Mapping Firms' Locations in Technological Space : A Topological Analysis of Patent Statistics

We propose a new method to characterize firms' inventive activities via topological data analysis (TDA) that represents high-dimensional data in a shape graph. Applying this method to 333 major firms' patents in 1976—2005 reveals substantial heterogeneity: some firms remain undifferentiated; others develop unique portfolios. Firms with unique trajectories, which we define graph-theoretically as "flares" in the Mapper graph, perform better. This association is statistically and economically significant, and continues to hold after we control for portfolio size and firm survivor-ship. Comparison with existing techniques suggests the method's usefulness for data visualization and exploratory empirical research more generally