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In this paper, we investigate L 0 -regularized logistic regression models, and design two fast and efficient algorithms for high-dimensional correlated data and massive data, respectively. Our first algorithm, the Variable Sorted Active Set (VSAS) algorithm, is based on the local quadratic approximation of the KKT conditions for L 0 -penalized maximum log-likelihood function in high-dimensional correlated data. We establish an L ∞ error upper bound for the estimator obtained by the VSAS algorithm and prove its optimal convergence rate. Moreover, when the target signal exceeds the detectable level, the estimator obtained by the VSAS algorithm can achieve the oracle estimator with high probability. Our second algorithm, Communication Effective Variable Sorted Active Set (CEVSAS), aims to solve high-dimensional and large-sample L 0 -regularized logistic regression models by reduce computational and communication costs, while maintaining estimation efficiency. Finally, simulations and real data demonstrate the effectiveness of our proposed VSAS and CEVSAS algorithms. • We develop a fast VSAS algorithm for L 0 regularized logistic regression involving high-dimensional correlated data. • An L ∞ upper bound is established on the estimation error of the solution sequence generated by VSAS algorithm. • The CEVSAS altorithm is proposed to reduce computational costs and ensure higher estimation efficiency. • We propose two adaptive versions of the VSAS and CEVSAS algorithms for selecting the optimal tuning parameters. [ABSTRACT FROM AUTHOR]

• Presenting a new multi-label feature selection method that efficiently combines manifold regularization and dependence maximization. • Introducing a HSIC-based measurement to evaluate the dependence between the manifold space and label space. • Developing an iterative optimization method to solve the objective function of our method MRDM with good convergence. • Conducting extensive experiments on various multi-label data sets to demonstrate the superiority of the proposed method. Feature selection is able to select more discriminative features for classification and plays an important role in multi-label learning to alleviate the effect of the curse of dimensionality. Recently, the multi-label feature selection methods based on the sparse regression model have received increasing attentions. However, most of these methods directly project original data space to label space in the regression model, which is inappropriate because the linear assumption between data space and label space doesn't hold in most cases. In the paper, we propose a feature selection method named multi-label feature selection via manifold regularization and dependence maximization (MRDM). In the regression model of MRDM, the original data space is projected to a low-dimensional manifold space, which not only has the same topological structure with the original data, but also has a strong dependence with the class labels. Then, an objective function involving l 2 , 1 -norm regularization is formulated, and an alternating optimization-based iterative algorithm is designed to obtain the sparse coefficients for multi-label feature selection. Extensive experiments on various multi-label data sets demonstrate the superiority of the proposed method compared with some state-of-the-art multi-label feature selection methods. [ABSTRACT FROM AUTHOR]

Biclustering (co-clustering, two-mode clustering), as one of the classical unsupervised learning methods, has been applied in many different fields in recent years. Different types of biclustering methods have been developed such as probabilistic methods, two-way clustering methods, variance minimization methods, and so on. However, few regression-based methods have been proposed to the best of our knowledge. Such methods have been applied in traditional clustering, which can improve both the computational efficiency and the clustering accuracy. In this paper, we present a penalized regression-based method for localizing the biclusters (PRbiclust). By imposing Truncated LASSO Penalty (TLP) and group TLP terms to penalize the column vectors and the row vectors in the regression model, the structure of biclusters in the data matrix is recovered. The model is formulated as an optimization problem with nonconvex penalties, and a computationally efficient algorithm is proposed to solve it. Convergence of the algorithm is proved. To extract the biclusters from the recovered data matrix, we propose a graph-based localization method. An evaluation criterion is also proposed to measure the efficiency of bicluster localization when noise entries exist. We apply the proposed method to both simulated datasets with different setups and a real dataset. Experiments show that this method can well capture the bicluster structure, and performs better than the existing works. [ABSTRACT FROM AUTHOR]