory Data Analysis

Cited by 48 publications

References 13 publications

Linear Transformations and thek-Means Clustering Algorithm

Linear Transformations and thek-Means Clustering Algorithm

Optimal predictive partitioning

Genetic Projection Pursuit Interpolation Model for Social Renewability Assessment of Water Resources

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