Master of Science

dissertationTopological data analysis (TDA) is an emerging field in data science. It lies at the intersection of algebraic topology, computational geometry, data analysis, machine learning, and data visualization. It captures geometric and topological information, which offers new insights into data. Topological data analysis is widely used in different disciplines, such as biology and neuroscience, business intelligence, and physics. Data cubes are data structures commonly used in astronomy for representing threedimensional (3D) universal spaces in various conditions. Most of them are generated from observations from surveys. In this thesis, we employ topological data analysis in the field of astronomy to build tools that help astronomers better understand their astronomical data cubes. First, we use contour tree (CT), a topological descriptor in TDA, to remove the noise from data cubes that arise from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) project of the Sloan Digital Sky Survey (SDSS). We demonstrate that contour tree is a good alternative for traditional Gaussian smoothing methods in denoising and simplifying MaNGA data cubes. Second we utilize persistent homology (PH), a classic technique in TDA, to detect cosmic voids and track their evolution from data cubes coming from Baryon Oscillation Spectroscopic Survey (BOSS) project of SDSS. We also built an interactive tool to visualize cosmic voids at different thresholds