Showing papers on "Dimensionality reduction published in 1973"

An Iterative Approach to the Feature Selection Problem

Abstract: The problem dealt with concerns feature selection or reducing the dimension of the data to be processed from n to k. By reducing the dimension of the data from n to k, classification time is generally reduced. Yet the dimension reduction should not be so great that classification accuracy is impaired. Thus, the general problem is considered of classifying an n-dimensional observation vector x into one of m-distinct classes where each class is normally distributed with mean and covariance. It is shown that the probability of misclassification is minimized if a maximum likelihood classification procedure is used to classify the data. The dimension of each observation vector to be processed is conveniently reduced by performing the transformation y = Bx, where B is a K by n matrix of rank k. Thus, the n-dimensional classification problem transforms into a k-dimensional classification problem.

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.