Multi-source partial multi-label learning via tensor decomposition and nonconvex regularization

Abstract

Multi-source partial multi-label learning (MSPMLL) aims to learn a multi-label classifier from training examples with multi-source features and multiple labels. Most of the existing MSPMLL models tackle each source independently to derive classifiers. Those methods cannot efficiently reveal the intrinsic structure and relationships among instances across different sources, nor deal with inconsistent labels caused by noise. To address those challenges, this paper proposes a tensor decomposition and nonconvex regularization approach to multi-source partial multi-label learning, nominated as MSPML-TLR. In this model, a hypergraph based affinity graph is constructed from each of multi-source data in the feature space. A tensor representation of multi-source multi-label data is proposed based on the affinity graphs. A multi-linear projection is learned to map the feature affinity space to a latent ground-truth label space via tensor robust principal component analysis. Furthermore, a notion called the parameterized tensorial logarithmic rank is designed to approximate the rank of the multi-linear projection and the latent ground-truth label tensor. Moreover, a hypergraph-based Laplacian regularization is imposed on each frontal slice of the latent ground-truth label tensor to preserve the topological structure of instances across multi-source feature spaces. An efficient algorithm is designed to implement MSPML-TLR and the convergence of the algorithm is rigorously proven. Extensive experiments on various real-world benchmark datasets demonstrate that the proposed model outperforms state-of-the-art methods in multi-label classification tasks.