Showing papers on "Geometric data analysis published in 1973"

Representation of Nonlinear Data Surfaces

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 ( m I ) 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-Loeve 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.

The effectiveness of direct graphical entry of topological and geometric data

Abstract: A study is described that was carried out to determine the feasibility of making interactive graphics terminals available for computer-aided instruction (CAI) in engineering and science courses.