Representation of Nonlinear Data Surfaces

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Abstract
This paper is concerned with the use of "intrinsic dimensionality" in the representation of multivariate data sets that lie on nonlinear surfaces. The term intrinsic refers to the small, local-region dimensionality ( mI) of the surface and is a measure of the number of parameters or factors that govern a data generating process. The number mI is usually much lower than the dimensionality that is given by the standard Karhunen-Loève expansion. Representation of the data is accomplished by transforming the data to a linear space of mI dimensions using a new noniterative mapping procedure. This mapping gives a significant reduction in dimensionality and preserves the geometric data structure to a large degree. Single-and two-surface data sets are considered. Numerical examples are presented to illustrate both techniques.

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