[20210402 : Colloquium]
Topological data analysis and its application to Korean music (Jeong-Ak) data
1. 일시 : 2021년 4월 2일 (금) 16:00-17:00
2. 장소 : Zoom을 이용한 실시간 온라인 강연
- Zoom링크 :
https://korea-ac-kr.zoom.us/j/85782653817?pwd=U3d5c2NCWHlCamJlMmErVXNCSUdCZz09
3. 연사 : 정재훈 교수 (포항공대 수학과)
4. 제목 : Topological data analysis and its application to Korean music (Jeong-Ak) data
5. 초록 : Topological Data Analysis (TDA) is rising field useful for the analysis of high-dimensional data structure. The main tool in TDA is persistent homology, introduced by Edelsbrunner et al. in 2002, where snapshots of the topological structure of the data set is taken at many different scales and the results are compared from one scale to the next. TDA via persistent homology provides an efficient way of analyzing the cycle or loop structures embedded in multi-dimensional data. Particularly the one-dimensional homology structure is closely related to the repeating patterns in music flow when it mapped to the proper topological space. In this talk, we first explain TDA and related research. Then we apply TDA to Korean Jeong-Ak music data written in Jeongganbo, particularly to Suyeonjang, Songuyeo, and Taryong, those well-known pieces played at the palace and among noble community. We define and determine the node elements of each music, characterized uniquely with its pitch and length. Then we transform the music into a graph and define the distance between the nodes as their adjacent occurrence rate. The graph is used as a point cloud whose homological structure is investigated by measuring the hole structure in each dimension. We identify cycles of each music, match those in Jeongganbo, and show how those cycles are interconnected. Finally, we will demonstrate a music piece composed by the machine based on the patterns found through TDA.