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Collaborative filtering is the oldest and simplest form of recommender systems. It used to be widely deployed in multitudes of internet and high-tech companies. In this paper, we prove that the collaborative filtering is wrong based on topological and geometric analysis of the algorithm. We show that the similarity graph of the collaborative filtering is a circle when the data is projected into 2D space by dimensionality reduction methods. By applying Poincare-Hopf Theorem to a class of vector fields defined on the 2D circle, we show that the collaborative filtering algorithm is ill-defined.

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Collaborative Filtering is Wrong and Here is Why

  • 会议论文

  • 发表日期：

    2025年

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  • Hao Wang

摘要

Collaborative filtering is the oldest and simplest form of recommender systems. It used to be widely deployed in multitudes of internet and high-tech companies. In this paper, we prove that the collaborative filtering is wrong based on topological and geometric analysis of the algorithm. We show that the similarity graph of the collaborative filtering is a circle when the data is projected into 2D space by dimensionality reduction methods. By applying Poincare-Hopf Theorem to a class of vector fields defined on the 2D circle, we show that the collaborative filtering algorithm is ill-defined.