  Multi-label classification studies the task where each example belongs to
multiple labels simultaneously. As a representative method, Ranking Support
Vector Machine (Rank-SVM) aims to minimize the Ranking Loss and can also
mitigate the negative influence of the class-imbalance issue. However, due to
its stacking-style way for thresholding, it may suffer error accumulation and
thus reduces the final classification performance. Binary Relevance (BR) is
another typical method, which aims to minimize the Hamming Loss and only needs
one-step learning. Nevertheless, it might have the class-imbalance issue and
does not take into account label correlations. To address the above issues, we
propose a novel multi-label classification model, which joints Ranking support
vector machine and Binary Relevance with robust Low-rank learning (RBRL). RBRL
inherits the ranking loss minimization advantages of Rank-SVM, and thus
overcomes the disadvantages of BR suffering the class-imbalance issue and
ignoring the label correlations. Meanwhile, it utilizes the hamming loss
minimization and one-step learning advantages of BR, and thus tackles the
disadvantages of Rank-SVM including another thresholding learning step.
Besides, a low-rank constraint is utilized to further exploit high-order label
correlations under the assumption of low dimensional label space. Furthermore,
to achieve nonlinear multi-label classifiers, we derive the kernelization RBRL.
Two accelerated proximal gradient methods (APG) are used to solve the
optimization problems efficiently. Extensive comparative experiments with
several state-of-the-art methods illustrate a highly competitive or superior
performance of our method RBRL.
