Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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A NODE PREDICTION ALGORITHM WITH THE MAPPER METHOD BASED ON DBSCAN AND GIOTTO-TDA

  • DONGJIN LEE (GRADUATE SCHOOL OF ARTIFICIAL INTELLIGENCE, POHANG UNIVERSITY OF SCIENCE AND TECHNOLOGY) ;
  • JAE-HUN JUNG (DEPARTMENT OF MATHEMATICS, POHANG UNIVERSITY OF SCIENCE AND TECHNOLOGY)
  • Received : 2023.11.30
  • Accepted : 2023.12.23
  • Published : 2023.12.25
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Abstract

Topological data analysis (TDA) is a data analysis technique, recently developed, that investigates the overall shape of a given dataset. The mapper algorithm is a TDA method that considers the connectivity of the given data and converts the data into a mapper graph. Compared to persistent homology, another popular TDA tool, that mainly focuses on the homological structure of the given data, the mapper algorithm is more of a visualization method that represents the given data as a graph in a lower dimension. As it visualizes the overall data connectivity, it could be used as a prediction method that visualizes the new input points on the mapper graph. The existing mapper packages such as Giotto-TDA, Gudhi and Kepler Mapper provide the descriptive mapper algorithm, that is, the final output of those packages is mainly the mapper graph. In this paper, we develop a simple predictive algorithm. That is, the proposed algorithm identifies the node information within the established mapper graph associated with the new emerging data point. By checking the feature of the detected nodes, such as the anomality of the identified nodes, we can determine the feature of the new input data point. As an example, we employ the fraud credit card transaction data and provide an example that shows how the developed algorithm can be used as a node prediction method.

Keywords

Acknowledgement

This work is supported by National Research Foundation of Korea under the grant number 2021R1A2C3009648 and POSTECH Basic Science Research Institute under the NRF grant number NRF2021R1A6A1A1004294412.

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