Nonparametric Optimization and Galactic Morphology

Abstract

This thesis examines two areas of overlap between Memory-Based Reasoning (MBR) and stochastic optimization. The first area is a solution to a galactic morphology problem from astronomy: given a faint, distorted image of a galaxy, how can we determine its structure automatically and quickly? Solving this problem is of importance to the field of astronomy, since there are now hundreds of millions of such images which have not been analyzed due to computational costs. The new algorithm, GMorph, follows the MBR paradigm by populating image space with several million "model" galaxies ahead of time. During run-time, we just find the model image nearest to the unknown image. The more interesting issues are dealing with image distortion and speed. GMorph uses "eigengalaxies" to address both. Eigenspace has only a fraction of the number of dimensions that image space does, so deconvolution is faster, more stable, and more accurate. We achieve significant improvements in speed over previously published techniques. We also introduce a new algorithm for optimization of similarity-based data. In a problem where only the similarity metric is defined, a gradient is rarely possible. The essence of MBR is the similarity metric among stored examples. The new algorithm, Pairwise Bisection, uses all pairs of stored examples to divide the space into many smaller spaces and uses a nonparametric statistic to decide on their promise. The nonparametric statistic is Kendall's tau, which is used to measure the probability that a given point is at an optimum. Because it is fundamentally nonparametric, the algorithm is also robust to non-Gaussian noise and outliers.