Enhancing Group Recommendation using Soft Impute Singular Value Decomposition

TL;DR

The paper addresses group recommendation under sparse, high-dimensional user-item data by introducing Group Soft-Impute SVD (GSI-SVD), a low-rank matrix completion approach that augments user-item data with a weighted group aggregation. The method solves a convex relaxation using the nuclear norm $||Z||_{*}$ and applies a soft-thresholded SVD update, enabling efficient, low-rank reconstruction with warm starts and geometric convergence. Empirical evaluation on Goodbooks, Movielens, and synthetic datasets shows that GSI-SVD can yield lower recovered ranks and competitive or improved recall for small groups, with performance comparable to baselines for larger groups. The work demonstrates a scalable mechanism for group-level recommendations in sparse settings and discusses future scalability improvements for very large groups and optimization strategies.

Abstract

The growing popularity of group activities increased the need to develop methods for providing recommendations to a group of users based on the collective preferences of the group members. Several group recommender systems have been proposed, but these methods often struggle due to sparsity and high-dimensionality of the available data, common in many real-world applications. In this paper, we propose a group recommender system called Group Soft-Impute SVD, which leverages soft-impute singular value decomposition to enhance group recommendations. This approach addresses the challenge of sparse high-dimensional data using low-rank matrix completion. We compared the performance of Group Soft-Impute SVD with Group MF based approaches and found that our method outperforms the baselines in recall for small user groups while achieving comparable results across all group sizes when tasked on Goodbooks, Movielens, and Synthetic datasets. Furthermore, our method recovers lower matrix ranks than the baselines, demonstrating its effectiveness in handling high-dimensional data.

Figures (4)

• Figure 1: Proposed Methodology
• Figure 2: Test error-Training error vs Nuclear norm.
• Figure 3: Log-scale plot of the relative error across iterations.
• Figure 4: Performance comparison of GSI-SVD, AF, and WBF for different user group sizes across (a) Goodbooks, (b) Movielens, and (c) Synthetic datasets.