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, Benzecri, 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.