Novel techniques of computational intelligence for analysis of astronomical structures

Abstract

The presence of manifolds is a common assumption in many applications including astronomy and computer vision. For instance, in astronomy low-dimensional stellar structures, such as streams, shells and globular clusters, can be found in the neighborhood of big galaxies such as the Milky Way. Since these structures are often buried in very large data sets, an algorithm which can not only recover the manifold, but also remove the background noise (or outliers) is highly desirable. While other works try to recover manifolds either by pushing all points towards manifolds or by down-sampling from dense regions, aiming to solve one of the problems, they generally fail to suppress the noise on manifolds and remove background noise simultaneously. Inspired by the collective behavior of biological ants in food-seeking process, we propose a new algorithm which employs several random walkers who are equipped with a local alignment measure to detect and denoise manifolds. During the walking process the agents release pheromone on data points which reinforces future movements. Over time the pheromone concentrates on the manifolds, while it fades in the background noise due to an evaporation procedure. We use the Markov Chain (MC) framework to provide a theoretical analysis of the convergence of the algorithm and its performance. Moreover, an empirical analysis, based on synthetic and real world data sets, is provided to demonstrate its applicability in different areas, such as: a) improving the performance of t-distributed stochastic neighbor embedding (t-SNE) and spectral clustering using the underlying MC formulas, b) recovering astronomical low-dimensional structures and c) improving the performance of the Fast Parzen Window density estimator.1 While the proposed MC in this chapter is non-homogeneous (because of changes in pheromone vector), the MC can still be consider homogeneous between two updates of the pheromone.