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Community structure division is a crucial problem in the field of network data analysis. Algorithms based on Markov chains are easy to use and provide promising solutions for community detection. In a Markov chain-based algorithm (i.e., MCL), a flow distribution matrix and a transition matrix are used to describe stochastic flows and transition probabilities, respectively, on a network. The dynamic interaction process between stochastic flows and transition probabilities in MCLs is manifested through an iterative process of updating the abovementioned two matrices. As one of the key mechanisms of MCLs, such a dynamic process for increasing the inhomogeneity directly affects the accuracy and computational cost of MCL-based methods. Inspired by a kind of positive feedback interaction of a dendritic network of tube-like amoeba cell pseudopodia (named the Physarum foraging network), a Physarum-inspired relationship among vertices is proposed to enhance the transition probability in the dynamic process of MCL-based community detection algorithms. Specifically, the proposed hybrid community detection algorithm can adaptively search for a better combination of parameters based on a genetic algorithm. Some experiments are carried out on both static and dynamic networks. The results show that the unique Physarum inspired algorithm achieved better computational efficiency and detection performance than other algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a novel low-rank structural model is proposed for segmenting data drawn from a high-dimensional space. Our method is based on the fact that all groups clustered from a high-dimensional dataset are distributed in multiple low-rank subspaces. In general, it’s a very difficult task to find the low-rank structures hidden in data. Different from the classical sparse subspace clustering (SSC) and low-rank representation (LRR) which all take two steps including building the affinity matrix and spectral clustering, we introduce a new rank constraint into our model. This constraint allows our model to learn a subspace indicator which can capture different clusters directly from the data without any postprocessing. To further approximate the rank constraint, a piecewise function is utilized as the relaxing item for the proposed model. Besides, under the subspace indicator constraints, the integer programming problem is avoided, which makes our algorithm more efficient and scalable. In addition, we prove the convergence of the proposed algorithm in theory and further discuss the general case in which subspaces don’t pass through the origin. Experiment results on both synthetic and real-world datasets demonstrate that our algorithm significantly outperforms the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Fuzzy K-Means (FKM) clustering is of great importance for analyzing unlabeled data. FKM algorithms assign each data point to multiple clusters with some degree of certainty measured by the membership function. In these methods, the fuzzy membership degree matrix is obtained based on the calculation of the distance between data points in the original space. However, this operation may lead to suboptimal results because of the influence of noises and redundant features. Besides, some FKM clustering methods ignore the importance of the weighting exponent. In this paper, we propose a novel FKM method called Fuzzy K-Means Clustering With Discriminative Embedding. Within this method, we simultaneously conduct dimensionality reduction along with fuzzy membership degree learning. To retain most information in the embedding subspace and improve the robustness of this method, principal component analysis is incorporated into our framework. An iterative optimization algorithm is proposed to solve the model. To validate the efficacy of the proposed method, we perform comprehensive analyses, including convergence behavior, parameter determination and computational complexity. Moreover, we also match a appropriate weighting exponent for each data set. Experimental results on benchmark data sets show that the proposed method is more discriminative and effective for clustering tasks. [ABSTRACT FROM AUTHOR]

Spectral clustering is a quite simple but effective method for solving graph clustering problem. It projects the original data points into a lower dimensional space with spectral embedding, and then relies on an algorithm to obtain the cluster labels. Since it involves eigendecomposition of the graph Laplacian matrix for embedding, spectral clustering has high time complexity and is not able to process large scale data. The performance of spectral clustering is also limited by a post-processing algorithm such as kmeans. To tackle the two issues, we propose a method called Orthogonal and Nonnegative Graph Reconstruction (ONGR) for large scale clustering. The two constraints serve as a structure constraint with which the graph reconstructed by the indicator matrix is structured. The proposed method has linear time complexity with respect to the data size that it mainly needs to implicitly construct a graph and iteratively perform economical singular value decomposition for a small size matrix. Moreover, the interpretability of the indicator matrix is offered due to the nonnegative constraint, and thus our method can provide the cluster labels with no post-processing. The experiments on benchmark datasets show the effectiveness of the proposed scalable clustering method. [ABSTRACT FROM AUTHOR]

Simultaneous feature selection and clustering is a major challenge in unsupervised learning. In particular, there has been significant research into saliency measures for features that result in good clustering. However, as datasets become larger and more complex, there is a need to adopt a finer-grained approach to saliency by measuring it in relation to a part of a model. Another issue is learning the feature saliency and advanced model parameters. We address the first by presenting a novel Gaussian mixture model, which explicitly models the dependency of individual mixture components on each feature giving a new component-based feature saliency measure. For the second, we use Markov Chain Monte Carlo sampling to estimate the model and hidden variables. Using a synthetic dataset, we demonstrate the superiority of our approach, in terms of clustering accuracy and model parameter estimation, over an approach using a model-based feature saliency with expectation maximisation. We performed an evaluation of our approach with six synthetic trajectory datasets obtaining an average clustering accuracy of 97 percent. To demonstrate the generality of our approach, we applied it to a network traffic flow dataset obtaining an accuracy of 93 percent for intrusion detection. Finally, we performed a comparison with state-of-the-art clustering techniques using three real-world trajectory datasets of vehicle traffic. Our approach achieved an average clustering accuracy of 96 percent compared to 77-95 percent for the other techniques. In conclusion, for the datasets considered, component based feature saliency measures gave improved clustering over those based on whole models. [ABSTRACT FROM AUTHOR]

In many real-world applications, we are often confronted with high dimensional data which are represented by various heterogeneous views. How to cluster this kind of data is still a challenging problem due to the curse of dimensionality and effectively integration of different views. To address this problem, we propose two parameter-free weighted multi-view projected clustering methods which perform structured graph learning and dimensionality reduction simultaneously. We can use the obtained structured graph directly to extract the clustering indicators, without performing other discretization procedures as previous graph-based clustering methods have to do. Moreover, two parameter-free strategies are adopted to learn an optimal weight for each view automatically, without introducing a regularization parameter as previous methods do. Extensive experiments on several public datasets demonstrate that the proposed methods outperform other state-of-the-art approaches and can be used more practically. [ABSTRACT FROM AUTHOR]

Spectral clustering has been playing a vital role in various research areas. Most traditional spectral clustering algorithms comprise two independent stages (e.g., first learning continuous labels and then rounding the learned labels into discrete ones), which may cause unpredictable deviation of resultant cluster labels from genuine ones, thereby leading to severe information loss and performance degradation. In this work, we study how to achieve discrete clustering as well as reliably generalize to unseen data. We propose a novel spectral clustering scheme which deeply explores cluster label properties, including discreteness, nonnegativity, and discrimination, as well as learns robust out-of-sample prediction functions. Specifically, we explicitly enforce a discrete transformation on the intermediate continuous labels, which leads to a tractable optimization problem with a discrete solution. Besides, we preserve the natural nonnegative characteristic of the clustering labels to enhance the interpretability of the results. Moreover, to further compensate the unreliability of the learned clustering labels, we integrate an adaptive robust module with \ell 2,p loss to learn prediction function for grouping unseen data. We also show that the out-of-sample component can inject discriminative knowledge into the learning of cluster labels under certain conditions. Extensive experiments conducted on various data sets have demonstrated the superiority of our proposal as compared to several existing clustering approaches. [ABSTRACT FROM PUBLISHER]