*Yi Liu, Rong Jin, Liu Yang*

We present a novel framework for multi-label learning that explicitly addresses the challenge arising from the large number of classes and a small size of training data. The key assumption behind this work is that two examples tend to have large overlap in their assigned class memberships if they share high similarity in their input patterns. We capitalize this assumption by first computing two sets of similarities, one based on the input patterns of examples, and the other based on the class memberships of the examples. We then search for the optimal assignment of class memberships to the unlabeled data that minimizes the difference between these two sets of similarities. The optimization problem is formulated as a constrained Non-negative Matrix Factorization (NMF) problem, and an algorithm is presented to efficiently find the solution. Compared to the existing approaches for multi-label learning, the proposed approach is advantageous in that it is able to explore both the unlabeled data and the correlation among different classes simultaneously. Experiments with text categorization show that our approach performs significantly better than several state-of-the-art classification techniques when the number of classes is large and the size of training data is small.

*Subjects:* 12. Machine Learning and Discovery

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