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Feature selection is the process of selecting subset of features that still provide maximum amount of the information that otherwise is provided by the entire set of conditional attributes. Many approaches have been proposed so far in literature for this purpose. Recently the rough set based approaches have become dominant. Majority of these approaches use attribute dependency to find significance of attributes. Problem with this measure is that it uses positive region to calculate dependency which is a computationally expensive job. As a consequence, it degrades the performance of the feature selection algorithms using this measure. In this paper, we have proposed a new heuristic based dependency calculation technique by avoiding the positive region. The proposed method uses a heuristics approach by finding the consistent records regarding each decision class in the dataset. Using this method, allows us to calculate dependency by avoiding the positive region, which ultimately enhances the computational efficiency of the underlying feature selection algorithm thus enabling it to be used for dataset beyond smaller size. In order to calculate dependency by using the proposed method, we have used a two-dimensional grid as intermediate data structure. Number of feature selection algorithms were used with proposed solution on various publically available datasets to justify it. A comparison framework was used to compare the proposed solution with conventional methods. Results have justified the proposed solution both in terms of its efficiency and effectiveness. [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]

• 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]

• A graph-based learning using multiple kernels and multiple views. • A self-weighted algorithm where each kernel of each view gets an appropriate weight automatically. • Robustness of the algorithm to reduce the effect of data outliers and noises present in the data set. • A unified framework for graph construction, kernel learning and label learning. The studies of hidden complex structures in data have popularized the use of graph-based learning methods in semi-supervised and unsupervised learning tasks. Kernelized graph-based methods are proven to perform better, but these methods suffer from the issue of appropriate kernel selection. Instead of using multiple views, these methods generally use a single view. But multi-view methods need a proper weight assignment technique to each view in proportion to their contribution to the learning task. To solve this, a novel Self-weighted Multi-view Multiple Kernel Learning (SMVMKL) framework is proposed using multiple kernels on multiple views that automatically assigns appropriate weight to each kernel of each view without introducing an additional parameter. But the real-world data that is either noisy or corrupt with outliers which may effect the performance of the proposed SMVMKL method. To deal with this, a Robust Self-weighted Multi-view Multiple Kernel Learning (RSMVMKL) framework using the l 2,1 -norm has also been proposed that reduces the effect of outliers present in the data set. Both the proposed methods have been evaluated on multiple benchmark data sets and result in a performance comparable with the other state-of-the-art multi-view methods considered in this paper. [ABSTRACT FROM AUTHOR]

• Low-rank quaternion tensor completion method, a novel approach to estimate missing pixels in color videos and images is proposed. • We respectively reconstruct a color image and a color video as a quaternion matrix (second-order tensor) and a third-order quaternion tensor by encoding the red, green, and blue channel pixel values on the three imaginary parts of a quaternion. • Under the definition of Tucker rank, the global low-rank prior to quaternion tensor is encoded as the nuclear norm of unfolding quaternion matrices. • Theoretically, the proposed method can be well used to recover missing entries of any multidimensional data with color structures. Low-rank quaternion tensor completion method, a novel approach to recovery color videos and images, is proposed in this paper. We respectively reconstruct a color image and a color video as a quaternion matrix (second-order tensor) and a third-order quaternion tensor by encoding the red, green, and blue channel pixel values on the three imaginary parts of a quaternion. Different from some traditional models which treat color pixel as a scalar and represent color channels separately, whereas, during the quaternion-based reconstruction, it is significant that the inherent color structures of color images and color videos can be completely preserved. Under the definition of Tucker rank, the global low-rank prior to quaternion tensor is encoded as the nuclear norm of unfolding quaternion matrices. Then, by applying the ADMM framework, we provide the tensor completion algorithm for any order (≥ 2) quaternion tensors, which theoretically can be well used to recover missing entries of any multidimensional data with color structures. Simulation results for color videos and color images recovery show the superior performance and efficiency of the proposed method over some state-of-the-art existing ones. [ABSTRACT FROM AUTHOR]