Some comments of Wolfe's `away step'
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ECML '98 Proceedings of the 10th European Conference on Machine Learning
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Core Vector Machines: Fast SVM Training on Very Large Data Sets
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The Journal of Machine Learning Research
Multilabel classification via calibrated label ranking
Machine Learning
Ml-rbf: RBF Neural Networks for Multi-Label Learning
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A transductive multi-label learning approach for video concept detection
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Two stage architecture for multi-label learning
Pattern Recognition
Classifier chains for multi-label classification
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Multilabel classifiers with a probabilistic thresholding strategy
Pattern Recognition
Generalized Core Vector Machines
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Random block coordinate descent method for multi-label support vector machine with a zero label
Expert Systems with Applications: An International Journal
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The existing multi-label support vector machine (Rank-SVM) has an extremely high computational complexity due to a large number of variables in its quadratic programming. When the Frank-Wolfe (FW) method is applied, a large-scale linear programming still needs to be solved at any iteration. Therefore it is highly desirable to design and implement a new efficient SVM-type multi-label algorithm. Binary core vector machine (CVM), as a variant of traditional SVM, is formulated as a quadratic programming with a unit simplex constraint, in which each linear programming in FW has an analytical solution. In this paper, we combine Rank-SVM with CVM to construct a novel SVM-type multi-label classifier (Rank-CVM) which is described as the same optimization form as binary CVM. At its any iteration of FW, there exist analytical solution and step size, and several useful recursive formulae for proxy solution, gradient vector, and objective function value, all of which reduce computational cost greatly. Experimental study on nine benchmark data sets shows that when Rank-CVM performs as statistically well as its rival Rank-SVM according to five performance measures, our method runs averagely about 13 times faster and has less support vectors than Rank-SVM in the training phase under C/C++ environment.