  Today's consumer goods markets are rapidly evolving with significant growth
in the number of information media as well as the number of competitive
products. In this environment, obtaining a quantitative grasp of heterogeneous
interactions of firms and customers, which have attracted interest of
management scientists and economists, requires the analysis of extremely
high-dimensional data. Existing approaches in quantitative research could not
handle such data without any reliable prior knowledge nor strong assumptions.
Alternatively, we propose a novel method called complex Hilbert principal
component analysis (CHPCA) and construct a synchronization network using Hodge
decomposition. CHPCA enables us to extract significant comovements with a time
lead/delay in the data, and Hodge decomposition is useful for identifying the
time-structure of correlations. We apply this method to the Japanese beer
market data and reveal comovement of variables related to the consumer choice
process across multiple products. Furthermore, we find remarkable customer
heterogeneity by calculating the coordinates of each customer in the space
derived from the results of CHPCA. Lastly, we discuss the policy and managerial
implications, limitations, and further development of the proposed method.
