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The Ohio State University

1. Zha, Xiao. Topological Data Analysis on Road Network Data.

Degree: Master of Mathematical Sciences, Mathematical Sciences, 2019, The Ohio State University

Many problems in science and engineering involve signal analysis. Engineers and scientists came up with many approaches to study signals. Recently, researchers propose a new frame- work, combining the time-delay embedding with the tools from computational topology, for the study of periodic signals. By applying time-delay embedding to the periodic signals, the periodic behaviors express themselves as topological cycles and we can use persistent homol- ogy to detect these topological features. In this thesis, we apply this method to analyze road network data, specifically vehicle flow data recorded by detectors placed on highways. First, we apply time-delay embedding to project the vehicle flow data into point cloud data in a high dimensional space. Then, we use persistent homology tools to detect the topological features and get persistence digram. Next, we can repeat the same experiment to vehicle flow data of different period. Fox example, in our experiment, we use the vehicle flow data of different weeks and months. Therefore, we get persistence diagrams corresponding to the vehicle flow data of different period. Finally, we calculate the bottleneck distance and wasserstein distance between these persistence diagrams and do hierarchical clustering. The dendrograms of the hierarchical clustering show us the patterns behind these vehicle flow data. Advisors/Committee Members: Mémoli, Facundo (Advisor), Wang , Yusu (Advisor).

Subjects/Keywords: Mathematics; TDA; road network data; time-delay embedding; persistent homology

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APA (6th Edition):

Zha, X. (2019). Topological Data Analysis on Road Network Data. (Masters Thesis). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu155563664988436

Chicago Manual of Style (16th Edition):

Zha, Xiao. “Topological Data Analysis on Road Network Data.” 2019. Masters Thesis, The Ohio State University. Accessed September 19, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu155563664988436.

MLA Handbook (7th Edition):

Zha, Xiao. “Topological Data Analysis on Road Network Data.” 2019. Web. 19 Sep 2019.

Vancouver:

Zha X. Topological Data Analysis on Road Network Data. [Internet] [Masters thesis]. The Ohio State University; 2019. [cited 2019 Sep 19]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu155563664988436.

Council of Science Editors:

Zha X. Topological Data Analysis on Road Network Data. [Masters Thesis]. The Ohio State University; 2019. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu155563664988436

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