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Spectral clustering (SC) is a hot research topic in graph theory today, which is centered on constructing similarity matrix. Many previous works have studied how to construct a higher-quality similarity matrix. However, most of these works ignore the connection between constructing similarity matrix and the overall distribution of the datasets. This problem will lead to low quality and lack of robustness in the similarity matrix when the data volume and dimensionality are expanded, which leads to poor clustering performance. Therefore, to solve the above problems, an Adaptive Fuzzy Spectral Clustering (AFSC) model is proposed in this paper. The model considers the local neighbor and global fuzzy affiliation information of the samples to construct the objective function, which can obtain the similarity matrix that satisfies the overall distribution of the datasets. Meanwhile, we propose a weight definition method to balance the above two kinds of information, which can prevent the adverse effect of information loss on the quality of the similarity matrix. The similarity matrix obtained by the AFSC model will have high quality and strong robustness, which leads to excellent clustering performance. In experiments, we verified that the AFSC model can obtain excellent clustering performance and outperform some state-of-the-art clustering models as it is applied to several datasets of different sizes and dimensions.

The performance of 5G mobile network cells is highly impacted by their evolving configuration and temporal environmental conditions, such as the number of connected devices or resource utilization. Evaluation of the performance of such a system is a complex task that requires the simultaneous analysis of multiple indicators and inspires the research community to work on zero-touch network service management. In this paper, we present a novel time series clustering method - Temporal and Multivariate Similarity Clustering (TMSC) - that incorporates Dynamic Time Warping with Limited Warping Length and Spectral Clustering, allowing for radio cell grouping based on realization of multiple Key Performance Indicators. We evaluated TMSC against state-of-the-art algorithms at a practical task of identifying cell configuration differences by clustering their performance metrics with a limited set of observations. The proposed algorithm outperformed other methods regarding the Normalized Mutual Information score achieved for more than 95% of the cases studied. We also display the potential for method generalization by evaluating it at the hand gesture recognition task, which yields satisfactory results.

As renewable energy sources are integrated into power systems, the complexity of their management increases. For the analysis of modern power systems, clustering algorithms have become indispensable tools. The representation of an electric power transmission system involves conceptualizing it as a graph—a mathematical structure depicting a set of nodes and edges. In the context of power systems, these nodes correspond to buses, and the edges represent branches. Weighting may be assigned to the edges to denote the strength of their connections. In this paper, spectral clustering and hierarchical agglomerative clustering have been employed to analyze the Italian transmission network. Spectral clustering relies on the eigenvalues and eigenvectors derived from the Laplacian matrix associated with the network. The hierarchical agglomerative clustering, based on Thévenin impedance to define the distances, merges the two closest clusters at each step. The primary objective of this research is to identify distinct areas within the network based solely on its topology. In pursuit of this goal, admittances and Thévenin impedances have been employed as weights in the graph representation. By utilizing these approaches, the research aims at uncovering meaningful structures and patterns within the power transmission system based on the inherent connectivity and strength of the network elements. The techniques have been used on two real network models to demonstrate the performance of the algorithms with different grid configurations.

Spectral clustering, a powerful algorithm in the field of AI, holds a significant role despite its inherent high time complexity. For data owners grappling with limitations such as small datasets and restricted computational resources, harnessing the computational capabilities of cloud computing and aggregating data from multiple sources can yield precise spectral clustering results. However, explicit data uploading to cloud servers poses privacy risks. In response to this challenge, we explore the outsourcing dilemma of spectral clustering in a cloud and multi-user environment and propose a quantum-secure and efficient solution. Specifically, by employing the CKKS homomorphic encryption algorithm within a dual non-collusive server model, we formulate a comprehensive and multi-user spectral clustering outsourcing scheme. Our approach addresses privacy concerns by introducing secure computation protocols for $L_{2}$ norm, exponential function, and negative half power function. We elaborate on efficient computational algorithms for each stage of spectral clustering, ensuring accurate clustering outcomes without compromising dataset privacy. Moreover, in our scheme, users only need to upload their encrypted dataset without requiring direct interaction with each other or the cloud server until obtaining clustering results. Finally, we argue the IND- $\mathcal {CPA}$ security of our design and substantiate its accuracy and efficiency through theoretical comparison analysis and experimental evaluations.

Tumor samples clustering based on subspace segmentation is an effective method to discover cancer subtypes. Accurate and reliable identifications of cancer subtypes are crucial for understanding cancer pathogenesis as well as clinical diagnosis and treatment. Joint learning-based subspace clustering methods utilize the high correlation between data affinity and data segmentation for better clustering results. However, existing joint learning-based methods only provide an approximation of the segmentation cost in the joint optimization term, which could lead to sub-optimal results. To address this problem, we propose an algorithm named joint learning of spectral clustering and low-rank representation based on precise segmentation cost (JLSLPS) for cancer subtype identification. In our method, we impose non-negative and symmetric constraints on the low-rank representation matrix so that the representation coefficient can be equivalent to data affinity for the precise representation of segmentation cost. Therefore, the spectral clustering objective can be represented precisely to guide the learning of data affinity and segmentation more effectively. Finally, we solve the optimization problem of JLSLPS by using the linearized alternating direction method with adaptive penalty. We run JLSLPS on 8 cancer gene expression datasets and used 9 state-of-the-art clustering methods for comparison. Experimental results show that our method can increase ACC by 1.00-7.95% and NMI by 2.7-12.22% compared with the other methods, which proves the superiority of the proposed method.

This study embarks on an in-depth analysis of the performance of various kernel functions, namely uniform, epanechnikov, triangular, and gaussian, in window-based and spectral clustering-based models. Employing seven distinct datasets, our approach evaluated both window sizes (25%, 50%, 75%, and 100%) and clustering clusters (ranging from 1 to 4). The kernel functions served as weighting functions for regression models, leading to the creation of 192 window-based and 192 clustering-based models. Our analysis underscores the dominance of the uniform kernel function. In most models where the Pred(0.25) was maximal and the Mean Absolute Error was minimal, the uniform kernel function was predominantly utilized. Further, our results exhibit varying outcomes between moving windows and spectral clustering across datasets. For instance, in the fpa_china dataset, while moving windows with a 50% size displayed no significant superiority over spectral-clustering with 1 cluster, spectral-clustering (1 cluster) demonstrated a significantly enhanced performance. However, in datasets like fpa_kitchenham, neither approach proved to be significantly better. This comprehensive exploration into the efficiency of kernel functions in moving windows and spectral-clustering models provides valuable insights for future research and applications in data modelling and analysis.

The paper deals with the separation of power system into coherent areas; this is a relevant issue for managing the network in both normal operating conditions and during anomalous events. In particular, the attention is focused on partitioning the power system in such a way as to group together frequency signals, measured by means of phasor measurement units (PMU), exhibiting similar oscillatory behavior after the occurrence of a fault or disturbance. Unfortunately, the increasingly massive presence of renewable energy sources is undermining the clustering methods defined so far, requiring new solutions to the problem. To overcome the considered drawbacks, the authors propose hereinafter to ( ${i}$ ) improve the grouping capabilities of an iterative spectral clustering method thanks to the definition of new parameters for similarity estimation (Modified Bray Curtis index) and cluster thresholding (weighted Fiedler value) as well as (ii) enhance its robustness with respect to both measurement noise and uncertainty affecting the PMUs by means of a deep test procedure. To this aim, particular attention is paid in the design and assessment stage to the definition of both filtering algorithm and measurement parameters (e.g., the length of the analysis window). Once defined these parameters, the method is capable of 100% correctly separating transmission network sections oscillating with similar trends in a number of tests conducted on simulated and actual signals, so highlighting the promising performance of the method highlighting its reliability and efficacy in different test conditions.

The joint analysis of large-scale datasets is crucial when studying complex processes involving diverse sensing sources and multiple variables. This paper proposes a multiview nonlinear manifold learning framework to fuse or combine data from different types of measurements. Spectral clustering techniques are employed to obtain a low-dimensional system representation, where the physical data are projected onto a low-dimensional Euclidean space that preserves the intrinsic geometry of the data. The theoretical properties of various multiview diffusion maps are examined, and algorithms for the efficient computation of multiview kernel representations are outlined. Measures of similarity are also derived, and the results are compared with other state-of-the-art methods for model reduction. Finally, multiple datasets obtained from transient stability simulations of a large-scale power system model are utilized to evaluate the effectiveness of the developed algorithms, thereby illustrating their superiority over other state-of-the-art multiview clustering approaches.

In multi-hop wireless networks (MWNs), hierarchical structures are important to achieve scalable routing control, as well as clustering algorithms for creating such structures and so have been extensively studied. Due to the constraints of MWNs as distributed systems, these clustering algorithms must be implemented in an autonomous and decentralized manner. In particular, ensuring transparency to network topology and node mobility is important. Spectral clustering is a technique for appropriately creating clusters regardless of the network topology. However, since this technique requires information on the entire network, it is difficult to implement it autonomously and in a decentralized manner. Therefore, autonomous and decentralized spectral clustering has only succeeded in simple grid networks. This paper proposes a spectral clustering algorithm that can be implemented in an autonomous and decentralized manner for any network topology. In this method, a certain spatial structure is generated in an autonomous and decentralized manner by using differential equation-based temporal evolution equations; clusters are then formed using the spatial structure yielded by the temporal evolution equations. We demonstrate that this method can realize spectral clustering in an autonomous and decentralized manner in a static network model and also can realize a stable cluster structure that responds to node movement in a dynamic network model.

Ongoing researches on multiple view data are showing competitive behavior in the machine learning field. Multi-view clustering has gained widespread acceptance for managing multi-view data and improves clustering efficiency. Large dimensionality in data from various views has recently drawn a lot of interest from researchers. How to efficiently learns the appropriate lower dimensional subspace which can manage the valuable information from the diverse views is challenging and considerable issue. To concentrate on the mentioned issue, we asserted a novel clustering approach for multiple view data through low-rank representation. We consider the importance of each view by assigning the weight control factor. We combine consensus representation with the degree of disagreement among lower rank matrices. The single objective function unifies all factors. Furthermore, we give the efficient solution to update the variable and to optimized the objective function through the Augmented Lagrange’s Multiplier strategy. Real-world datasets are utilized in this study to exemplify the efficiency of the introduced technique, and it is contemplated to preceding algorithms to demonstrate its superiority.

Widespread inculcation of smart meter data in modern grid is motivating stakeholders to utilize it for demand response management and achieving energy sustainability goals. One of the methods being used in this regard is Non-Intrusive Load Monitoring (NILM); for disaggregating individual devices from a combined load profile. This study combines two spectral clustering strategies using voting-based consensus clustering technique in such a way as to achieve the benefits of both parent strategies. The voters in the consensus are taken to be the solutions proposed by Spectral Cluster-Mean (SC-M) and Spectral Cluster-Eigen Vector (SC-EV) algorithms with different window sizes to achieve diversity. Currently, Spectral Clustering for NILM has been used by few research works and so far, no one technique has achieved higher accuracy in detecting various kinds of devices. The proposed strategy was evaluated on real world data set (REFIT). The results have shown enhanced overall performance by up to 6%. An in-depth analysis of various tuning parameters of SC-M and SC-EV is also presented. These novel contributions increase the feasibility of using spectral clustering and voting based consensus clustering for NILM and may open further avenues of research in this direction.

In this era of technology advancement, huge amount of data is collected from different disciplines. This data needs to be stored, processed and analyzed to understand its nature. Networks or graphs arise to model real-world systems in the different fields. Early work in network theory adopted simple graphs to model systems where the system’s entities and interactions among them are modeled as nodes and static, single-type edges, respectively. However, this representation is considered limited when the system’s entities interact through different sources. Multi-view networks have recently attracted attention due to its ability to consider the different interactions between entities explicitly. An important tool to understand the structure of multi-view networks is community detection. Community detection or clustering reveals the significant communities in the network which provides dimensionality reduction and a better understanding of the network. In this paper, a new robust clustering algorithm is proposed to detect the community structure in multi-view networks. In particular, the proposed approach constructs a 3-mode tensor from the normalized adjacency matrices that represent the different views. The constructed tensor is decomposed into a self-representation and error components where the extracted self-representation tensor is used to detect the community structure of the multi-view network. Moreover, a common subspace is computed among all views where the contribution of each view to the common subspace is optimized. The proposed method is applied to several real-world data sets and the results show that the proposed method achieves the best performance compared to other state-of-the-art algorithms.

Previous natural image segmentation algorithms through subspace learning method have over-segmentation issues in the pre-segmentation process, which will compromise the edge information, and the subspace learning model cannot effectively utilize the nonlinear structure in the image data and has weak resistance to multiple noises. To address these problems, a multi-kernel subspace learning method based on weight truncated Schatten-p norm for image segmentation is designed in this paper. First, the original natural image pre-processing operation, which is conducting adaptive morphological reconstruction watershed transformation on the image, then the original pixels are aggregated to form a superpixel image, of which the obtained superpixel block would retain more comprehensive local information; Secondly, perform feature extraction for each superpixel block, and stack the obtained feature vectors into the desired feature matrix; Then, it is input into the weighted truncated Schatten-p low-rank multi-kernel subspace learning model to obtain a similarity matrix with cluster structure on the diagonal; Finally, the similarity matrix is used as the adjacency matrix in the spectral clustering model, and the final feature data clustering and image segmentation results are obtained by the optimization solution. The final experimental results demonstrate that contrasts to existing clustering models, the proposed method accomplishes the best clustering property on two public datasets; Compared with seven segmentation algorithms on the BSDS500 dataset, and achieved the best segmentation effect on two evaluation metrics.

Oil reheating has a significant impact on global health due to its extensive consumption, especially in South Asia, and severe health risks. Nevertheless, food image analysis using multispectral imaging systems(MISs) has not been applied to oil reheating analysis despite their vast application in rapid food quality screening. To that end, the paper discusses the application of a low-cost MSI to estimate the ‘reheat cycle count classes’ (number of times an oil sample is recursively heated) and identify ‘critical classes’ at which substantial changes in the oil sample have materialized. Firstly, the reheat cycle count class is estimated with Bhattacharyya distance between the reheated and a pure oil sample as the input. The classification was performed using a support vector machine classifier that resulted in an accuracy of 83.34% for reheat cycle count identification. Subsequently, an unsupervised clustering procedure was introduced using a modified spectral clustering (SC) algorithm to distinguish critical classes under reheating. In addition, laboratory experiments were performed to ascertain the ramifications of the reheating process with a chemical analysis. The chemical analysis of the coconut oil samples used in the experiment coincided with the image analysis results and was statistically significant ( $p < 0.05$ ). Accordingly, the proposed work closes the gap for using multispectral imaging for oil reheating and proposes a novel algorithm for unsupervised detection of critical property changes in the oil. Hence, the proposed research work is significant in its practical implications, contribution to food image analysis, and unsupervised classification mechanisms.

Spectral clustering makes use of the spectrum of an input affinity matrix to segment data into disjoint clusters. The performance of spectral clustering depends heavily on the quality of the affinity matrix. Commonly used affinity matrices are constructed by either the Gaussian kernel or the self-expressive model with sparse or low-rank constraints. A technique called diffusion which acts as a post-process has recently shown to improve the quality of the affinity matrix significantly, by taking advantage of the contextual information. In this paper, we propose a variant of the diffusion process, named Self-Supervised Diffusion, which incorporates clustering result as feedback to provide supervisory signals for the diffusion process. The proposed method contains two stages, namely affinity learning with diffusion and spectral clustering. It works in an iterative fashion, where in each iteration the clustering result is utilized to calculate a pseudo-label similarity so that it can aid the affinity learning stage in the next iteration. Extensive experiments on both synthetic and real-world data have demonstrated that the proposed method can learn accurate and robust affinity, and thus achieves superior clustering performance.

Clustering has been troubled by varying shapes of sample distributions, such as line and spiral shapes. Spectral clustering and density peak clustering are two feasible techniques to address this problem, and have attracted much attention from academic community. However, spectral clustering still cannot well handle some shapes of sample distributions in the space of extracted features, and density peak clustering encounters performance problems because it cannot mine the local structures of data and well deal with non-uniform distributions. In order to solve above problems, we propose the density gain-rate peak clustering (DGPC), a new type of density peak clustering method, and then embed it in spectral clustering for performance promotion. Firstly, in order to well handle non-uniform sample distributions, we propose density gain-rate for density peak clustering. Density gain-rate is based on the assumption that the density of a clustering center will be higher with the reduce of the radius. Even under non-uniform distributions, the cluster center in low density region will still have a significant density gain-rate thus can be detected. We combine density gain-rate in density peak clustering to construct DGPC method. Then in the framework of spectral clustering, we use our new density peak clustering to cluster the samples by their extracted features from a similarity graph of these samples, such as the neighbor-based similarity graph or the self-expressiveness similarity graph. Compared with the previous spectral clustering and density peak clustering, our method leads to better clustering performances on varying shapes of sample distributions. The experiment measures the performances of our clustering method and existing clustering methods by NMI and ACC on seven real-world datasets to illustrate the effectiveness of our method.

The clustering effect of the spectral clustering algorithm depends on the calculation of the similarity between samples. Although a better clustering effect of the spectral clustering algorithm can be obtained using the Gaussian kernel function to calculate the similarity between samples, it relies on the setting of the kernel parameter. Therefore, an adaptive density-sensitive similarity measure based spectral clustering (DSSC) algorithm is proposed for improving the clustering effect. Specifically, firstly, the Euclidean distances between samples are calculated to get the nearest neighbors of each sample. Secondly, the standard deviation of distances between each sample and its nearest neighbors is calculated as the density parameter. Thirdly, the density-sensitive distances between each sample and its nearest neighbors are calculated. Finally, the similarities between each sample and its nearest neighbors are calculated to construct a similarity matrix. In addition, the proposed DSSC algorithm is parallelized on Dask distributed parallel computing platform with CPU+GPU, which can improve the computational efficiency of the DSSC algorithm by taking full advantage of the CPU and GPU resources. A series of experiments are conducted to verify the effectiveness of the proposed DSSC algorithm on several synthetic datasets and UCI datasets, and the results show that the DSSC algorithm not only achieves satisfactory clustering results, but also obtains better efficiency of performing large-scale clustering analysis.

Spectral clustering is a well-known graph-theoretic clustering algorithm. Although spectral clustering has several desirable advantages (such as the capability of discovering non-convex clusters and applicability to any data type), it often leads to incorrect clustering results because of high sensitivity to noise points. In this study, we propose a robust spectral clustering algorithm known as KNN-SC that can discover exact clusters by decreasing the influence of noise points. To achieve this goal, we present a novel approach that filters out potential noise points by estimating the density difference between data points using $k$ -nearest neighbors. In addition, we introduce a novel method for generating a similarity graph in which various densities of data points are effectively represented by expanding the nearest neighbor graph. Experimental results on synthetic and real-world datasets demonstrate that KNN-SC achieves significant performance improvement over many state-of-the-art spectral clustering algorithms.

Single-cell RNA sequencing(scRNA-seq) technology has boomed in the past decade which makes it possible to study biological problems at the resolution of cellular-level. Currently, the research mainly focuses on exploring the cellular heterogeneity, involving studies about identifying cell type identification, cell lineage tracing, spatial model reconstruction of complex organizations, etc. Clustering analysis is always the most effective way in grouping single cells in previous studies. However, existing scRNA-seq clustering methods separate pre-processing and clustering tasks that complicated the problem. In addition, the emergence of big data further limits the traditional clustering algorithms' application on scRNA-seq data. Therefore, developing novel clustering methods and improving clustering accuracy for growing scRNA-seq data is a continuous task. In this paper, we propose a highly integrated Deep Subspace Clustering Denoise Network named DSCD, which integrates denoise, dimension reduction and clustering in a unified framework. Based on the neural network architecture of autoencoder, DSCD discovers the low dimensional latent structure within scRNA-seq data from the compressed representation. Furthermore, we add a novel self-expressive denoise layer to learning the global relationships between single cells, which is the main innovation of DSCD. Experimental results on the synthetic data demonstrate the effectiveness of the novel denoise layer. From the clustering results on 5 real scRNA-seq datasets, we find that DSCD outperforms the related subspace clustering algorithms and state of the art methods. In conclusion, DSCD responds well to the rapidly increasing scRNA-seq data scale, greatly reduces human interference in dimension reduction and handles the noisy scRNA-seq data in proper way thus obtain a higher clustering accuracy.

Standard methods of subspace clustering are based on self-expressiveness in the original data space, which states that a data point in a subspace can be expressed as a linear combination of other points. However, the real data in raw form are usually not well aligned with the linear subspace model. Therefore, it is crucial to obtain a proper feature space for performing high quality subspace clustering. Inspired by the success of Convolutional Neural Networks (CNN) for extraction powerful features from visual data and the block diagonal prior for learning a good affinity matrix from self-expression coefficients, in this paper, we propose a jointly trainable feature extraction and affinity learning framework with the block diagonal prior, termed as Convolutional Subspace Clustering Network with Block Diagonal prior (ConvSCN-BD), in which we solve the joint optimization problem in ConvSCN-BD via an alternating minimization algorithm, which updates the parameters in the convolutional modules and the self-expression coefficients with stochastic gradients descent and updates other variables with close-form solutions alternatingly. In addition, we derive the connection between the block diagonal prior and the subspace structured norm, and reveal that using the block diagonal prior on the affinity matrix is essentially incorporating the feedback information from spectral clustering. Experiments on three benchmark datasets demonstrated the effectiveness of our proposal.

Subspace segmentation assumes that data comes from the union of different subspaces and the purpose of segmentation is to partition the data into the corresponding subspace. Low-rank representation (LRR) is a classic spectral-type method for solving subspace segmentation problems, that is, one first obtains an affinity matrix by solving a LRR model and then performs spectral clustering for segmentation. This paper proposes a group norm regularized factorization model (GNRFM) inspired by the LRR model for subspace segmentation and then designs an Accelerated Augmented Lagrangian Method (AALM) algorithm to solve this model. Specifically, we adopt group norm regularization to make the columns of the factor matrix sparse, thereby achieving a purpose of low rank, which means no Singular Value Decompositions (SVD) are required and the computational complexity of each step is greatly reduced. We obtain affinity matrices by using different LRR models and then performing cluster testing on different sets of synthetic noisy data and real data, respectively. Compared with traditional models and algorithms, the proposed method is faster and more robust to noise, so the final clustering results are better. Moreover, the numerical results show that our algorithm converges fast and only requires approximately ten iterations.

Spectral clustering is a very popular graph-based clustering technique that partitions data groups based on the input data similarity matrix. Many past studies based on spectral clustering, however, do not consider the global discriminative structure of the dataset. Also, the benefits of using more than one kernel have not been fully exploited with respect to spectral clustering, although it has been established by these past studies that using more than one kernel in clustering can result in a more accurate clustering than those obtained with a single kernel. Multi-kernel approaches, however, tend to be more time consuming compared to single kernel methods. To compensate these drawbacks, we integrate a global discriminative term into the clustering with an adaptive neighbor framework. This is done to preserve both the global geometric information and global discriminative information in a dual kernel space, in an attempt to optimize clustering performance. Via co-regularization, we utilize more than one kernel space to take advantage of the benefits of multiple kernels. We, however, use two heterogeneous kernels to help us reduce clustering time, since the ability to quickly process data is as equally important as its accuracy in this era of information explosion. Since these different kernel spaces admit the same underlying clustering of the data, we approach the problem looking for clustering consistent across the two kernel views. Hence we are able to detect the non-linear intrinsic geometrical information of the dataset. We perform clustering using the obtained indicator matrix from our modified Laplacian utilizing k-means. Our Experimental outcomes show that our approach gives satisfactory results in terms of accuracy and NMI, with time-to-cluster savings in comparison to other state-of-the-art clustering methods using both synthetic and public datasets.

Controlled islanding is known as a last resort to prevent power system blackouts. The most important challenge in this context is the appropriate selection of separation points in a very short time considering the practical constraints. In this regard, several islanding methods have been proposed until now. Among them, the methods that provide the appropriate solutions are usually very complicated and difficult to implement in the real-time application of power system separation. Also, all methods result in one islanding solution, which may not be optimal due to the limitation of the commonly used objective function. To overcome these limitations and reach a comprehensive solution, this paper proposes a straightforward multi-solution approach through a suggested hierarchical spectral clustering algorithm. In this concept, the most desirable islanding scenario could be selected based on secondary criteria to reach more sustainable islands. In the proposed method, the hierarchical clustering algorithm, which has good records in other applications, is improved such that the generator coherency constraint can be considered in the clustering process. Meanwhile, the transmission lines without remote-controllable circuit breakers could be easily excluded from the islanding solutions. The proposed method is tested using the model of the IEEE 39-bus test system. Furthermore, to evaluate the computational effectiveness and accuracy of the method in a large-scale grid, the model of Khorasan Regional Electric Company (KREC) power system (which is the biggest part of Iran power system) is used. The comparative analysis with the state-of-the-art methods verifies the superiority of the proposed approach.

In numerous applications the rapid increase of data size with time makes classical clustering algorithms too slow because of the high computational cost. In the present contribution, a novel method for online spectral clustering algorithm is introduced, which can be applied for simulation of structure and properties of titanate in chemical engineering. The proposed algorithm uses the recent results in the emerging field of graph signal processing. It avoids the costly computation of the eigenvectors by filtering random signals on the graph, and only a few derivative operations are needed to update the clustering result when a new data arrives. Initial simulations are presented using both simulated and real data sets, illustrating the relevance of the proposed algorithm.

The spectral clustering is a typical and efficient clustering algorithm. However, the performance of spectral algorithm depends on the determination of the appropriate similarity matrix and the number of clusters. We propose a new spectral clustering algorithm based on fast search of natural neighbors (FSNN-SC) in this paper. In the algorithm, we design a fast search algorithm to obtain the natural characteristic value supk of natural neighbor algorithm in order to improve the efficiency of searching neighbors and to construct a high-quality similarity matrix. At the same time, we design a deep traversal algorithm to adaptively determine the cluster number C. The experimental results verify that our methods are able to improve the search efficiency and find correct number of clusters. The compared experiments show that the accuracy and efficiency of the proposed algorithm are better than others.

Multi-view spectral clustering (MVSC) has become a popular approach to harvest knowledge about group information from multiple views of data, owned by different parties. A high quality MVSC approach usually requires collecting massive amount of data from each view party, in order to perform MVSC algorithm in a centralized manner. However, such centralized MVSC approach raises serious privacy concerns, not only in terms of the sensitivity property of many real-world data such as medical or financial records, but also in terms of the regulations from authorities to preclude centralized operations. Hence it is crucial to design new paradigm for training spectral clustering model on multi-view data in industrial scenarios. In this article, we propose a distributed and secure framework named Federated Multi-view Spectral Clustering (FMSC), in which a group of view parties collaboratively perform a MVSC model, but couldn't learn the data of other participants. FMSC is inspired by the concept of federated learning, and utilize Homomorphic Encryption (HE) and Differential Privacy (DP) to achieve secure and private clustering. We conduct a series of extensive experiments to verify the effectiveness of FMSC on both synthetic and real-world datasets. Evaluations show that FMSC achieves respectable clustering results over conventional centralized approaches.

Spectral cluster based on multi-view data has proven effective for clustering multi-source real-world data because consensus and complementary information of multi-view data ensure the result of clustering. Feature learning is the vital step in spectral clustering, and excellent feature representations can effectively improve spectral clustering performance. In this article, we propose Multi-View Spectral Clustering via ELM-Autoencoder Ensemble Features Representations Learning (MvSC-EF-ELM). First, Extreme Learning Machine as an Autoencoder(ELM-AE) learns feature representations by adopting a singular value decomposition, which reconstructs the inputs using the embedding feature space. Second, the single view and multi-view spectral clustering algorithm are applied embedding feature representations space into the eigenspace and cluster's them, respectively. Experiments on benchmark datasets demonstrate that our approach empirically validates the power of ELM-AE for feature learning from raw data and may effectively facilitate multi-view spectral clustering and induce superior clustering results.

Imbalance learning is a hot topic in the data mining and machine learning domains. Data-level, algorithm-level and ensemble solutions are the three main methods proposed thus far to address imbalance learning. To alleviate the issues of data explosion and feature selection in multilayer perceptron based on simultaneous two-sample representation(S2SMLP), in this paper, firstly, spectral clustering is exploited to select majority samples so as to construct a smaller training dataset for the classifier. We divide all majority samples into many clusters through spectral clustering, extract different numbers of representative samples from a cluster according to the size of each cluster, the average distance between the minority class and all samples of the cluster, then construct the training dataset of the classifier by combining these extracted samples from the majority class and all minority samples. Secondly, we propose a novel feature selection method based on the pairwise samples distance constraint, which considers the class labels of paired samples, select the features which push two similar samples closer together and pull two different samples farther apart. Finally, we conduct extensive experiments on 44 two-class imbalanced datasets and four high-dimensional DNA microarray datasets. The experimental results demonstrate that our proposed algorithms outperform some state-of-the-art algorithms in terms of $F\textrm {-measure},G\textrm {-mean}$ and AUC.

User-POI rating matrix is one of the current research hotspot of POI recommendation algorithms, the goal of which is to obtain the POIs with the highest user satisfaction. However, most existing POI recommendation algorithms ignore the diversity of recommended POI list, and the POIs in the recommended list are usually similar to each other, which cannot effectively broad the user’s perspectives. To solve this problem, a diverse and personalized recommendation method EBPRMF (Embedded Bayesian Personalized Ranking Matrix Factorization) that integrates the embedded features of the geographic-social relationships of POIs is proposed. First, by embedding and compressing the geographic and social relationships between POIs, a geographic-social relationship embedding model is constructed to evaluate the coupled correlation between POIs. The correlation between all POIs forms a POI correlation matrix. And then the spectral clustering method is leveraged to cluster the POIs according to the correlation matrix, and several different POI clusters can be obtained. Next, the Bayesian personalized ranking matrix factorization model is proposed to select POI that is close to the user’s preference from each cluster, and finally a recommendation list of POIs that is both diverse and personalized is obtained. Experimental results demonstrate that the geographic-social relationship embedding model can well represent the location and social relationship between POIs, and has a good clustering effect. The diversity of recommendation list is high, and the sorted list can be well satisfied with user preferences.

Isoperimetric graph partitioning, which is also known as the Cheeger cut, is NP-hard in its original form. In the literature, multiple modifications to this problem have been proposed to obtain approximation algorithms for clustering applications. In the context of image segmentation, a heuristic continuous relaxation to this problem introduced by Leo Grady and Eric L. Schwartz has yielded good quality results. This algorithm is based on solving a linear system of equations involving the Laplacian of the image graph. Furthermore, the same algorithm applied to a maximum spanning tree (MST) of the image graph was shown to produce similar results at a much lesser computational cost. However, the data reduction step (i.e., considering an MST, a much sparser graph compared to the original graph) leading to a faster yet useful algorithm has not been analyzed. In this paper, we revisit the isoperimetric graph partitioning problem and rectify a few discrepancies in the simplifications of the heuristic continuous relaxation, leading to a better interpretation of what is really done by this algorithm. We then use the power watershed (PW) framework to show that is enough to solve the relaxed isoperimetric graph partitioning problem on the graph induced by the union of MSTs (UMST) with a seed constraint. The UMST has a lesser number of edges compared to the original graph, thus improving the speed of sparse matrix multiplication. Furthermore, given the interest of PW framework in solving the relaxed seeded isoperimetric partitioning problem, we discuss the links between the PW limit of the discrete isoperimetric graph partitioning and watershed cuts. We then illustrate with experiments, a detailed comparison of solutions to the relaxed seeded isoperimetric partitioning problem on the original graph with the ones on the UMST and an MST. Our study opens many research directions, which are discussed in the conclusion section.

Robust multi-view spectral clustering (RMSC) minimizes the rank of probability matrix to recover a common transition probability matrix from the matrices calculated by each single view and achieves promising performance. However, for the clustering task, the underlying structure of the low-rank probability matrix is readily accessible. Yet, RMSC ignores a priori target rank information, and it does not efficiently depict the complementary information between different views. To address these problems, we propose a novel multi-view Markov chain spectral clustering method with a priori rank information. To be specific, we encourage the target rank constraint by minimizing the partial sum of singular values instead of the nuclear norm and construct a global graph from the concatenated features to exploit the complementary information embedded in different views. The objective function can be optimized efficiently by using the augmented Lagrangian multiplier algorithm. Extensive experimental results on one synthetic and eight benchmark datasets demonstrate that the proposed method outperforms the state-of-the-art approaches.

As the last resort of emergency control, controlled islanding is an effective means of preventing fault propagation and a system-wide blackout. However, conventional ac transmission lines are unavailable to be employed for power exchange between these islands. To make full use of the dc power modulation capability of voltage source converter-based high-voltage direct current (VSC-HVdc) links, a new controlled islanding model is put forward for an ac/VSC-HVdc hybrid grid to minimize the composite power-flow disruption, in which the dc-terminals belonging to a VSC-HVdc link are placed in different islands. To solve this model, a semi-supervised spectral clustering-based approach is proposed by transforming the problem into a weighted undirected graph segmentation problem. The novelty of this paper is to find an optimal islanding solution in real time such that the power exchanges between islands are implemented via a VSC-HVdc link to reduce the generation-load imbalance. The simulation results on the IEEE 39-bus system and a real-world system verify the effectiveness and superiority of the proposed approach.

Unsupervised polarimetric synthetic aperture radar (PolSAR) image classification is an important task in PolSAR automatic image analysis and interpretation. Generally, a group of features is insufficient to effectively classify PolSAR images, especially in multiple terrain scenarios. Therefore, multiple features need to be extracted for PolSAR image classification. However, how to combine and integrate these features effectively to fully utilize each feature's information and discriminability need to be determined. Such integrated work has traditionally received little attention. In this paper, a novel unsupervised classification framework for PolSAR images is proposed. First, a PolSAR image is oversegmented via a fast superpixel segmentation method. Second, five feature vectors are extracted from PolSAR images via superpixels, resulting in five corresponding similarity matrices that are constructed by using Gaussian kernels. Third, consensus similarity network fusion (CSNF), originally proposed and widely used for biomedical sciences, is employed to combine and integrate the five similarity matrices to obtain a fused similarity matrix. Fourth, spectral clustering method, based on the fused similarity matrix, is used to cluster the PolSAR image. Finally, a novel classification postprocessing procedure is presented and exploited to smooth the initial clusters and correct some misclassified pixels. The extensive experimental results conducted on one simulated and two real-world PolSAR images demonstrate the feasibility and superiority of the proposed method compared with five other state-of-the-art classification approaches.

Spectral clustering transforms the data clustering problem into a graph-partitioning problem and classifies data points by finding the optimal sub-graphs. Traditional spectral clustering algorithms use Gaussian kernel function to construct the similarity matrix, so they are sensitive to the selection of scale parameter. In addition, they need to randomly determine the initial cluster centers at the clustering stage and the clustering performance is not stable. Therefore, this paper presents an algorithm on the basis of message passing, which makes use of a density adaptive similarity measure, describing the relations between data points and obtaining high-quality cluster centers through message passing mechanism in AP clustering. The performance of clustering is optimized by this method. The experiments show that the proposed algorithm can effectively deal with the clustering problem of multi-scale datasets. Moreover, its clustering performance is very stable, and the clustering quality is better than traditional spectral clustering algorithm and k-means algorithm.

In this paper, we propose a data-driven model for predicting the travel speed of urban roads, based on GPS trajectories of vehicles. Though this is a strategically important task in many traffic monitoring systems, the problem has not yet been well-solved given the following two challenges. The first is the effective modeling approach that can predict the urban road travel speed faced with the data sparsity problem, i.e., many road segments may not be traveled by any GPS-equipped vehicles in some time slots. Second, the traffic condition influences the travel speed on a road but it is hard to capture the pattern as it fluctuates irregularly. To address these problems, we propose to utilize the probabilistic principal component analysis-based model to predict the urban road travel speed, which can handle the problem of data sparsity. In addition, to improve the prediction performance of the probabilistic generative model, we incorporate the traffic condition to partition roads into clusters using a spectral clustering method. Implementing prediction on each cluster brings smaller traffic condition variability within clusters and make it capable of parallel computing. We evaluate our proposed method in a case study for the citywide road network of Shanghai, using GPS trajectories generated by over 13000 taxis over a period of one month. Empirical results demonstrate that the model outperforms the competing methods in terms of both effectiveness and robustness.

Spectral clustering has become one of the most popular clustering algorithms in recent years. In real-world clustering problems, the data points for clustering may have considerable noise. To the best of our knowledge, no single clustering algorithm is able to identify all different types of cluster structures. In the existing spectral clustering methods, little effort has been made to explicitly handle both the possibly considerable noise in data points and the robustness of clustering methods, which often degrades the clustering performance. In this paper, motivated by resampling and matrix aggregation, we propose a method for robust spectral clustering. In our method, we first construct multiple transition probability matrices, each is constructed by a subset of randomly selected features. Then, these matrices can be used to recover a shared low-rank similarity matrix, which is the input to the spectral clustering, and several sparse matrices, which represent the noise. The corresponding optimization problem has a low-rank constraint on the transition probability matrix. To solve the corresponding optimization problem, an optimization procedure based on the scheme of Augmented Lagrangian Method of Multipliers is designed. Experimental results on several real-world datasets show that our method has superior performance over several state-of-the-art clustering methods.