Matrix Factorization From a Few Dominators.

Area of Science:

• Data Science
• Machine Learning
• Computational Mathematics

Background:

• Real-world datasets often have nonuniformly distributed observations, unlike the uniform distribution assumed by many existing matrix completion algorithms.
• The Pareto principle, where a few causes dominate effects, is applicable to matrix completion problems with sparse data.

Purpose of the Study:

• To propose a novel matrix factorization approach for recovering large-scale matrices from nonuniformly distributed observations.
• To address the limitations of existing algorithms that assume uniform data distribution.

Main Methods:

• A matrix factorization technique is employed to reconstruct a matrix from a dominating submatrix, identified using a term frequency-inverse document frequency-inspired importance measure for rows and columns.
• The selected submatrix is recovered using a base matrix factorization algorithm, and its factors are then used to infer the factors of the entire matrix via linear regression.

Main Results:

• The proposed method demonstrates effectiveness in recovering matrices from nonuniformly distributed observations.
• Numerical experiments validate the approach's performance in challenging data scenarios.

Conclusions:

• The developed framework offers an effective solution for matrix completion with sparse, nonuniform data.
• The approach is inherently suitable for parallel and distributed computing, making it viable for massive datasets.