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• 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]

• Design a branch and bound strategy for identifying non-contributed points and non-longest paths. • Construct a much smaller DAG than those constructed by the existing algorithms. • Design a strategy for deleting points in the Hash table timely. • Propose a new data structure for storing Small-DAG to avoid topological sorting. • Propose a new algorithm for larger-scale MLCS problems with lower time and space cost. Finding the multiple longest common subsequences (MLCS) among many long sequences (i.e., the large scale MLCS problem) has many important applications, such as gene alignment, disease diagnosis, and documents similarity check, etc. It is an NP-hard problem (Maier et al., 1978). The key bottle neck of this problem is that the existing state-of-the-art algorithms must construct a huge graph (called direct acyclic graph, briefly DAG), and the computer usually has no enough space to store and handle this graph. Thus the existing algorithms cannot solve the large scale MLCS problem. In order to quickly solve the large-scale MLCS problem within limited computer resources, this paper therefore proposes a branch and bound irredundant graph algorithm called Big-MLCS, which constructs a much smaller DAG (called Small-DAG) than the existing algorithms do by a branch and bound method, and designs a new data structure to efficiently store and handle Small-DAG. By these schemes, Big-MLCS is more efficient than the existing algorithms. Also, we compare the proposed algorithm with two state-of-the-art algorithms through the experiments, and the results show that the proposed algorithm outperforms the compared algorithms and is more suitable to large-scale MLCS problems. [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]