We study multi-label classification (MLC) with three important real-world issues: online updating, label space dimensional reduction (LSDR), and cost-sensitivity. Current MLC algorithms have not been designed to address these three issues simultaneously. In this paper, we propose a novel algorithm, cost-sensitive dynamic principal projection (CS-DPP) that resolves all three issues. The foundation of CS-DPP is an online LSDR framework derived from a leading LSDR algorithm. In particular, CS-DPP is equipped with an efficient online dimension reducer motivated by matrix stochastic gradient, and establishes its theoretical backbone when coupled with a carefully-designed online regression learner. In addition, CS-DPP embeds the cost information into label weights to achieve cost-sensitivity along with theoretical guarantees. Experimental results verify that CS-DPP achieves better practical performance than current MLC algorithms across different evaluation criteria, and demonstrate the importance of resolving the three issues simultaneously.
