Spectral ensemble clustering with doubly stochastic co-association matrix

Weighted adaptively ensemble clustering method based on fuzzy Co-association matrix

SummaryCluster ensemble combines multiple base clustering results in a suitable way to improve the accuracy of the clustering result. In the conventional cluster ensemble frameworks, pairwise constraints and constraint projections have not been used together, and spectral clustering algorithm is rarely adopted to serve as the consensus function. In this paper, we design a constraint projections for semi‐supervised spectral clustering ensemble (CPSSSCE) model. It takes advantages of spectral clustering algorithm and executes semi‐supervised learning twice. Compared to traditional cluster ensemble approaches, CPSSSCE is characterized by several properties. First, the original data are transformed to lower‐dimensional representations by constraint projection before base clustering. Second, a similarity matrix is constructed using the base clustering results and modified using pairwise constraints. Third, the spectral clustering algorithm is applied to process the similarity matrix to obtain a consensus cluster result. Extensive experiments on standard University of California Irvine Machine Learning Repository (UCI) and Microsoft datasets demonstrated that the CPSSSCE is superior to other cluster ensemble algorithms including a semi‐supervised spectral clustering ensemble.

Spectral Clustering (SC) is an effective clustering method for its excellent performance in partitioning non-linearly distributed data. On the other hand, Ensemble Clustering (EC), a different clustering technology, can promote cluster quality by ensembling the results of base clusterings. In this work, we concentrate on an EC framework that utilizes SC as the base method. Nevertheless, SC suffers from scalability due to its high computational complexity in constructing the Laplacian graph and computing the corresponding eigendecomposition. In the past decades, many efforts have been made to it. However, SC suffers from the scalability issue in processing extensive data, especially in web-scale scenarios. Additionally, EC requires multiple clustering results as the ensemble bases, which further aggravates resource consumption. To address this issue, LiteWSEC, a simple yet efficient Lightweight Framework for Web-scale Spectral Ensemble Clustering, is proposed to cluster web-scale data with limited resource requirements. It adopts the Web-scale Spectral Clustering (WSC) as the base method, which has minimal space overhead without computing overall embedding explicitly. LiteWSEC is highly flexible in the memory requirement, which is adaptive to the available resource. It can partition web-scale data (e.g., <inline-formula><tex-math notation="LaTeX">$n $</tex-math></inline-formula> = 8,000 k) in an resource-limited host (e.g., memory is restricted to 1 GB). Experiments on real-world, large-scale, and web-scale datasets demonstrate both the efficiency and effectiveness of LiteWSEC over state-of-the-art SC and EC methods.

A robust adaptive clustering analysis method for automatic identification of clusters

Cluster ensembles are approaches to combine different clustering results to obtain a robust consensus partitioning. However, many cluster ensemble methods suffer from the problem of scalability since the extensive cost of calculating co-association matrix, which makes it hard to perform cluster ensemble on large scale datasets. In this paper, we proposed a scalable co-association cluster ensemble framework using a compressed version of co-association matrix formed by selecting representative points of origin instances. Experiments show that our method could get a comparable performance on medium size datasets to existing co-association ensemble method like CSPA or spectral clustering, and is able to handle large scale datasets.

P42-T Feasibility of an international normative database for nerve excitability studies

Evaluation measures for cluster ensembles based on a fuzzy generalized Rand index

Ensemble clustering based on evidence extracted from the co-association matrix

Moderate diversity for better cluster ensembles

Each clustering algorithm usually optimizes a qualification metric during its learning process. The qualification metric in traditional clustering algorithms considers all the features of under-consideration dataset equally; it means each feature participates in the clustering process equivalently. Considering that some features have more information than the others in a dataset (due to their lower information or their higher variances, etc.), we proposes a fuzzy weighted clustering algorithm. We name this new clustering algorithm, Fuzzy Weighted Locally Adaptive Clustering (FWLAC) algorithm. The proposed FWLAC algorithm is capable of handling imbalanced clustering. However, FWLAC algorithm suffers from its sensitivity to the two parameters that should be tuned manually. The performance of FWLAC algorithm is affected by well-tuning of its parameters. So the paper proposes two solutions to well-tuning of its two parameters. In the first solution, we propose a simple clustering ensemble framework to show the sensitivity of the WLAC algorithm to its manual well-tuning. Although it is not a try-and-error procedure, it is like a grid search, where we use different pairs of values for both parameters h 1 and h 2. Per each pair of values for parameters h 1 and h 2, the algorithm produces a partitioning. So after the grid search, we obtain a large number of partitionings. We break any of the partitionings into its clusters, and then they form an ensemble of clusters. Finally the consensus partitioning is extracted from them by a consensus function. The algorithm is not data dependent at all. For all datasets, we use a similar grid search and a similar set of values for the parameters h 1 and h 2. In this way we have proposed an alternative solution to parameter selection. We use a selection phase to select/remove some clusters from our ensemble of clusters to obtain an elite ensemble of clusters. To do this, a stability measure, normalized mutual information (NMI), was used to validate a cluster. The paper shows the effectiveness of the proposed clustering frameworks both theoretically and experimentally.

The clustering ensemble technique that integrates multiple clustering results can improve the accuracy and robustness of the final clustering. In many clustering ensemble algorithms, the co-association matrix (CA matrix), which reflects the frequency of any two samples being partitioned into the same cluster, plays an important role. However, generally, the CA matrix is highly sparse with low value density, which may limit the performance of an algorithm based on it. To handle these issues, in this paper, we propose a growing tree model (GoT). In this model, the CA matrix is firstly refined by the shortest path technique so that its sparsity will be mitigated. Then, a set of representative prototype examples is discovered. Finally, to handle the low value density of the CA matrix, the prototypes gradually connect to their neighborhood, which likes a set of trees growing up. The rationality of the discovered prototype examples is illustrated by theoretical analysis and experimental analysis. The working mechanism of the GoT is visually shown on synthetic data sets. Experimental analyses on eight UCI data sets and eight image data sets show that the GoT outperforms nine representative clustering ensemble algorithms.

Ensemble clustering has recently emerged as a powerful tool for aggregating multiple clustering results into a probably better and more robust clustering result. While many ensemble clustering techniques have been developed in recent years, there is still a potential drawback in most of the existing algorithms. They generally neglect the possible noise inside the ensemble of base clusterings, which may exhibit a negative influence on the robustness of the consensus result. To address this, this paper proposes a new ensemble clustering algorithm based on noise-aware graph decomposition. The co-association matrix is first constructed to accumulate information from multiple base clusterings, and then sparsified by means of K-nearest neighbors. By treating the sparsified co-association matrix as the similarity matrix, the corresponding graph is further decomposed into two parts, i.e., the corruption(noise) graph and the good(denoised) graph. In particular, the denoised graph as well as its spectral embedding can be learned simultaneously by solving a trace minimization problem. Finally, upon the learned spectral embedding, the k-means discretization is performed to obtain the final consensus clustering. Experiments on multiple real-world datasets have shown the superiority of the proposed algorithm.

Classification is a familiar technique used to classify objects. Clustering techniques are employed to segment data into multiple groups. Objects present in clusters exhibit similar characteristics. Machine learning classifiers applied on Functional Magnetic Resonance Imaging (fMRI) data facilitate to classify cognitive states. Clustering methods, such as K-means, Hierarchical, Spectral, and Consensus Clustering Evidence Accumulation (CCEAC) are used to segment brain regions effectively using fMRI data. Selection of voxels as features is a challenging task for cognitive state classification. In this paper, a new hybrid method for classification has been proposed by combining both clustering and classifier. K-means, Hierarchical, Spectral, and CCEAC are applied on StarPlus fMRI data, to obtain clusters. The dissimilarity metrics normalized Mutual Information (NMI), Variation of Information (VI) and Rand Index (RI) are used in CCEAC for selection of optimal clusters. The main focus of the present work is to choose few number of voxels as features by using clustering methods and then built classifier based on fewer voxels. The proposed method has been evaluated on standard Starplus data and has shown good classification accuracy for few number of voxels.

Community detection in graphs can be viewed as the estimation of a partition map that remains stable under admissible perturbations of graph topology and node attributes. While modern graph neural networks (GNNs) achieve strong empirical accuracy, they often exhibit severe assignment drift under minor perturbations, leading to illusory community structures. In this work, we propose DISPEL-GNN, a stability-aware graph learning framework that integrates spectral operator regularization, Bayesian uncertainty modeling, and risk-aware dynamic attention for perturbation-bounded community detection. The model explicitly constrains graph operators through uniform spectral norm bounds, high-frequency energy suppression, and commutator alignment while dynamically modulating message passing based on node-level spectral risk and epistemic uncertainty. We further formalize instability via assignment of drift functional and establish perturbation bounds linking drift to operator norms and spectral gaps, complemented by a PAC-Bayesian generalization guarantee. Extensive experiments on real-world benchmarks including Cora, Citeseer, Pubmed, Cora-Full, and DBLP demonstrate that DISPEL-GNN consistently reduces assignment drift by 18–35% under feature noise and edge perturbations while improving clustering quality with up to +3.0 NMI and +0.04 ARI compared to strong baselines such as GAT and Bayesian GNNs. The normalized mutual information (NMI), adjusted Rand index (ARI), and PAC-Bayesian (PAC) constraints serve as evaluative and theoretical instruments in this study. Additional studies on synthetic graphs with controlled spectral gaps confirm that the proposed method maintains stable community assignments in low-gap regimes where classical spectral and GNN-based methods degrade sharply. These results establish DISPEL-GNN as a mathematically grounded and practically effective framework for robust and interpretable community detection. A metric-wise dominance analysis shows that DISPEL-GNN achieves metric-wise dominance across most accuracy and robustness criteria, with minor tradeoffs in modularity on selected datasets. These results indicate that explicitly modeling stability and uncertainty provides a principled pathway toward reliable and interpretable community detection in noisy graph environments.

Many stability measures, such as Normalized Mutual Information NMI, have been proposed to validate a set of partitionings. It is highly possible that a set of partitionings may contain one or more high quality clusters but is still adjudged a bad cluster by a stability measure, and as a result, is completely neglected. Inspired by evaluation approaches measuring the efficacy of a set of partitionings, researchers have tried to define new measures for evaluating a cluster. Thus far, the measures defined for assessing a cluster are mostly based on the well-known NMI measure. The drawback of this commonly used approach is discussed in this paper, after which a new asymmetric criterion, called the Alizadeh--Parvin--Moshki--Minaei criterion APMM, is proposed to assess the association between a cluster and a set of partitionings. We show that the APMM criterion overcomes the deficiency in the conventional NMI measure. We also propose a clustering ensemble framework that incorporates the APMM's capabilities in order to find the best performing clusters. The framework uses Average APMM AAPMM as a fitness measure to select a number of clusters instead of using all of the results. Any cluster that satisfies a predefined threshold of the mentioned measure is selected to participate in an elite ensemble. To combine the chosen clusters, a co-association matrix-based consensus function by which the set of resultant partitionings are obtained is used. Because Evidence Accumulation Clustering EAC can not derive the co-association matrix from a subset of clusters appropriately, a new EAC-based method, called Extended EAC EEAC, is employed to construct the co-association matrix from the chosen subset of clusters. Empirical studies show that our proposed approach outperforms other cluster ensemble approaches.