🍩 Database of Original & Non-Theoretical Uses of Topology

1. Mapping Firms' Locations in Technological Space: A Topological Analysis of Patent Statistics (2020)

   Emerson G. Escolar, Yasuaki Hiraoka, Mitsuru Igami, Yasin Ozcan

   Abstract

   Where do firms innovate? Mapping their locations in technological space is difficult, because it is high dimensional and unstructured. We address this issue by using a method in computational topology called the Mapper algorithm, which combines local clustering with global reconstruction. We apply this method to a panel of 333 major firms’ patent portfolios in 1976–2005 across 430 technological areas. Results suggest the Mapper graph captures salient patterns in firms’ patenting histories, and our measures of their uniqueness (the length of “flares”) are correlated with firms’ financial performances in a statistically and economically significant manner. We then compare this approach with a widely used clustering method by Jaffe (1989) to highlight additional findings.

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   • Patent statistics
   • Patents
   • Mapper
   • Principal component analysis