Applying Newton's Law of Cooling to Transaction Scoring in DMP User Profiling

Background: In DMP user or product profiling, a common scoring requirement is to assign a normalized score based on transactions, considering time decay.

Requirements: More recent transactions should have higher weight, with decreasing influence that slows over time; all scores must be normalized to the 0‑100 range.

Data format: Input consists of user ID, date, category ID, and order count; the output is a user ID’s purchase intention score for each category.

Implementation: The author models transaction heat using Newton’s law of cooling, where heat decays exponentially with time, analogous to a hot object cooling toward ambient temperature.

Mathematical formulation: The cooling rate is proportional to the temperature difference between the object and the ambient; after integration and applying boundary conditions (heat = 100 at the transaction day, heat = 1 after 180 days, ambient = 0), the constant α is derived.

Example: A corpse temperature scenario is used to illustrate how to estimate the constant from observed cooling data.

Normalization: Raw scores are log‑scaled if the spread is too large, then mapped via a sigmoid‑like function to the open interval (0, 1) and finally scaled to 0‑100.