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Recently the graph-based semi-supervised classification arouses vast amount of interest in remote sensing as it can utilize only a few labeled samples and large numbers of unlabeled samples to enhance the classification accuracy on various types of terrains. However in most of the conventional methods, multiple features (e.g. the scattering components, texture, color, etc) are concatenate together into a long vector for graph construction and classification. This not only ignores the physical attribute of features, but also causes so-called curse of dimensionality and limits the performances of classification. Inspired by the multi-view machine learning, we propose a spatial multi-attribute graph model and rank the attributes of polarimetric synthetic aperture radar (PolSAR) data for terrain classification in this paper. It firstly constructs multiple graphs according to the physical attributes of the groups of features based on different similarity metrics, then automatically optimizes a balanced weight for each graph and combines the spatial information between pixels for label propagation and classification. Since it takes into account of the physical properties from PolSAR data for feature fusion and graph construction, the mechanically feature stacking and curse of dimensionality can be avoided. Experimental results on synthesized PolSAR data and real ones show enhanced classification accuracy of the proposed method compared with state-of-the-art graph-based methods when only a small number of labeled samples are available. Our empirical studies also indicate that the covariance matrix play predominant roles for PolSAR classification. [ABSTRACT FROM AUTHOR]

Abstract: Low rank representation is capable of capturing the global structure of mixed subspaces which are usually assumed to be independent. However, its computation is time-consuming. In practice, the data always distributes on subspaces that intersect or even overlap with each other. So the local structure of the data among the overlapping parts is important. Sparsity is a good property to accelerate the algorithm and capture the local linear structure. The drawback is that it breakups the low rank property of the reconstruction coefficient matrix when combining with low rank representation. In order to combine the two advantages properly, in this paper, we introduce a new constraint to the low rank representation matrix, which is called sparse congruency. Fortunately, we find that this new constraint is a simplification to the low rank and sparse constraints. Several experiments are implemented to demonstrate the efficiency of our method in semi-supervised classification. [Copyright &y& Elsevier]

Semi-supervised Non-negative Matrix Factorization (NMF) can not only utilize a fraction of label information, but also effectively learn local information of the objectives, such as documents and faces. Semi-supervised NMF is an efficient technique for dimensionality reduction of high dimensional data. In this paper, we propose a novel semi-supervised NMF, called Dual-graph regularized Non-negative Matrix Factorization with Sparse and Orthogonal constraints (SODNMF). Dual-graph model is added into semi-supervised NMF, and the manifold structures of the data space and the feature space are taken into account simultaneously. In addition, the sparse constraint is used in SODNMF, which can simplify the calculation and accelerate the processing speed. The most important is that SODNMF makes use of bi-orthogonal constraints, which can avoid the non-correspondence between images and basic vectors. Therefore, it can effectively enhance the discrimination and the exclusivity of clustering, and improve the clustering performance. We give the objective function, the iterative updating rules and the convergence proof. Empirical experiments demonstrate encouraging results of our novel algorithm in comparison to four algorithms within some state-of-the-art algorithms through a set of evaluations based on three real datasets. [ABSTRACT FROM AUTHOR]

Based on spectral graph theory, spectral clustering is an optimal graph partition problem. It has been proven that the spectral clustering is equivalent to nonnegative matrix factorization (NMF) under certain conditions. Based on the equivalence, some spectral clustering methods are proposed, but the global discriminative information of the dataset is neglected. In this paper, based on the equivalence between spectral clustering and NMF, we simultaneously maximize the between-class scatter matrix and minimize the within-class scatter matrix to enhance the discriminating power. We integrate the geometrical structure and discriminative structure in a joint framework. With a global discriminative regularization term added into the nonnegative matrix factorization framework, we propose two novel spectral clustering methods, named global discriminative-based nonnegative and spectral clustering (GDBNSC-Ncut and GDBNSC-Rcut) These new spectral clustering algorithms can preserve both the global geometrical structure and global discriminative structure. The intrinsic geometrical information of the dataset is detected, and clustering quality is improved with enhanced discriminating power. In addition, the proposed algorithms also have very good abilities of handling out-of-sample data. Experimental results on real word data demonstrate that the proposed algorithms outperform some state-of-the-art methods with good clustering qualities. [ABSTRACT FROM AUTHOR]

Subspace segmentation based salient object detection has received increasing interests in recent years. To preserve the locality and similarity of regions, a grouping effect of representation is introduced to segment the salient object and background in subspace. Then a new saliency map is calculated by incorporating this local graph regularizer into coding, which explicitly explores the data self-representation model and thus locate more accurate salient regions. Moreover, a heuristic object-based dictionary from background superpixels is obtained in border set removing the image regions within the potential object regions. Experimental results on four large benchmark databases demonstrate that the proposed method performs favorably against eight recent state-of-the-art methods in terms of three evaluation criterions, with a reduction of MAE by 19.8% than GR and 29.3% than CB in the two SED datasets, respectively. Meanwhile, our method also runs faster than the comparative detection approaches. [ABSTRACT FROM AUTHOR]

Feature selection algorithms eliminate irrelevant and redundant features, even the noise, while preserving the most representative features. They can reduce the dimension of the dataset, extract essential features in high dimensional data and improve learning quality. Existing feature selection algorithms are all carried out in data space. However, the information of feature space cannot be fully exploited. To compensate for this drawback, this paper proposes a novel feature selection algorithm for clustering, named self-representation based dual-graph regularized feature selection clustering (DFSC). It adopts the self-representation property that data can be represented by itself. Meanwhile, the local geometrical information of both data space and feature space are preserved simultaneously. By imposing the l 2,1 -norm constraint on the self-representation coefficients matrix in data space, DFSC can effectively select the most representative features for clustering. We give the objective function, develop iterative updating rules and provide the convergence proof. Two kinds of extensive experiments on some datasets demonstrate the effectiveness of DFSC. Extensive comparisons over several state-of-the-art feature selection algorithms illustrate that additionally considering the information of feature space based on self-representation property improves clustering quality. Meanwhile, because the additional feature selection process can select the most important features to preserve the intrinsic structure of dataset, the proposed algorithm achieves better clustering results compared with some co-clustering algorithms. [ABSTRACT FROM AUTHOR]

Abstract: A simple deterministic algorithm for community detection is provided by using two rounds of minimum spanning trees. By comparing the first round minimum spanning tree (1st-MST) with the second round spanning tree (2nd-MST) of the network, communities are detected and their overlapping nodes are also identified. To generate the two MSTs, a distance matrix is defined and computed from the adjacent matrix of the network. Compared with the resistance matrix or the communicability matrix used in community detection in the literature, the proposed distance matrix is very simple in computation. The proposed algorithm is tested on real world social networks, graphs which are failed by the modularity maximization, and the LFR benchmark graphs for community detection. [Copyright &y& Elsevier]

Abstract: Motivated by social and biological interactions, a novel type of phase transition model is provided in order to investigate the emergence of the clustering phenomenon in networks. The model has two types of interactions: one is attractive and the other is repulsive. In each iteration, the phase of a node (or an agent) moves toward the average phase of its neighbors and moves away from the average phase of its non-neighbors. The velocities of the two types of phase transition are controlled by two parameters, respectively. It is found that the phase transition phenomenon is closely related to the topological structure of the underlying network, and thus can be applied to identify its communities and overlapping groups. By giving each node of the network a randomly generated initial phase and updating these phases by the phase transition model until they reach stability, one or two communities will be detected according to the nodes’ stable phases, confusable nodes are moved into a set named . By removing the detected communities and the nodes in , another one or two communities will be detected by an iteration of the algorithm, …. In this way, all communities and the overlapping nodes are detected. Simulations on both real-world networks and the LFR benchmark graphs have verified the efficiency of the proposed scheme. [Copyright &y& Elsevier]

Abstract The study of community structure in complex networks has always been a subject of great concern in various fields. Community structure can reflect the dynamic characteristics and functions of complex networks. In recent years, there has been numerous methods proposed for community detection. Natural computing methods are inspired by nature Which have the ability of self-adaptation, self-organization and self-learning. This kind of methods can solve the complex problem that traditional calculation method cannot solve. With the effective network partition evaluation function proposed, the community detection problem can also be regarded as a kind of optimization problem. Therefore, natural computing methods are widely applied in community detection. This paper summarizes the application of natural computing inspired method in community detection, and briefly introduces its basic framework and development course. Highlights • This paper summarizes the application of natural computing inspired method in community detection. • We give a detailed overview of several situations of complex network structure. • We summarize the community structure in complex network and the evaluation index of its partition results. • We introduce the basic framework of the heuristic method of natural computing. [ABSTRACT FROM AUTHOR]

Community detection in complex networks, is to detect the community structure with the internal structure relatively compact and the external structure relatively sparse, according to the topological relationship among nodes in the network. In this paper, we propose a compactness function which combines the weight of nodes, and use it as the objective function to carry out the node label propagation. Firstly, according to the node degree, we find the sets of core nodes which have great influence on the network. The more the connections between the core nodes and the other nodes are, the larger the amount of the information these kernel nodes receive and transform. Then, according to the similarity of the nodes between the core nodes sets and the nodes degree, we assign weights to the nodes in the network. So the label of the nodes with great influence will be the priority in the label propagation process, which effectively improves the accuracy of the label propagation. The compactness function between nodes and communities in this paper is based on the nodes influence. It combines the connections between nodes and communities with the degree of the node belongs to its neighbor communities based on calculating the node weight. The function effectively uses the information of nodes and connections in the network. The experimental results show that the proposed algorithm can achieve good results in the artificial network and large-scale real networks compared with the 8 contrast algorithms. [ABSTRACT FROM AUTHOR]

In recent years, a variety of feature selection algorithms based on subspace learning have been proposed. However, such methods typically do not exploit information about the underlying geometry of the data. To overcome this shortcoming, we propose a novel algorithm called subspace learning-based graph regularized feature selection (SGFS). SGFS builds on the feature selection framework of subspace learning, but extends it by incorporating the idea of graph regularization, in which a feature map is constructed on the feature space in order to preserve geometric structure information on the feature manifold. Additionally, the L 2,1 -norm is used to constrain the feature selection matrix to ensure the sparsity of the feature array and avoid trivial solutions. The resulting method can provide more accurate discrimination information for feature selection. We evaluate SGFS by comparing it against five other state-of-the-art algorithms from the literature, on twelve publicly available benchmark data sets. Empirical results suggest that SGFS is more effective than the other five feature selection algorithms. [ABSTRACT FROM AUTHOR]

Sparse Representation based Graphs (SRGs) have attracted increasing interests in very recent years. However, for lacking global constraints on solutions to sparse representation, SRGs cannot accurately reveal data structure when data are grossly corrupted. In this paper, in order to achieve robust classification of wide range of datasets when only a small number of labeled samples are available, we advance a new semi-supervised kernel low-rank representation graph (SKLRG), by combining low-rank representation (LRR) with graphs and kernel trick. A kernel projection is first learned to find high-dimensional space where data have possible low-rank structure. Then a low-rank representation of the projected data is calculated from which we can derive a SKLRG matrix to evaluate data affinity and classify corrupted patterns. The proposed SKLRG can naturally reveal the relationship among data in the projected space, and can capture the global structure of complex data and implements more robust subspace segmentation. Moreover, connected weights of SKLRG are refined by pairwise constrains where label information is explored to further improve the classification results. Some experiments are taken on some benchmark datasets and Synthetic Aperture Radar (SAR) images that are corrupted by speckle noise. The results show that the proposed SKLRG can achieve better performance than its counterparts when there are only a small number of labeled samples. [ABSTRACT FROM AUTHOR]

Abstract: Graph-based semi-supervised learning has been widely researched in recent years. A novel Low-Rank Representation with Local Constraint (LRRLC) approach for graph construction is proposed in this paper. The LRRLC is derived from the original Low-Rank Representation (LRR) algorithm by incorporating the local information of data. Rank constraint has the capacity to capture the global structure of data. Therefore, LRRLC is able to capture both the global structure by LRR and the local structure by the locally constrained regularization term simultaneously. The regularization term is induced by the locality assumption that similar samples have large similarity coefficients. The measurement of similarity among all samples is obtained by LRR in this paper. Considering the non-negativity restriction of the coefficients in physical interpretation, the regularization term can be written as a weighted -norm. Then a semi-supervised learning framework based on local and global consistency is used for the classification task. Experimental results show that the LRRLC algorithm provides better representation of data structure and achieves higher classification accuracy in comparison with the state-of-the-art graphs on real face and digit databases. [Copyright &y& Elsevier]

Abstract: Recognizing human actions in a video sequence using small number of labeled data are very desirable in practical applications. In this paper an action recognition approach via Labeled Kernel Sparse Coding (LKSC) and sparse L1 graph is proposed under the framework of semi-supervised learning framework. Inspired by the fact that kernel trick can capture the nonlinear similarity of features, we extend the sparse representation classifier (SRC) is extended to the empirical kernel projection space. By using the calculated sparse coding coefficients of both labeled and unlabeled samples as the graph weights, a sparse L1 graph is established in a parameter-free manner. Some experiments are taken on Weizmann human action datasets and a movie sequence of a ballet dance, to investigate the performance of our proposed method, and the results show that it is insensitive to the only parameter σ, and can achieve high recognition rate when using some number of labeled samples. [Copyright &y& Elsevier]