Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article

Degree

Master of Science

Program

Statistics and Actuarial Sciences

Supervisor

Yu, Hao

2nd Supervisor

Kulperger, Reg J.

Co-Supervisor

3rd Supervisor

Valluri, Sree R.

Co-Supervisor

Abstract

Elastic distances, e.g. dynamic time warping (DTW), evaluate the similarity between query and reference sequences by dynamic programming. The 1-Nearest-Neighbor predictor with DTW is one benchmark in time series classification. However, DTW is less efficient in astronomical time series because of ignorance of the information in time stamps and its dependence on the shape and magnitude between query and reference sequences. We apply two elastic distances which integrate the information in the time domain, time warp editing distance (TWED) and Skorohod distance, which is calculated by using Fre ́chet distance, to three astronomical datasets to compare with DTW and Euclidean distance. The first dataset aims to classify signals emitted from various astronomical sources with multiple bandpasses from the Large Synoptic Survey Telescope (LSST). The TWED shows the optimal 1-NN classification performance with a 0.74 loose accuracy. In the second dataset, we explore the possibility of shrinking the size of the gravitational wave (GW) template banks to reduce the computational waste of matching data with similar templates. With the threshold of 5%, similar templates can be removed without losing the effectualness of the template bank. In the final dataset from LIGO and Virgo detections, we establish an early warning process of GW by locating the coincident period between detectors. Though DTW distance outperforms others, TWED achieves a 0.72 detection ratio and a 0.47 average significant ratio. These results of three astrophysical datasets reveal the applicability of elastic distances in the astrophysical domain, especially TWED.

Summary for Lay Audience

Elastic distances, e.g. dynamic time warping (DTW), evaluate the similarity between query and reference sequences by dynamic programming. Unlike Euclidean distance, elastic distances allow misalignment between indices. With minimal matching by misalignment, the traditional DTW distance embedded in the 1-Nearest Neighbor predictor (1-NN) is one benchmark used in time series classification. But DTW is less efficient in astrophysical time series because DTW distance focuses only on shape and magnitude between sequences and ignores the information in distortion in time stamps. To overcome this, in this thesis, we introduce two elastic distances which integrate the misalignment in the time domain: time warp editing distance (TWED) and Skorohod distance, which is calculated by using Fre ́chet distance. Then we apply two elastic distances in three astrophysical datasets and compare them with Euclidean and DTW distances, to explore the applicability of elastic distances in the astrophysical field. The first dataset aims to classify signals emitted from various astronomical sources with multiple bandpasses from the Large Synoptic Survey Telescope (LSST). The TWED shows the optimal 1-NN classification performance with the highest accuracy. We also have experiments on gravitational wave datasets. In 2015, LIGO and Virgo Collaborations generated multiple template banks and detected the first GW signal by matched filtering. In the second dataset, we simulate GW from the merger of binary black holes and construct a toy template bank. By evaluating the elastic distance between templates, we shrink the size of the template bank to reduce the computational waste of matching data with similar templates. With the threshold of 5%, similar templates can be removed without losing the effectualness of the template bank. In the final dataset with raw data from GW detections, we establish an early warning process of GW by locating the coincident period between detectors, where coincidence is measured by elastic distance. Though DTW distance outperforms others, TWED achieves a 0.72 detection ratio and a 0.47 average significant ratio. These results reveal the applicability of elastic distances in the astrophysical domain, especially TWED.

Additional Files
Xiyang_Zhang_Thesis_Change_Report.docx (71 kB)
Download

Share

COinS