Real-Time Principal-Component Analysis

Abstract

A recently written computer program implements dominant-element-based gradient descent and dynamic initial learning rate (DOGEDYN), which was described in Method of Real-Time Principal-Component Analysis (NPO-40034) NASA Tech Briefs, Vol. 29, No. 1 (January 2005), page 59. To recapitulate: DOGEDYN is a method of sequential principal-component analysis (PCA) suitable for such applications as data compression and extraction of features from sets of data. In DOGEDYN, input data are represented as a sequence of vectors acquired at sampling times. The learning algorithm in DOGEDYN involves sequential extraction of principal vectors by means of a gradient descent in which only the dominant element is used at each iteration. Each iteration includes updating of elements of a weight matrix by amounts proportional to a dynamic initial learning rate chosen to increase the rate of convergence by compensating for the energy lost through the previous extraction of principal components. In comparison with a prior method of gradient-descent-based sequential PCA, DOGEDYN involves less computation and offers a greater rate of learning convergence. The sequential DOGEDYN computations require less memory than would parallel computations for the same purpose. The DOGEDYN software can be executed on a personal computer.