Optimizing multivariate performance measures from multi-view data

To date, many machine learning applications have multiple views of features, and different applications require specific multivariate performance measures, such as the F-score for retrieval. However, existing multivariate performance measure optimization methods are limited to single-view data, while traditional multi-view learning methods cannot optimize multivariate performance measures directly. To fill this gap, in this paper, we propose the problem of optimizing multivariate performance measures from multi-view data, and an effective method to solve it. We propose to learn linear discriminant functions for different views, and combine them to construct an overall multivariate mapping function for multiview data. To learn the parameters of the linear discriminant functions of different views to optimize a given multivariate performance measure, we formulate an optimization problem. In this problem, we propose to minimize the complexity of the linear discriminant function of each view, promote the consistency of the responses of different views over the same data points, and minimize the upper boundary of the corresponding loss of a given multivariate performance measure. To optimize this problem, we develop an iterative cuttingplane algorithm. Experiments on four benchmark data sets show that it not only outperforms traditional single-view based multivariate performance optimization methods, but also achieves better results than ordinary multi-view learning methods.