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ABSTRACT:
Two quite different forms of nonlinear principal component analysis have been proposed in the literature. The first one is associated with the names of Guttman, Burt, Hayashi, Benzécri, McDonald, De Leeuw, Hill, Nishisato. We call it multiple correspondence analysis. The second form has been discussed by Kruskal, Shepard, Roskam, Takane, Young, De Leeuw, Winsberg, Ramsay. We call it nonmetric principal component analysis. The two forms have been related and combined, both geometrically and computationally, by Albert Gifi. In this paper we discuss the relationships in more detail, and propose an alternative algorithm for nonlinear principal component analysis which combines features of both previous approaches.

SUGGESTED CITATION:
Jan de Leeuw, "Nonlinear Principal Component Analysis" (October 30, 2005). Department of Statistics, UCLA. Department of Statistics Papers. Paper 2005103001.
http://repositories.cdlib.org/uclastat/papers/2005103001