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Topological Data Analysis on Road Network Data

Zha, Xiao
http://rave.ohiolink.edu/etdc/view?acc_num=osu155563664988436

Abstract Details

2019, Master of Mathematical Sciences, Ohio State University, Mathematical Sciences.
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.
Facundo Mémoli (Advisor)
Yusu Wang (Advisor)
54 p.
Mathematics
TDA; road network data; time-delay embedding; persistent homology

Recommended Citations

Citations

  • Zha, X. (2019). Topological Data Analysis on Road Network Data [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu155563664988436

    APA Style (7th edition)

  • Zha, Xiao. Topological Data Analysis on Road Network Data. 2019. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu155563664988436.

    MLA Style (8th edition)

  • Zha, Xiao. "Topological Data Analysis on Road Network Data." Master's thesis, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu155563664988436

    Chicago Manual of Style (17th edition)

osu155563664988436
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This open access ETD is published by The Ohio State University and OhioLINK.