Fast Global and Local Semi-Supervised Learning via Matrix Factorization

Matrix factorization has demonstrated outstanding performance in machine learning. Recently, graph-based matrix factorization has gained widespread attention. However, graph-based methods are only suitable for handling small amounts of data. This paper proposes a fast semi-supervised learning method using only matrix factorization, which considers both global and local information. By introducing bipartite graphs into symmetric matrix factorization, the technique can handle large datasets effectively. It is worth noting that by utilizing tag information, the proposed symmetric matrix factorization becomes convex and unconstrained, i.e., the non-convex problem min x ( 1 − x 2 ) 2 is transformed into a convex problem. This allows it to be optimized quickly using state-of-the-art unconstrained optimization algorithms. The computational complexity of the proposed method is O ( n m d ) , which is much lower than that of the original symmetric matrix factorization, which is O ( n 2 d ) , and even lower than that of other anchor-based methods, which is O ( n m d + m 2 n + m 3 ) , where n represents the number of samples, d represents the number of features, and m ≪ n represents the number of anchors. The experimental results on multiple public datasets indicate that the proposed method achieves higher performance in less time.