Searching for Multiple Low-dimensional Needles in a Higher-dimensional Haystack
Peter Tino
Department of Complex and Adaptive Systems
University of Birmingham, UK
Abstract. The data can be distributed around an unknown number of low-dimensional noisy manifolds of diverse and unknown dimensionalities, immersed in a (possibly intense) background noise. It is up to us to detect all the distinct manifolds, construct smooth models of their skeletons and provide the corresponding explicit probabilistic noisy manifold models. To that end, we will generalize Generative Topographic Mapping to abstract latent spaces, so that arbitrary low-dimensional manifolds can be modeled (including non-orientable ones, e.g., Moebius strip). We will show how such latent spaces can be constructed through a dedicated manifold crawling procedure and then smoothly embedded in the data space. Finally, the noisy manifolds are captured by endowing the embedded latent spaces with suitable probabilistic models. We will illustrate the methodology in the context of detection of low-dimensional manifold structures emerging in astrophysics. In particular, we will show how a dwarf galaxy disruption process in a galaxy cluster can be analyzed in a new way through probabilistic modelling of streams, bubbles and shells forming part of the "jellyfish" galactic structure. We will also demonstrate how this methodology can be used to study formation of large-scale dark matter filaments and dynamics around them in cosmological simulations.