Multi-view learning for multivariate performance measures optimization

In this paper, we propose the problem of optimizing multivariate performance measures from multi-view data, and an effective method to solve it. This problem has two features: the data points are presented by multiple views, and the target of learning is to optimize complex multivariate performance measures. We propose to learn a linear discriminant functions for each view, and combine them to construct a overall multivariate mapping function for mult-view data. To learn the parameters of the linear discriminant functions of different views to optimize multivariate performance measures, we formulate a optimization problem. In this problem, we propose to minimize the complexity of the linear discriminant functions of each view, encourage the consistences of the responses of different views over the same data points, and minimize the upper boundary of a given multivariate performance measure. To optimize this problem, we employ the cutting-plane method in an iterative algorithm. In each iteration, we update a set of constrains, and optimize the mapping function parameter of each view one by one.