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Inverse regression method in data structure analysis

Inverse regression method in data structure analysis In order to explore the nonlinear structure hidden in high-dimensional data, some dimension reduction techniques have been developed, such as the Projection Pursuit technique (PP). However, PP will involve enormous computational load. To overcome this, an inverse regression method is proposed. In this paper, we discuss and develop this method. To seek the interesting projective direction, the minimization of the residual sum of squares is used as a criterion, and spline functions are applied to approximate the general nonlinear transform function. The algorithm is simple, and saves the computational load. Under certain proper conditions, consistency of the estimators of the interesting direction is shown. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Inverse regression method in data structure analysis

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Publisher
Springer Journals
Copyright
Copyright © 1991 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02009685
Publisher site
See Article on Publisher Site

Abstract

In order to explore the nonlinear structure hidden in high-dimensional data, some dimension reduction techniques have been developed, such as the Projection Pursuit technique (PP). However, PP will involve enormous computational load. To overcome this, an inverse regression method is proposed. In this paper, we discuss and develop this method. To seek the interesting projective direction, the minimization of the residual sum of squares is used as a criterion, and spline functions are applied to approximate the general nonlinear transform function. The algorithm is simple, and saves the computational load. Under certain proper conditions, consistency of the estimators of the interesting direction is shown.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 14, 2005

References