Discriminative semi-supervised feature selection via manifold regularization.

Feature selection has attracted a huge amount of interest in both research and application communities of data mining. We consider the problem of semi-supervised feature selection, where we are given a small amount of labeled examples and a large amount of unlabeled examples. Since a small number of labeled samples are usually insufficient for identifying the relevant features, the critical problem arising from semi-supervised feature selection is how to take advantage of the information underneath the unlabeled data. To address this problem, we propose a novel discriminative semi-supervised feature selection method based on the idea of manifold regularization. The proposed approach selects features through maximizing the classification margin between different classes and simultaneously exploiting the geometry of the probability distribution that generates both labeled and unlabeled data. In comparison with previous semi-supervised feature selection algorithms, our proposed semi-supervised feature selection method is an embedded feature selection method and is able to find more discriminative features. We formulate the proposed feature selection method into a convex-concave optimization problem, where the saddle point corresponds to the optimal solution. To find the optimal solution, the level method, a fairly recent optimization method, is employed. We also present a theoretic proof of the convergence rate for the application of the level method to our problem. Empirical evaluation on several benchmark data sets demonstrates the effectiveness of the proposed semi-supervised feature selection method.

Robust regularized kernel regression.

Robust regression techniques are critical to fitting data with noise in real-world applications. Most previous work of robust kernel regression is usually formulated into a dual form, which is then solved by some quadratic program solver consequently. In this correspondence, we propose a new formulation for robust regularized kernel regression under the theoretical framework of regularization networks and then tackle the optimization problem directly in the primal. We show that the primal and dual approaches are equivalent to achieving similar regression performance, but the primal formulation is more efficient and easier to be implemented than the dual one. Different from previous work, our approach also optimizes the bias term. In addition, we show that the proposed solution can be easily extended to other noise-reliable loss function, including the Huber- epsilon insensitive loss function. Finally, we conduct a set of experiments on both artificial and real data sets, in which promising results show that the proposed method is effective and more efficient than traditional approaches.