Bi-Orthogonal Non-negative Tensor tri-Factorization for Tensorized Label Learning

Recently, multimedia data analysis based on non-negative tensor factorization (NTF) has become a hot research topic, but these methods mainly focus on 2-factor factorization and cannot effectively explore the complex structures hidden in multimedia data, especially for graph multimedia data. In this paper, analysis for 3-factor NTF X = U * C * G T is provided in detail. Specifically, constrained 3-factor NTF helps provide new features to constrained 2-factor NTF. We herein study bi-orthogonal constraint due to the fact that it leads to rigorous interpretability of clustering. After that, we apply it to multimedia data label learning and produce a novel co-multi-view label learning based on bi-orthogonal 3-factor NTF. Extensive experiments show the capability of bi-orthogonal 3-factor NTF on simultaneously clustering anchors and samples of the input data matrix.