Matrix Co-completion for Multi-label Classification with Missing Features and Labels
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We consider a challenging multi-label classification problem where both feature matrix and label matrix have missing entries. An existing method concatenated and as [; ] and applied a matrix completion (MC) method to fill the missing entries, under the assumption that [; ] is of low-rank. However, since entries of take binary values in the multi-label setting, it is unlikely that is of low-rank. Moreover, such assumption implies a linear relationship between and which may not hold in practice. In this paper, we consider a latent matrix that produces the probability σ(Z_ij) of generating label Y_ij, where σ(·) is nonlinear. Considering label correlation, we assume [; ] 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.
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