Multi-Manifold learning in comparison of astronomical observations and numerical simulations

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Canducci, Marco ORCID: https://orcid.org/0000-0003-2264-9743 (2022). Multi-Manifold learning in comparison of astronomical observations and numerical simulations. University of Birmingham. Ph.D.

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Abstract

The intrinsic nature of noisy and complex data sets is often concealed in low-dimensional structures embedded in a higher dimensional space. Number of methodologies have been developed to extract and represent such structures in the form of manifolds (i.e. geometric structures that locally resemble continuously deformable intervals of Rj 1). Usually a-priori knowledge of the manifold’s intrinsic dimensionality is required. Additionally, their performance can often be hampered by the presence of a significant high-dimensional noise aligned along the low-dimensional core manifold. In real-world applications, the data can contain several low-dimensional structures of different dimensionalities. This work describes a framework for dimensionality estimation and reconstruction of multiple noisy manifolds embedded in a noisy environment. The workings of the framework are demonstrated on different synthetic data sets, presenting challenging features for state-of-the-art techniques in Multi-Manifold learning. Through these worked examples it is shown how the proposed methodology is able to model abstract and topologically
challenging manifolds such as Möbius strip and toroids (also higher dimensional). The comparison with existing techniques is organized along the two separate aspects of the methodology, namely manifold approximation and probabilistic modelling. The framework is then applied to astronomical complex data set containing simulated gas volume particles from a particle simulation of a dwarf galaxy interacting with its host galaxy cluster and a Dark Matter simulation of the Large Scale Structure (LSS) of the Universe (Cosmic Web).
Detailed analysis of the recovered 1D and 2D manifolds can help in understanding the nature of Star Formation in such complex systems and to link the kinematic properties of Dark Matter filaments with their galaxies. An additional case study is presented for the modelling of cavities in a Jellyfish galaxy. Tracking their evolution through time may help in understanding their origin.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):