# Matrix Co-completion for Multi-label Classification with Missing Features and Labels Source: [Matrix Co-completion for Multi-label Classification with Missing Features and Labels]() Collection index: [llms.txt]() Data updated: 2025-10-25T21:02:11.964Z Authors: Miao Xu, Gang Niu, Bo Han, Ivor W. Tsang, Zhi-Hua Zhou, Masashi Sugiyama Published: 2018-05-23T13:39:29.000Z ## Abstract 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 $\\sigma(Z\_{ij})$ of generating label $Y\_{ij}$, where $\\sigma(\\cdot)$ 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()