Matrix completion on learnt graphs: Application to collaborative filtering

Aanchal Mongia

doi:10.1016/j.eswa.2021.115652

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Matrix completion on learnt graphs: Application to collaborative filtering

2021-12-01

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Aanchal Mongia

Angshul Majumdar *

DOI：10.1016/j.eswa.2021.115652

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Abstract

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There are two broad frameworks for collaborative filtering. Chronologically, the neighborhood based models came first - they were based on linear interpolation where the interpolation weights were proportional to the similarities between users' and items'. Latent factor models were introduced later; they were based on the underlying assumption that the data matrix is low-rank. Both the approaches essentially completed the partially observed rating matrix. These two approaches were later combined by regularizing the latent factor model with graph Laplacian computed from the similarities defined in the neighborhood based models. However, this graph was computed from partially observed data and may have failed to represent the true similarities. This work addresses this issue; instead of computing the graph and assuming it to be fixed during the matrix completion process, we will alternate between updating (refining) the graph assuming the matrix to be fully observed, and completing the matrix, assuming the graph to be fixed. Benchmarking with fixed graph techniques as well as state-of-the-art collaborative filtering algorithms on popular Movielens datasets have shown that our proposed approach indeed improves over the rest.

Keywords:

Matrix completion

Graph representation

Collaborative filtering

Recommender system

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