Correlation maximization machine for multi-modalities multiclass classification

Support vector machine (SVM) learns the maximum margin to separate training examples that belong to two classes and has been widely used in many pattern recognition tasks due to its high effectiveness. However, conventional SVM suffers from the following deficiencies: (1) SVM cannot take full advantage of multiple modalities in a dataset if they are available, and (2) SVM trains the marginal hyper-plane by solving the quadratic programming problem, and thus costs too much computational overheads. In this paper, we propose a correlation maximization machine (CMM) model to overcome the aforementioned deficiencies by integrating two modalities in a dataset to boost the classification performance and utilizing randomized nonlinear features to output labels from multiple classes. In particular, CMM reveals the nonlinear relationships among both modalities by generating randomized nonlinear features for each modality. CMM learns to project these features into a common subspace with a constraint that their coefficients are highly correlated, and narrows the gap between the coefficients of both modalities and the class indicator of each training example to deal with multiclass classification problem. At the classification stage, CMM indicates the classes of a test example by using the summation of its coefficients of both modalities. Since the objective function of CMM is non-convex, it is quite difficult to obtain the global minimum. In this paper, we developed a block coordinate descent-based algorithm to optimize CMM and theoretically proved its convergence to a local minimum. Experimental results of face recognition on three popular face image datasets and experimental results of image retrieval on CIFAR-10, NUS-Wide, and Wikipedia datasets demonstrate that CMM outperforms the representative methods.