Where do firms innovate? Mapping their locations and directions in technological space is challenging due to its high dimensionality. 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 then compare our approach with existing techniques to further demonstrate its use in data visualization and exploration.

翻译：在技术空间中绘制位置和方向图因其高度多维性而具有挑战性。 我们提出一种新的方法,通过地形数据分析(TDA)来描述公司的发明活动,该方法在形状图中代表了高维数据。 将这种方法应用于1976-2005年的333个大公司的专利,揭示了巨大的差异性:一些公司仍然没有差异;另一些公司则开发了独特的组合。 具有独特的轨迹的公司,我们在地图图中将其图形-理论定义为“Flares ”, 其表现更好。 这个协会具有统计和经济意义,并且在我们控制投资组合规模和公司生存能力之后继续维持。 然后我们将我们的方法与现有技术进行比较,以进一步展示其在数据可视化和探索中的用途。