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 survivorship. Comparison with existing techniques suggests the method 's usefulness for data visualization and exploratory empirical research more generally .
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 survivorship. We further illustrate Mapper 's usefulness for exploratory data analysis in comparison with existing techniques .
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1976-2005
1976--2005
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Comparison with existing techniques suggests the method
We further illustrate Mapper
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data visualization and exploratory empirical research more generally
exploratory data analysis in comparison with existing techniques