School of Commerce, Meiji University, Tokyo, Japan.
Research Institute of Economy, Trade and Industry, Tokyo, Japan.
PLoS One. 2021 Feb 3;16(2):e0245531. doi: 10.1371/journal.pone.0245531. eCollection 2021.
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.
如今，消费品市场发展迅速，信息媒体数量和竞争产品数量都显著增长。在这种环境下，要定量掌握企业和客户之间的异质互动，这引起了管理科学家和经济学家的兴趣，这需要分析极高维度的数据。现有的定量研究方法，如果没有可靠的先验知识或强假设，就无法处理此类数据。相反，我们提出了一种称为复杂希尔伯特主成分分析（CHPCA）的新方法，并使用 Hodge 分解构建了一个同步网络。CHPCA 使我们能够提取数据中具有时间领先/延迟的重要共变，而 Hodge 分解对于识别相关性的时间结构很有用。我们将该方法应用于日本啤酒市场数据，并揭示了多个产品中与消费者选择过程相关的变量的共变。此外，我们通过计算每个客户在 CHPCA 结果得出的空间中的坐标，发现了显著的客户异质性。最后，我们讨论了所提出方法的政策和管理意义、局限性和进一步发展。
