Due to the "curse of dimensionality" issue, how to discard redundant features and select informative features in high-dimensional data has become a critical problem, and there are many researches dedicated to solving this problem. Unsupervised feature selection technique, which doesn't require any prior category information to conduct with, has gained a prominent place in pre-processing high-dimensional data among all feature selection techniques, and it has been applied to many neural networks and learning systems related applications, e.g., pattern classification. In this paper, we propose an efficient method for unsupervised feature selection via Orthogonal basis Clustering and reliable Local Structure Preserving, which is referred to OCLSP briefly. Our OCLSP method consists of an orthogonal basis clustering together with an adaptive graph regularization, which realize the functionality of simultaneously achieving excellent cluster separation and preserving the local information of data. Besides, we exploit an efficient alternative optimization algorithm to solve the challenging optimization problem of our proposed OCLSP method, and we perform a theoretical analysis of its computational complexity and convergence. Eventually, we conduct comprehensive experiments on nine real-world datasets to test the validity of our proposed OCLSP method, and the experimental results demonstrate that our proposed OCLSP method outperforms many state-of-the-art unsupervised feature selection methods in terms of clustering accuracy and normalized mutual information, which indicates that our proposed OCLSP method has a strong ability in identifying more important features.

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Community detection is an important topic in network analysis, and recently many community detection methods have been developed on top of the Nonnegative Matrix Factorization (NMF) technique. Most NMF-based community detection methods only utilize the first-order proximity information in the adjacency matrix, which has some limitations. Besides, many NMF-based community detection methods involve sparse regularizations to promote clearer community memberships. However, in most of these regularizations, different nodes are treated equally, which seems unreasonable. To dismiss the above limitations, this paper proposes a community detection method based on node centrality under the framework of NMF. Specifically, we design a new similarity measure which considers the proximity of higher-order neighbors to form a more informative graph regularization mechanism, so as to better refine the detected communities. Besides, we introduce the node centrality and Gini impurity to measure the importance of nodes and sparseness of the community memberships, respectively. Then, we propose a novel sparse regularization mechanism which forces nodes with higher node centrality to have smaller Gini impurity. Extensive experimental results on a variety of real-world networks show the superior performance of the proposed method over thirteen state-of-the-art methods.

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