Pattern-Based Recommender System Using Nuclear Norm Minimization of Three-Mode Tensor and Quantum Fidelity-Based K-Means

Abstract

Recommender systems (RSs) consist of predicting missing ratings based on the observed ones. This problem corresponds to matrix completion where users are its rows and items are its columns and it contains the observed ratings. An efficient RS is the one promoting the personal relevancy of its users which is not the case in the matrix completion process. It takes into account all the rates for prediction without including the users’ and items’ characteristics. Patterns are the key enablers of such solutions. In this work, we present a three-mode tensor representation with two aspects namely user–item interactions (observed ratings) and item–item relationship (detected similarities). To capture the similarities, the patterns are grouped in an equivalent manner using a bi-quantum clustering process (Quantum K-means). This step is adopted to consider only the relevant observed ratings in the prediction process and express item-to-item relationship using fidelity distance. Then, for each missing rating r that a user u might give to an item i in the future, a sub-tensor is created according to the detected patterns. This sub-tensor then is completed by minimizing its rank. This problem is NP-hard, hence a surrogate is used which is the nuclear norm. The effectiveness of the proposed approach is measured according to information retrieval evaluation criteria: precision, recall and [Formula: see text]-measure. The proposed approach improved the precision of the state-of-the-art methods by 20[Formula: see text].