Do Similarity Measures Measure Similarity? How User Activity Creates Phantom Correlation in Recommender Systems

Item-item similarity is one of the oldest and most foundational signals in recommender systems: two items are assumed to be similar when the same users consume them. Despite the sparsity and scale of interaction data, the implicit assumption across the field is that item co-occurrence reflects genuine shared preference, capturing what users like together. In this paper, we demonstrate that a substantial fraction of observed item-item similarity is an artifact of variance in user activity rather than shared taste. Even if every user consumed items completely independently, differing only in their total consumption volume, standard similarity measures still detect strong associations between items. We term this phenomenon phantom correlation: spurious item association that emerges strictly from heterogeneous user activity in the complete absence of preference structure. Starting from minimal formal assumptions, we show that independent consumption under varying activity is described by a Rasch model, and we derive how the resulting association depends on item popularity for each similarity measure. By comparing our theoretical baseline against real-world benchmark datasets, we reveal the extent to which popular similarity measures reflect phantom correlation, which bears on how item co-occurrence is interpreted and used in collaborative filtering.