Digital Commons Network^™

Machine Learning With Topological Data Analysis, Ephraim Robert Love

Doctoral Dissertations

Topological Data Analysis (TDA) is a relatively new focus in the fields of statistics and machine learning. Methods of exploiting the geometry of data, such as clustering, have proven theoretically and empirically invaluable. TDA provides a general framework within which to study topological invariants (shapes) of data, which are more robust to noise and can recover information on higher dimensional features than immediately apparent in the data. A common tool for conducting TDA is persistence homology, which measures the significance of these invariants. Persistence homology has prominent realizations in methods of data visualization, statistics and machine learning. Extending ML with …

Improving The Data Quality In Gravitation-Wave Detectors By Mitigating Transient Noise Artifacts, Kentaro Mogushi

Doctoral Dissertations

“The existence of gravitational waves (GWs), small perturbations in spacetime produced by accelerating massive objects was first predicted in 1916 as solutions of Einstein’s Theory of General Relativity (Einstein, 1916). Detecting and analyzing GWs produced by sources allows us to probe astrophysical phenomena.

The era of GW astronomy began from the first direct detection of the coalescence of a binary black hole in 2015 by the collaboration of the advanced Laser Interferometer Gravitational-wave Observatory (LIGO) (Aasi et al., 2015) and advanced Virgo (Abbott et al., 2016a). Since 2015, LIGO-Virgo detected about 50 confident transient events of GW signals (Abbott et …