Mathematical formulation of the purchase funnel by using knowledge space theory

The retail industry provides customers with goods or services. Analyzing the purchase behavior of customers is critical for expanding the business. Therefore, managing the repurchase intention of customers is crucial. A sequence of purchase behaviors by each customer constitutes a set of purchase Customer Journeys (purchase CJs), which detail purchase pathways and repurchase behaviors. Purchase CJs are the actual retail transaction data. This study investigated purchase CJs and proposed a purchase funnel called CJ graph (CJG) by measure theory and knowledge space theory with actual retail transaction data. To achieve this objective, a Customer Journey Block (CJB), denoting “touchpoint,” is defined as a series of purchase behaviors during a period and used as the base of this method. Each touchpoint is allotted a measurable function, named Purchase Measure (PM). By integrating all the CJBs of purchase CJs, the Purchase Measure Graph (PMG) can be constructed as the primary structure of the PM knowledge structure. Finally, when all CJs are coordinatized with CJ codes, knowledge space theory is used to develop the Customer Journey Graph (CJG). In this method, knowledge bases are used as the spanning framework of the CJ knowledge space, and the filtering property of the purchase funnel is illustrated. Furthermore, to validate the feasibility of the proposed method, a set of two-year and one million transactions retail data generated from more than thirty-six thousand customers was segmented by Recency, Frequency, and Monetary (RFM) model. Thus, the corresponding PMGs and CJGs of various (12, here) customer segments are detailed, and the resultant knowledge bases of the primary purchases and secondary re-purchases are applied to analyze and predict the customer purchase behaviors accurately.