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 type and 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 methodby Jaffe (1989) to highlight additional findings .
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 .
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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
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
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a panel of
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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 type and length of
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
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) are correlated with firms' financial performances in a
in the Mapper graph, perform better. This association is
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manner. We then compare this approach with a widely used clustering methodby Jaffe (1989) to highlight additional findings
, 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