Efficient Rectangular Maximal-Volume Algorithm for Rating Elicitation in Collaborative Filtering

TL;DR

This paper introduces a fast, generalized Rectangular Maxvol algorithm for selecting seed sets in collaborative filtering, allowing flexible rank choices and improving recommendation quality for cold start problems.

Contribution

It presents a novel, efficient algorithm that generalizes Maxvol for seed set selection with variable rank, enhancing collaborative filtering methods.

Findings

The proposed algorithm is faster than existing methods.

It provides theoretical error bounds for seed set selection.

Comparative analysis shows improved performance over state-of-the-art approaches.

Abstract

Cold start problem in Collaborative Filtering can be solved by asking new users to rate a small seed set of representative items or by asking representative users to rate a new item. The question is how to build a seed set that can give enough preference information for making good recommendations. One of the most successful approaches, called Representative Based Matrix Factorization, is based on Maxvol algorithm. Unfortunately, this approach has one important limitation --- a seed set of a particular size requires a rating matrix factorization of fixed rank that should coincide with that size. This is not necessarily optimal in the general case. In the current paper, we introduce a fast algorithm for an analytical generalization of this approach that we call Rectangular Maxvol. It allows the rank of factorization to be lower than the required size of the seed set. Moreover, the paper includes the theoretical analysis of the method's error, the complexity analysis of the existing methods and the comparison to the state-of-the-art approaches.