Showing papers on "Dimensionality reduction published in 1971"

An Algorithm for Finding Intrinsic Dimensionality of Data

Abstract: An algorithm for the analysis of multivariant data is presented along with some experimental results. The basic idea of the method is to examine the data in many small subregions, and from this determine the number of governing parameters, or intrinsic dimensionality. This intrinsic dimensionality is usually much lower than the dimensionality that is given by the standard Karhunen-Loeve technique. An analysis that demonstrates the feasability of this approach is presented.

Redundancy in Feature Extraction

Abstract: Given two random variables X and Y, a definition is offered that gives a condition for Y to be redundant with respect to X. It is shown that if such redundancy exists, then observations on Y, i.e., pattern vector elements related to Y, can be eliminated without increasing the classification error. A test for redundancy is developed and applied to the problem of preprocessing pattern vectors to eliminate redundant vector elements.

Walsh Orthogonal Functions in Geometrical Feature Extraction

Abstract: Walsh functions are used in designinq a feature extraction algorithm. The ?axis-symmetry? property of the Walsh functions is used to decompose geometrical patterns. An axissymmetry (a.s.)-histogram is obtained from the Walsh spectrum of a pattern by adding the squares of the spectrm coefficients that correspond to a given a.s.-number ? and plotting these against ?. Since Walsh transformation is not positionally invariant, the sequency spectrum does not specify the pattern uniquely. This disadvantage is overcome by performing a normalization on the input pattern through Fourier transformation. The a.s.-histogram is obtained from the Walsh spectrum coefficients of the Fourier-normalized rather than the original pattern. Such histogram contains implicit information about symmetries, periodicities, and discontinuities present in a figure. It is shown that a.s.-histograms result in great dimensionality reduction in the feature space, which leads to a computationally simpler classification task, and that patterns which differ only in translations or 90° rotation have equal a.s.-histograms.

The Dimensionality of Time

Abstract: Kant, as we have seen, flatly maintains that mono-dimensionality is a necessary feature of time. But is this indeed so? Specifically, let us investigate whether a coherent two-dimensional picture of time can be given.

Discriminatory dimensionality reduction (Corresp.)

Abstract: Truncated optimal entropy-minimizing expansions can serve to characterize classes of multivariate data. A method is presented here by which the level of truncation and the corresponding dimensionalities of the class subspaces can be chosen to ensure adequate discrimination. The subspaces are chosen to maximize the average margin of correct classification of the paradigms of one class subject to constraints on the other margins.