Online primal–dual learning for a data-dependent multi-kernel combination model with multiclass visual categorization applications

The task of visual categorization becomes very challenging as the number of samples or classes increases. This is mainly due to large memory requirements or a crowded semantic space, which causes class separation difficulties. In this paper, a new approach called OPrDuM2 (online primal–dual multiple kernel multiple class) is proposed. This new algorithm can significantly reduce the complexity of visual categorization. Under this approach, an elegant heterogeneous feature fusion machine is used to consolidate complementary class-discriminative information, and online learning is applied to deal with large sample sizes. To be specific, a data-dependent multi-kernel machine that fuses multiple heterogeneous features in a nonlinear manner is defined by extending the multi-kernel learning model, and multivariate hinge loss and conservative updating rules are used to increase the sample-level sparsity in the model. Given the intrinsic hierarchical structure of samples, features, and classes, an innovative triple mixed-norm regularizer with strong convexity is utilized to facilitate optimization. An iterative solution is derived using the language of duality, leading to a low regret bound of OT, where T is the number of online iterations. This paper details a proof of the algorithm’s convergence, and describes extensive visual data classification experiments that demonstrate the effectiveness and robustness of this new approach.