Understanding the Sparsity: Augmented Matrix Factorization with Sampled Constraints on Unobservables
By Yongfeng Zhang, Min Zhang, Yi Zhang, Yiqun Liu, Shaoping Ma. 2014
18 citations recorded by the source corpus.
An important problem of matrix completion/approximation based on Matrix Factorization (MF) algorithms is the existence of multiple global optima; this problem is especially serious when the matrix is sparse, which is common in real-world applications such as personalized recommender systems. In this work, we clarify data sparsity by bounding the solution space of MF algorithms. We present the conditions that an MF algorithm should satisfy for reliable completion of the unobservables, and we further propose to augment current MF algorithms with extra constraints constructed by compressive sampling on the unobserved values, which is well-motivated by the theoretical analysis. Model learning and optimal solution searching is conducted in a properly reduced solution space to achieve more accurate and efficient rating prediction performances. We implemented the proposed algorithms in the Map-Reduce framework, and comprehensive experimental results on Yelp and Dianping datasets verified the effectiveness and efficiency of the augmented matrix factorization algorithms.
Subfields: Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mathematics
In Computational Mechanics
In Computational Theory and Mathematics
Citations in the corpus
- Daily-Aware Personalized Recommendation based on Feature-Level Time Series Analysis (2015, background): “For example, [40] reported that about 49% of the users in Yelp made only a single review.”
- Incorporating Phrase-level Sentiment Analysis on Textual Reviews for Personalized Recommendation (2015, background): “Copyright is held by the owner/author(s).”