革新知能統合研究センター

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Topological Data Analysis Team (https://aip.riken.jp/labs/generic_tech/topology_data_anl/) at RIKEN AIP

Speaker 1 (15:00-15:25): Yasu Hiraoka
Title: Overview of topological data analysis
Abstract: Topological data analysis (TDA) is an emerging concept in applied mathematics in which we characterize “shape of massive and complex data” using topological methods. In particular, persistent homology and mapper are nowadays applied to a wide variety of scientific and engineering problems including materials science, life science and social networks etc. By combining various mathematics such as topology, representation theory, statistics and probability theory, our group has succeeded in making topological data analysis powerful and general methods for practical problems. In this talk, I will explain an overview of recent progress of TDA.

Speaker 2 (15:30-16:10): Ippei Obayashi
Title: Software and applications of persistent homology
Abstract: I will introduce practical aspect of persistent homology.
The topics will be software, useful matmethacal tools (the combination
of machine learning and inverse analysis), and applications to
materials science.

Speaker 3 (16:15-16:55): Emerson Escolar
Title: Mapping Firms’ Locations in Technological Space: A Topological Analysis of Patent Statistics
Abstract: Mapper, one of the main tools of topological data analysis, is able to compactly summarize and represent complicated high-dimensional data in a graph. In this work, we apply this method to 333 major firms’ patents in 1976-2005 to visualize firms’ technological space of inventive activities as a Mapper graph. We observe branch-like structures called “flares” related to firms with unique trajectories in the Mapper graph, and thus propose an algorithm to extract them. We find statistically and economically significant correlations between the flares and financial performance. This talk is based on joint work (https://arxiv.org/abs/1909.00257) with Yasuaki Hiraoka, Mitsuru Igami, and Yasin Ozcan.