A nonlinear extension of principal component analysis for clustering and spatial differentiation.: An article from: IIE Transactions
Book Details
Author(s)Agus Sudjianto, Gary S. Wasserman
ISBN / ASINB00096Q0JK
ISBN-13978B00096Q0J9
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This digital document is an article from IIE Transactions, published by Institute of Industrial Engineers, Inc. (IIE) on December 1, 1996. The length of the article is 3648 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.
From the author: The limitations in the use of linear principal component analysis (PCA) for identifying morphological features of data sets are discussed. A nonlinear extension of PCA is introduced to provide this capability. It differs from ordinary PCA methods only in that the objective function involves a nonlinear transformation of the principal components. The procedure is shown to be closely related to the exploratory projection pursuit (EPP) algorithm proposed by Friedman (1987), and thus its usefulness in clustering and spatial differentiation applications is apparent. An efficient gradient ascent algorithm is proposed for implementation, based upon the use of a stochastic approximation. The inherent computational advantages in the suggested implementation over other EPP methods are evident, given that EPP methods require the estimation of a density function at every iteration. The nonlinear extension is evaluated by using several well-known datasets, including Fisher's (1936) Iris data. An industrial application of the technique is also presented. Necessary conditions for convergence are shown.
Citation Details
Title: A nonlinear extension of principal component analysis for clustering and spatial differentiation.
Author: Agus Sudjianto
Publication:IIE Transactions (Refereed)
Date: December 1, 1996
Publisher: Institute of Industrial Engineers, Inc. (IIE)
Volume: v28 Issue: n12 Page: p1023(6)
Distributed by Thomson Gale
From the author: The limitations in the use of linear principal component analysis (PCA) for identifying morphological features of data sets are discussed. A nonlinear extension of PCA is introduced to provide this capability. It differs from ordinary PCA methods only in that the objective function involves a nonlinear transformation of the principal components. The procedure is shown to be closely related to the exploratory projection pursuit (EPP) algorithm proposed by Friedman (1987), and thus its usefulness in clustering and spatial differentiation applications is apparent. An efficient gradient ascent algorithm is proposed for implementation, based upon the use of a stochastic approximation. The inherent computational advantages in the suggested implementation over other EPP methods are evident, given that EPP methods require the estimation of a density function at every iteration. The nonlinear extension is evaluated by using several well-known datasets, including Fisher's (1936) Iris data. An industrial application of the technique is also presented. Necessary conditions for convergence are shown.
Citation Details
Title: A nonlinear extension of principal component analysis for clustering and spatial differentiation.
Author: Agus Sudjianto
Publication:IIE Transactions (Refereed)
Date: December 1, 1996
Publisher: Institute of Industrial Engineers, Inc. (IIE)
Volume: v28 Issue: n12 Page: p1023(6)
Distributed by Thomson Gale
