Spectral Clustering Research Articles

A comprehensive review of community detection in graphs

The study of complex networks has significantly advanced our understanding of community structures which serves as a crucial feature of real-world graphs. Detecting communities in graphs is a challenging problem with applications in sociology, biology, and computer science. Despite the efforts of an interdisciplinary community of scientists, a satisfactory solution to this problem has not yet been achieved. This review article delves into the topic of community detection in graphs, which serves as a thorough exposition of various community detection methods from perspectives of modularity-based methods, spectral clustering, probabilistic modeling, and deep learning. Along with the methods, a new community detection method designed by us is also presented. Additionally, the performance of these methods on the datasets with and without ground truth is compared. In conclusion, this comprehensive review provides a deep understanding of community detection in graphs.

A restarted large-scale spectral clustering with self-guiding and block diagonal representation

Spectral clustering, a prominent unsupervised machine learning method, involves a critical task of constructing a similarity matrix. In existing approaches, this matrix is either computed once for all or updated alternatively. However, the former struggles to capture comprehensive relationships among data points, and the latter is often impractical for large-scale problems. This study introduces a new clustering framework with self-guidance and a block diagonal representation, retaining valuable information from previous cycles. To our knowledge, this is the first application of such a framework to spectral clustering, with a key distinction being the reclassification of samples in each cycle. To reduce computational overhead, we employ a block diagonal representation with Nyström approximation for constructing the similarity matrix. Theoretical results justify the rationality of approximate computations in spectral clustering. Comprehensive experiments on benchmark datasets demonstrate the superiority of our proposed algorithms over state-of-the-art methods for large-scale clustering. Notably, our framework has the potential to enhance clustering algorithms, performing well even with a randomly chosen initial guess.

Semi-supervised clustering guided by pairwise constraints and local density structures

Clustering based on local density peaks and graph cut (LDP-SC) is one of the state-of-the-art algorithms in unsupervised clustering, which first divides the data set to be multiple local trees, and then aggregates these local trees to obtain the final clustering result. However, for complex data sets, there might exist data points from different classes in the same local tree. In this article, we use pairwise constraint information to resolve this issue and propose a semi-supervised local density peaks and graph cut based clustering algorithm (SLDPC). In particular, SLDPC proposes intra-cluster conflict resolution and inter-cluster conflict resolution steps to split the local trees which are inconsistent with the provided pairwise constraint information. Theoretically, we show that the two steps will finish in a finite number of operations and the split local trees will be consistent with the pairwise constraint information. Subsequently, root node redirection and noise filtering steps are designed to avoid the local trees becoming too fragmented. Finally, we exploit the E2CP algorithm to further improve the similarity matrix between local trees using the pairwise constraint information, and the spectral clustering algorithm is adopted to obtain the clustering result. Experiments on multiple widely used synthetic and real-world data sets show that SLDPC is superior to LDP-SC and several other semi-supervised prominent clustering algorithms for most of the cases.

Optimizing Patient Stratification in Healthcare: A Comparative Analysis of Clustering Algorithms for EHR Data

Advanced data analytics are increasingly being employed in healthcare research to improve patient classification and personalize medicinal therapies. In this paper, we focus on the critical problem of clustering electronic health record (EHR) data to enable appropriate patient categorization. In the era of personalized medicine, optimizing patient classification is critical to healthcare analytics. This research presents a comparative assessment of different clustering algorithms for Electronic Health Record (EHR) data, with the goal of improving the efficacy and productivity of patient clustering methods. Our study focuses on Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (Fuzzy TOPSIS) as a Multi-Criteria Decision-Making (MCDM) strategy, includes an in-depth assessment of eight clustering algorithms: K-Means, DBSCAN, Hierarchical Clustering, Mean Shift, Affinity Propagation, Spectral Clustering, Gaussian Mixture Models (GMM), as well as Self-Organizing Maps. The evaluation factors used for evaluation in this research are Cluster Quality Metrics, Scalability, Robustness to Noise, Cluster Shape and Density, Interpretability, Cluster Number, Dimensionality, and Consistency and Stability. These criteria and alternatives were chosen after conducting a thorough assessment of the literature and consulting with domain experts. All participated specialists actively engaged in the decision-making process, bringing unique insights into the best clustering algorithms for healthcare data. The results of this study illustrate each algorithm’s strengths and weaknesses in the setting of patient stratification, providing insight into their performance across multiple dimensions. The fuzzy TOPSIS MCDM strategy is a reliable instrument for synthesizing expert opinions and methodically evaluating the found clustering alternatives. This study advances healthcare analytics by giving practitioners and researchers with informative perspectives on the selection of clustering algorithms designed to address the unique problems of patient stratification utilizing EHR data.

Fast Clustering by Directly Solving Bipartite Graph Clustering Problem.

Spectral clustering (SC) has been widely used in many applications and shows excellent performance. Its high computational cost limits its applications; many strategies including the anchor technique can partly alleviate the high computational cost problem. However, early methods ignore the fact that SC usually involves two stages: relaxation and postprocessing, i.e., it relaxes the discrete constraints to continuous constraints, and then conducts the postprocessing to get the discrete solution, which is time-consuming and deviates from directly solving the primal problem. In this article, we first adopt the bipartite graph strategy to reduce the time complexity of SC, and then an improved coordinate descent (CD) method is proposed to solve the primal problem directly without singular value decomposition (SVD) and postprocessing, i.e., directly solving the primal problem not approximately solving. Experiments on various real-world benchmark datasets show that the proposed method can get better solutions faster with better clustering performance than traditional optimization methods. Furthermore, it can jump out of local minima of traditional methods and continue to obtain better local solutions. Moreover, compared with other clustering methods, it also shows its superiority.

A low-rank ODE for spectral clustering stability

Spectral clustering is a well-known technique which identifies k clusters in an undirected graph, with n vertices and weight matrix W∈Rn×n, by exploiting its graph Laplacian L(W). In particular, the k clusters can be identified by the knowledge of the eigenvectors associated with the k−1 smallest non zero eigenvalues of L(W), say λ2,…,λk (recall that λ1=0). Identifying k is an essential task of a clustering algorithm, since if λk+1 is close to λk the reliability of the method is reduced. The k-th spectral gap λk+1−λk is often considered as a stability indicator. This difference can be seen as an unstructured distance between L(W) and an arbitrary symmetric matrix L⋆ with vanishing k-th spectral gap. A more appropriate structured distance to ambiguity such that L⋆ represents the Laplacian of a graph has been proposed in Andreotti et al. (2021) [2]. This is defined as the minimal distance between L(W) and Laplacians of graphs with the same vertices and edges, but with weights that are perturbed such that the k-th spectral gap vanishes. In this article we consider a slightly different approach, still based on the reformulation of the problem into the minimization of a suitable functional in the eigenvalues. After determining the gradient system associated with this functional, we introduce a low-rank projected system, suggested by the underlying low-rank structure of the extremizers of the problem. The integration of this low-rank system, requires both a moderate computational effort and a memory requirement, as it is shown in some illustrative numerical examples.

Stacked Network to Realize Spectral Clustering With Adaptive Graph Learning

Stacked Network to Realize Spectral Clustering With Adaptive Graph Learning

Deep Tensor Spectral Clustering Network via Ensemble of Multiple Affinity Tensors.

Tensor spectral clustering (TSC) is an emerging approach that explores multi-wise similarities to boost learning. However, two key challenges have yet to be well addressed in the existing TSC methods: (1) The construction and storage of high-order affinity tensors to encode the multi-wise similarities are memory-intensive and hampers their applicability, and (2) they mostly employ a two-stage approach that integrates multiple affinity tensors of different orders to learn a consensus tensor spectral embedding, thus often leading to a suboptimal clustering result. To this end, this paper proposes a tensor spectral clustering network (TSC-Net) to achieve one-stage learning of a consensus tensor spectral embedding, while reducing the memory cost. TSC-Net employs a deep neural network that learns to map the input samples to the consensus tensor spectral embedding, guided by a TSC objective with multiple affinity tensors. It uses stochastic optimization to calculate a small part of the affinity tensors, thereby avoiding loading the whole affinity tensors for computation, thus significantly reducing the memory cost. Through using an ensemble of multiple affinity tensors, the TSC can dramatically improve clustering performance. Empirical studies on benchmark datasets demonstrate that TSC-Net outperforms the recent baseline methods.

Identifying highly-valued bank customers with current accounts based on the frequency and amount of transactions

We hypothesize that highly-valued bank customers with current accounts can be identified by a high frequency of transactions in large amounts of money. To test our hypothesis, we employ machine learning predictive models to real data, including 407851 transactions of 4760 customers with current accounts in a local bank in Jordan. Thus, we exploit three clustering algorithms: density-based spatial clustering of applications with noise, spectral clustering, and ordering points to identify the clustering structure. The two segments of customers (generated from the clustering process) have different transactional characteristics. Our customer behavioral segmentation accuracy is, at best, 0.99 and at least 0.82. Likewise, we build three classification models using our segmented data: a neural network, a support vector machine, and a decision tree. Our predictive models have an accuracy of 0.97 at best and 0.90 at least. Our experimental results confirm that the frequency and amount of transactions of bank customers with current accounts are most likely sufficient indicators for recognizing those customers whom banks highly value. Our predictive models state that the two most critical indicators are the deposit and withdrawal transactions performed on ATMs. In contrast, the least significant indicators are the transactions of credit cards and credit cheques.

Greedy recursive spectral bisection for modularity-bound hierarchical divisive community detection

Spectral clustering techniques depend on the eigenstructure of a similarity matrix to assign data points to clusters, so that points within the same cluster exhibit high similarity and are compared to those in different clusters. This work aimed to develop a spectral method that could be compared to clustering algorithms that represent the current state of the art. This investigation conceived a novel spectral clustering method, as well as five policies that guide its execution, based on spectral graph theory and embodying hierarchical clustering principles. Computational experiments comparing the proposed method with six state-of-the-art algorithms were undertaken in this study to evaluate the clustering methods under scrutiny. The assessment was performed using two evaluation metrics, specifically the adjusted Rand index, and modularity. The obtained results furnish compelling evidence, indicating that the proposed method is competitive and possesses distinctive properties compared to those elucidated in the existing literature. This suggests that our approach stands as a viable alternative, offering a robust choice within the spectrum of available same-purpose tools.

Development of hierarchical two-stage constrained spectral clustering algorithm to enhance power system distribution network resiliency under zonal attacks

Development of hierarchical two-stage constrained spectral clustering algorithm to enhance power system distribution network resiliency under zonal attacks

Quantitative Stylistic Analysis of Middle Chinese Texts Based on the Dissimilarity of Evolutive Core Word Usage

Stylistic analysis enables open-ended and exploratory observation of languages. To fill the gap in the quantitative analysis of the stylistic systems of Middle Chinese, we construct lexical features based on the evolutive core word usage and scheme a Bayesian method for feature parameters estimation. The lexical features are from the Swadesh list, each of which has different word forms along with the language evolution during the Middle Ages. We thus count the varied word of those entries along with the language evolution as the linguistic features. With the Bayesian formulation, the feature parameters are estimated to construct a high-dimensional random feature vector to obtain the pair-wise dissimilarity matrix of all the texts based on different distance measures. Finally, we perform the spectral embedding and clustering to visualize, categorize, and analyze the linguistic styles of Middle Chinese texts. The quantitative result agrees with the existing qualitative conclusions and, furthermore, betters our understanding of the linguistic styles of Middle Chinese from both the inter-category and intra-category aspects. It also helps unveil the special styles induced by the indirect language contact.

Effects of vitamin D signaling in cardiovascular disease: centrality of macrophage polarization.

Among the leading causes of natural death are cardiovascular diseases, cancer, and respiratory diseases. Factors causing illness include genetic predisposition, aging, stress, chronic inflammation, environmental factors, declining autophagy, and endocrine abnormalities including insufficient vitamin D levels. Inconclusive clinical outcomes of vitamin D supplements in cardiovascular diseases demonstrate the need to identify cause-effect relationships without bias. We employed a spectral clustering methodology capable of analyzing large diverse datasets for examining the role of vitamin D's genomic and non-genomic signaling in disease in this study. The results of this investigation showed the following: (1) vitamin D regulates multiple reciprocal feedback loops including p53, macrophage autophagy, nitric oxide, and redox-signaling; (2) these regulatory schemes are involved in over 2,000 diseases. Furthermore, the balance between genomic and non-genomic signaling by vitamin D affects autophagy regulation of macrophage polarization in tissue homeostasis. These findings provide a deeper understanding of how interactions between genomic and non-genomic signaling affect vitamin D pharmacology and offer opportunities for increasing the efficacy of vitamin D-centered treatment of cardiovascular disease and healthy lifespans.

A study on diversion behavior in weaving segments: Individualized traffic conflict prediction and causal mechanism analysis

Lane change behavior disrupts traffic flow and increases the potential for traffic conflicts, especially on expressway weaving segments. Focusing on the diversion process, this study incorporating individual driving patterns into conflict prediction and causation analysis can help develop individualized intervention measures to avoid risky diversion behaviors. First, to minimize measurement errors, this study introduces a lane line reconstruction method. Second, several unsupervised clustering methods, including k-means, agglomerative clustering, gaussian mixture, and spectral clustering, are applied to explore diversion patterns. Moreover, machine learning methods, including Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM), Attention-based LSTM, eXtreme Gradient Boosting (XGB), Support Vector Machine (SVM), and Multilayer Perceptron (MLP), are employed for real-time traffic conflict prediction. Finally, mixed logit models are developed using pre-conflict condition data to investigate the causal mechanisms of traffic conflicts. The results indicate that the K-means algorithm with four clusters exhibits the highest Calinski-Harabasz and Silhouette scores and the lowest Davies-Bouldin scores. With superior classification accuracy and generalization ability, the LSTM is used to develop the personalized traffic conflict prediction model. Sensitivity analysis indicates that incorporating the diversion patterns into the LSTM model results in an improvement of 3.64% in Accuracy, 7.15% in Precision, and 1.34% in Recall. Results from the four mixed logit models indicate significant differences in factors contributing to traffic conflicts within each diversion pattern. For instance, increasing the speed difference between the target vehicle and the right preceding vehicle benefits traffic conflict during acceleration diversions but decreases the likelihood of traffic conflicts during deceleration diversions. These results can help traffic engineers propose individualized solutions to reduce unsafe diversion behavior.

Graph Convolutional Spectral Clustering for Electricity Market Data Clustering

As the power grid undergoes transformation and the Internet’s influence grows, the electricity market is evolving towards informatization. The expanding scale of the power grid and the increasing complexity of operating conditions have generated a substantial amount of data in the power market. The traditional power marketing model is no longer suitable for the modern power market’s development trend. To tackle this challenge, this study employs random forest and RBF models for processing electricity market data. Additionally, it explores the synergy of graph convolutional network and spectral clustering algorithms to enhance the accuracy and efficiency of data mining, enabling a comprehensive analysis of data features. The experimental results successfully extracted various electricity consumption features. This approach contributes to the informatization efforts of power grid enterprises, enhances power data perception capabilities, and offers reliable support for decision makers.

Characterization of neurofibrillary tangle immunophenotype signatures to classify tangle maturity in Alzheimer's disease.

Tau aggregation into neurofibrillary tangles in Alzheimer's disease (AD) is a dynamic process involving changes in tau phosphorylation, isoform composition, and morphology. To facilitate studies of tangle maturity, we developed an image analysis pipeline to study antibody labeling signatures that can distinguish tangle maturity levels in AD brain tissue. Using fluorescent immunohistochemistry, we co-labeled AD brain tissue with four antibodies that bind different tau epitopes. Mean fluorescence intensity of each antibody was measured, and spectral clustering was used to identify tangle immunophenotypes. Five distinct tangle populations were identified, and different tangle maturity immunophenotypes were identified with increasing Braak stage. Early tangle immunophenotypes were more prevalent in later affected regions and advanced immunophenotypes were associated with ghost morphology. Our findings indicate that tangle populations characterized by advanced tau immunophenotypes are associated with higher Braak stage and more mature morphology, providing a new framework for defining tangle maturity levels using tau antibody signatures. Populations of neurofibrillary tangles exist in Alzheimer's disease. The immunophenotype of neurofibrillary tangle populations relates to their maturity. The most advanced immunophenotypes are associated with higher Braak stage. The most advanced immunophenotypes are associated with ghost morphology. The most immature immunophenotypes are associated with later affected regions.

Inoculation with Bacillus thuringiensis reduces uptake and translocation of Pb/Cd in soil-wheat system: A life cycle study

Microbial inoculation is an important strategy to reduce the supply of heavy metals (HMs) in soil-crop systems. However, the mechanisms of microbial inoculation for the availability of HMs in soil and their accumulation/transfer in crops remain unclear. Here, the inhibitory effect of inoculation with Bacillus thuringiensis on the migration and accumulation of Pb/Cd in the soil-wheat system during the whole growth period was investigated by pot experiments. The results showed that inoculation with Bacillus thuringiensis increased soil pH and available nutrients (including carbon, nitrogen, and phosphorus), and enhanced the activities of nutrient-acquiring enzymes. Dominance analysis showed that dissolved organic matter (DOM) is the key factor affecting the availability of HMs. The content of colored spectral clusters and humification characteristics of DOM were significantly improved by inoculation, which is conducive to reducing the availability of Pb/Cd, especially during the flowering stage, the decrease was 12.8 %. Inoculation decreased Pb/Cd accumulation in the shoot and the transfer from root to shoot, with the greatest decreases at the jointing and seedling stages (27.0–34.1 % and 6.9–11.8 %), respectively. At the maturity stage, inoculation reduced the Pb/Cd accumulation in grain (12.9–14.7 %) and human health risk (4.1–13.2 %). The results of Pearson correlation analysis showed that the availability of Pb/Cd was positively correlated with the humification of DOM. Least square path model analysis showed that Bacillus thuringiensis could significantly reduce Pb/Cd accumulation in the grain and human health risks by regulating DOM spectral characteristics, the availability of HMs in soil and metals accumulation/transport in wheat at different growth stages. This study revealed the inhibition mechanism of Bacillus thuringiensis on migration of Pb/Cd in a soil-wheat system from a viewpoint of a full life cycle, which offers a valuable reference for the in-situ remediation of HM-contaminated soil and the safe production of food crops in field.

Adaptive weighted multi-view subspace clustering method for recognizing urban functions from multi-source social sensing data

ABSTRACT Multi-source social sensing data provide new opportunities to identify urban functions from the perspective of human activity. The information embedded in multi-source data typically needs to be fused to obtain a comprehensive view of urban functions. Although multi-view clustering has been successfully used to fuse multi-source social sensing data, the adaptive determination of fusion weights for high-dimensional and noisy multi-source social sensing data remains challenging. Therefore, this study proposes an adaptive weighted multi-view subspace clustering (AWMSC) method. First, we use two neural networks to map multi-source data into a common latent representation and multiple specific latent representations, which serve as the query vector and input vectors of the attention mechanism, respectively. Then, the weight of each type of data is calculated based on the attention mechanism. Finally, the specific latent representations of the multi-source data are weighted and fused into a shared subspace representation, which is used as the input of the spectral clustering algorithm to obtain clustering results. AWMSC is applied to identify urban functional zones in Beijing using bus transactions, taxi trajectories, and points of interest datasets. The results show that AWMSC outperforms the typical single-view, weighted-average, and representative multi-view methods. AWMSC can obtain a comprehensive understanding of urban functional zones which may help government departments make more accurate strategic decisions.

Self-supervised spectral clustering with spectral embedding for hyperspectral image classification

ABSTRACT Spectral clustering, as an algorithm based on graph theory and spectral theory, has shown excellent performance in the classification tasks of hyperspectral images in recent years. Although better results have been achieved, some challenges still exist. The inclusion of a priori information can increase the performance of spectral clustering algorithms; however, in practice, it is often unable to meet the demand for a priori information; at the same time, spectral clustering for the quality of the similarity matrix is demanding, and some of the current algorithms are to improve the similarity matrix from the aspect of data planning, and ultimately for the label feature matrices are diluted. In response to the above problems, this paper proposes a self-supervised spectral clustering with spectral embedding (SESSC). The algorithm obtains a low-dimensional representation of the data through spectral embedding, which can simplify clustering while preserving feature information; then uses the similarity matrix about the data and the guidance of the sample constraint information to obtain a new similarity matrix in order to further refine the structural graph, and the result can feed back and optimize the label feature matrix and the low-dimensional representation of the data. Additionally, we introduce a fractional theory in the update of the sample variable matrix, which assures the integrity and validity of the information in the update. Experimental results show that the proposed algorithm has better performance in hyperspectral image classification than existing spectral clustering algorithms.

Speaker Diarization Using Bi-LSTM and Spectral Clustering

Speaker Diarization Using Bi-LSTM and Spectral Clustering