Multi-label core vector machine with a zero label

Multi-label core vector machine (Rank-CVM) is an efficient and effective algorithm for multi-label classification. But there still exist two aspects to be improved: reducing training and testing computational costs further, and detecting relevant labels effectively. In this paper, we extend Rank-CVM via adding a zero label to construct its variant with a zero label, i.e., Rank-CVMz, which is formulated as the same quadratic programming form with a unit simplex constraint and non-negative ones as Rank-CVM, and then is solved by Frank–Wolfe method efficiently. Attractively, our Rank-CVMz has fewer variables to be solved than Rank-CVM, which speeds up training procedure dramatically. Further, the relevant labels are effectively detected by the zero label. Experimental results on 12 benchmark data sets demonstrate that our method achieves a competitive performance, compared with six existing multi-label algorithms according to six indicative instance-based measures. Moreover, on the average, our Rank-CVMz runs 83 times faster and has slightly fewer support vectors than its origin Rank-CVM.