Detection of Gravitational Wave using Topological based Data Analysis: Non-spinning Binary Black Holes Coalescing event
Gravitational waves are one of the direct predictions of Einstein’s equations and produced by a broad range of events in a vast wide frequency ranges. Binary black holes coalescing is one of the strongest sources of gravitational waves. In this research we decided to present a guideline to detect gravitational waves from non-spinning binary black holes coalescing with simulation and computational approaches, by using topological data analysis. For this purpose, we simulated 2000 samples of gravitational wave time series caused by non-spinning binary black holes coalescing and systematic noise in a same number as well. By applying the Gaussian kernel and performing sliding window embedding method to construct a higher dimension field than the simulated time-series, we computed persistent homology in template of betti curves. Betti curves have been resistant toward noises and can be considered as feature vectors. We have utilized the obtained feature vectors as input in a support vector machine learning model (SVM). The results indicate the maximum value of accuracy is 0.973 according to the different signal to noise ratio for embedding-dimension of 8 and time-delay of 1.