Multi-label Minimax Probability Machine with Multi-manifold Regularisation

Semi-supervised learning i.e., learning from a large number of unlabelled data and exploiting a small percentage of labelled data has attracted centralised attention in recent years. Semi-supervised problem is handled mainly using graph based Laplacian and Hessian regularisation methods. However, neither the Laplacian method which leads to poor generalisation nor the Hessian energy can properly forecast the data points beyond the range of the domain. Thus, in this paper, the Laplacian-Hessian semi-supervised method is proposed, which can both predict the data points and enhance the stability of Hessian regulariser. In this paper, we propose a Laplacian-Hessian Multi-label Minimax Probability Machine, which is Multi-manifold regularisation framework. The proposed classifier requires mean and covariance information; therefore, assumptions related to the class conditional distributions are not required; rather, a upper bound on the misclassification probability of future data is obtained explicitly. Furthermore, the proposed model can effectively utilise the geometric information via a combination of Hessian-Laplacian manifold regularisation. We also show that the proposed method can be kernelised on the basis of a theorem similar to the representer theorem for handling non-linear cases. Extensive experimental comparisons of our proposed method with related multi-label algorithms on well known multi-label datasets demonstrate the validity and comparable performance of our proposed approach.