We consider a challenging multi-label classification problem where both feature matrix \X and label matrix \Y have missing entries. An existing method concatenated \X and \Y as [\X;\Y] and applied a matrix completion (MC) method to fill the missing entries, under the assumption that [\X;\Y] is of low-rank. However, since entries of \Y take binary values in the multi-label setting, it is unlikely that \Y is of low-rank. Moreover, such assumption implies a linear relationship between \X and \Y which may not hold in practice. In this paper, we consider a latent matrix Z that produces the probability σ(Zij) of generating label Yij, where σ(⋅) is nonlinear. Considering label correlation, we assume [\X;Z] is of low-rank, and propose an MC algorithm based on subgradient descent named co-completion (COCO) motivated by elastic net and one-bit MC. We give a theoretical bound on the recovery effect of COCO and demonstrate its practical usefulness through experiments.
@article{arxiv.1805.09156,
title = {Matrix Co-completion for Multi-label Classification with Missing Features and Labels},
author = {Miao Xu and Gang Niu and Bo Han and Ivor W. Tsang and Zhi-Hua Zhou and Masashi Sugiyama},
journal= {arXiv preprint arXiv:1805.09156},
year = {2018}
}