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# Multi-label Subspace Ensemble

*Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics*, PMLR 22:1444-1452, 2012.

#### Abstract

A challenging problem of multi-label learning is that both the label space and the model complexity will grow rapidly with the increase in the number of labels, and thus makes the available training samples insufficient for training a proper model. In this paper, we eliminate this problem by learning a mapping of each label in the feature space as a robust subspace, and formulating the prediction as finding the group sparse representation of a given instance on the subspace ensemble. We term this approach as “multi-label subspace ensemble (MSE)”. In the training stage, the data matrix is decomposed as the sum of several low-rank matrices and a sparse residual via a randomized optimization, where each low-rank part defines a subspace mapped by a label. In the prediction stage, the group sparse representation on the subspace ensemble is estimated by group lasso. Experiments on several benchmark datasets demonstrate the appealing performance of MSE.