Principal Components and Extensions

In this paper, we discuss some extensions of principal components analysis. We focus in particular on extensions that deal with categorical multivariate data. We also briefly discuss various approaches that try to enable the techniques that handle nonlinearities in the data. Keywords: categorical data; eigenvalue decomposition; nonlinear multivariate analysis; optimal scoring; projection methods

[1]  George Michailidis,et al.  Graph Layout Techniques and Multidimensional Data Analysis , 1999 .

[2]  J. Leeuw,et al.  The Gifi system of descriptive multivariate analysis , 1998 .

[3]  R. Fisher.  THE PRECISION OF DISCRIMINANT FUNCTIONS , 1940 .

[4]  Jan de Leeuw,et al.  Correctness of Kruskal's algorithms for monotone regression with ties , 1977 .

[5]  H. Hirschfeld.  A Connection between Correlation and Contingency , 1935, Mathematical Proceedings of the Cambridge Philosophical Society.

[6]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

[7]  Adam Krzyzak,et al.  Piecewise Linear Skeletonization Using Principal Curves , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  R. Tibshirani,et al.  Penalized Discriminant Analysis , 1995 .

[9]  R. Tibshirani,et al.  Flexible Discriminant Analysis by Optimal Scoring , 1994 .

[10]  George Michailidis,et al.  Data Visualization through Graph Drawing , 2001, Comput. Stat..

[11]  Lei Xu,et al.  Topological local principal component analysis , 2003, Neurocomputing.

[12]  Forrest W. Young,et al.  Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features , 1976 .

[13]  Robert A. Koyak,et al.  On Measuring Internal Dependence in a Set of Random Variables , 1987 .

[14]  J. Leeuw,et al.  On the prehistory of Correspondence Analysis , 1983 .

[15]  Jan de Leeuw,et al.  Homogeneity analysis withk sets of variables: An alternating least squares method with optimal scaling features , 1988 .

[16]  J. Friedman,et al.  Estimating Optimal Transformations for Multiple Regression and Correlation. , 1985 .

[17]  Jason Bond,et al.  Homogeneity Analysis in Xlisp-Stat , 1996 .

[18]  P. Delicado.  Another Look at Principal Curves and Surfaces , 2001 .

[19]  Bernhard Schölkopf,et al.  Nonlinear Component Analysis as a Kernel Eigenvalue Problem , 1998, Neural Computation.

[20]  Jan de Leeuw,et al.  Multilevel homogeneity analysis with differential weighting , 2000 .