A New Approach to Collaborative Filtering: Operator Estimation with Spectral Regularization

2008/02/11 by Jacob Abernethy, Abernethy, Jacob, Francis Bach +5 · 2 citations
Engineering · #Advanced Adaptive Filtering Techniques #FOS: Computer and information sciences #Indoor and Outdoor Localization Technologies #Machine Learning (cs.LG) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.0802.1430

openalex publication_date 2008/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a general approach for collaborative filtering (CF) using spectral regularization to learn linear operators from "users" to the "objects" they rate. Recent low-rank type matrix completion approaches to CF are shown to be special cases. However, unlike existing regularization based CF methods, our approach can be used to also incorporate information such as attributes of the users or the objects -- a limitation of existing regularization based CF methods. We then provide novel representer theorems that we use to develop new estimation methods. We provide learning algorithms based on low-rank decompositions, and test them on a standard CF dataset. The experiments indicate the advantages of generalizing the existing regularization based CF methods to incorporate related information about users and objects. Finally, we show that certain multi-task learning methods can be also seen as special cases of our proposed approach.

Citations

• Empirical Analysis of Predictive Algorithms for Collaborative Filtering
• Local Minima and Convergence in Low-Rank Semidefinite Programming
• Consistency of trace norm minimization

Cited by

• A double iteratively reweighted algorithm for solving group sparse nonconvex optimization models
• Efficient Pairwise Learning Using Kernel Ridge Regression: an Exact Two-Step Method

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