Scalable Multi-View Semi-Supervised Classification via Adaptive Regression

With the advent of multi-view data, multi-view learning has become an important research direction in machine learning and image processing. Considering the difficulty of obtaining labeled data in many machine learning applications, we focus on the multi-view semi-supervised classification problem. In this paper, we propose an algorithm named multi-view semi-supervised classification via adaptive regression (MVAR) to address this problem. Specifically, regression-based loss functions with $\ell _{2,1}$ matrix norm are adopted for each view and the final objective function is formulated as the linear weighted combination of all the loss functions. An efficient algorithm with proved convergence is developed to solve the non-smooth $\ell _{2,1}$ -norm minimization problem. Regressing to class labels directly makes the proposed algorithm efficient in calculation and can be applied to large-scale data sets. The adaptively optimized weight coefficients balance the contributions of different views automatically, which makes the performance robust against the existence of low-quality views. With the learned projection matrices and bias vectors, predictions for out-of-sample data can be easily made. To validate the effectiveness of MVAR, comparisons are made with some benchmark methods on real-world data sets and in the scene classification scenario as well. The experimental results demonstrate the effectiveness of our proposed algorithm.