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

Moderate diversity for better cluster ensembles

The classic Fuzzy C-means (FCM) algorithm has limited clustering performance and is prone to misclassification of border points. This study offers a bi-directional FCM clustering ensemble approach that takes local information into account (LI_BIFCM) to overcome these challenges and increase clustering quality. First, various membership matrices are created after running FCM multiple times, based on the randomization of the initial cluster centers, and a vertical ensemble is performed using the maximum membership principle. Second, after each execution of FCM, multiple local membership matrices of the sample points are created using multiple K-nearest neighbors, and a horizontal ensemble is performed. Multiple horizontal ensembles can be created using multiple FCM clustering. Finally, the final clustering results are obtained by combining the vertical and horizontal clustering ensembles. Twelve data sets were chosen for testing from both synthetic and real data sources. The LI_BIFCM clustering performance outperformed four traditional clustering algorithms and three clustering ensemble algorithms in the experiments. Furthermore, the final clustering results has a weak correlation with the bi-directional cluster ensemble parameters, indicating that the suggested technique is robust.

Spectral ensemble clustering with doubly stochastic co-association matrix

In remotely sensed data, two commonly held ways are used to obtain a relevant partitioning. The first one consists to apply several clustering algorithms individually, then to choose the best partition. The second commonly held way consists to apply the same clustering algorithm with several initializations and to choose the best partition. It is worth noting that the best partition is chosen according to a given evaluation criterion. Conversely, the Clustering ensembles can provide the best partition with high accuracy and consequently overcome limitations of traditional approaches. Clustering ensembles usually involve two stages. First, multiple partitions are obtained through several runs of initial clustering analysis. Subsequently, the specific consensus function is used in order to find a final consensus partition from multiple input partitions. In this paper, we investigate this technique in the unsupervised classification by using Synthetic data and composite data image. The first stage is assumed by four clustering algorithms, the well-known k-means algorithm, the k-harmonic means algorithm, Fuzzy c-means and the self-organizing map. The best clustering is obtained according to WB index. The relabeling and the voting methods are used in the second stage. Experimental results obtained are satisfactory.

Ensemble clustering has made significant progress in improving clustering performance by integrating multiple basic partitions. However, the conventional ensemble clustering methods rarely combine the rich information from both basic partitions and feature space comprehensively and efficiently. Facing the limitation, we design an Ensemble Clustering Based on Manifold Broad Learning System (EC-MBLS) in this paper. EC-MBLS firstly constructs a fuzzy partition matrix to capture the cluster-wise similarities from basic partitions. Then a manifold broad learning system (MBLS) is designed to learn a better consensus partition, which is guided by the global cluster structure of data and constrained by the local affinity of data. An efficient solution is finally provided to optimize the MBLS. Compared with the state-of-the-art ensemble clustering methods, experiments on multiple real-world clustering tasks are carried out to demonstrate the effectiveness of EC-MBLS.

The paper proposes a weakly supervised binary classification method which combines manifold regularization and fuzzy clustering ensemble methodologies. We assume that the class labels can be fully supervised, defined in terms of a probability distribution or not specified at all. The co-association matrix of fuzzy clustering ensemble is used as the similarity matrix. This matrix is represented in a low-rank form that significantly speeds up calculations and saves memory. Numerical experiments using Monte Carlo modeling demonstrate the efficiency of the method.

Clustering ensemble (CE), renowned for its robust and potent consensus capability, has garnered significant attention from scholars in recent years and has achieved numerous noteworthy breakthroughs. Nevertheless, three key issues persist: (1) the majority of CE selection strategies rely on preset parameters or empirical knowledge as a premise, lacking adaptive selectivity; (2) the construction of co-association matrix is excessively one-sided; (3) the CE method lacks a more macro perspective to reconcile the conflicts among different consensus results. To address these aforementioned problems, a dual-level clustering ensemble algorithm with three consensus strategies is proposed. Firstly, a backward clustering ensemble selection framework is devised, and its built-in selection strategy can adaptively eliminate redundant members. Then, at the base clustering consensus level, taking into account the interplay between actual spatial location information and the co-occurrence frequency, two modified relation matrices are reconstructed, resulting in the development of two consensus methods with different modes. Additionally, at the CE consensus level with a broader perspective, an adjustable Dempster–Shafer evidence theory is developed as the third consensus method in present algorithm to dynamically fuse multiple ensemble results. Experimental results demonstrate that compared to seven other state-of-the-art and typical CE algorithms, the proposed algorithm exhibits exceptional consensus ability and robustness.

Clustering ensembles combine multiple partitions of data into a single clustering solution. It is an effective technique for improving the quality of clustering results. Current clustering ensemble algorithms are usually built on the pairwise agreements between clusterings that focus on the similarity via consensus functions, between data objects that induce similarity measures from partitions and re-cluster objects, and between clusters that collapse groups of clusters into meta-clusters. In most of those models, there is a strong assumption on IIDness (i.e., independent and identical distribution), which states that base clusterings perform independently of one another and all objects are also independent. In the real world, however, objects are generally likely related to each other through features that are either explicit or even implicit. There is also latent but definite relationship among intermediate base clusterings because they are derived from the same set of data. All these demand a further investigation of clustering ensembles that explores the interdependence characteristics of data. To solve this problem, a new coupled clustering ensemble (CCE) framework that works on the interdependence nature of objects and intermediate base clusterings is proposed in this article. The main idea is to model the coupling relationship between objects by aggregating the similarity of base clusterings, and the interactive relationship among objects by addressing their neighborhood domains. Once these interdependence relationships are discovered, they will act as critical supplements to clustering ensembles. We verified our proposed framework by using three types of consensus function: clustering-based, object-based, and cluster-based. Substantial experiments on multiple synthetic and real-life benchmark datasets indicate thatCCEcan effectively capture the implicit interdependence relationships among base clusterings and among objects with higher clustering accuracy, stability, and robustness compared to 14 state-of-the-art techniques, supported by statistical analysis. In addition, we show that the final clustering quality is dependent on the data characteristics (e.g., quality and consistency) of base clusterings in terms of sensitivity analysis. Finally, the applications in document clustering, as well as on the datasets with much larger size and dimensionality, further demonstrate the effectiveness, efficiency, and scalability of our proposed models.

One-to-one correspondences between [formula omitted]-partitions, [formula omitted]-equivalences and [formula omitted]-pseudometrics

The link-based cluster ensemble (LCE) method is applied to a high resolution satellite precipitation estimation (HSPE) algorithm, a modified form of the Precipitation Estimation from Remotely Sensed Imagery using an Artificial Neural Network Cloud Classification (PERSIANN-CCS) algorithm. The HSPE involves the following four steps: (1) segmentation of infrared cloud images into patches; (2) cloud patch feature extraction; (3) clustering and classification of cloud patches using cluster ensemble technique; and (4) dynamic application of brightness temperature (Tb) and rain rate relationships, derived using satellite observations. The LCE method combines multiple data partitions from different clustering in order to cluster the cloud patches. The results show that using the cluster ensemble increase the performance of rainfall estimates if compared to the HSPE algorithm using Self Organizing Map (SOM). The Heidke Skill Score (HSS) is improved 5% to 7% at medium and high level of rainfall thresholds.

In multi-scale information systems, the information is often characterized at multi scales and multi levels. To facilitate the computational process of multi-scale information systems, we employ the matrix method to represent the multi-scale information systems and to select the optimal scale combination of multi-scale decision information systems in this study. To this end, we first describe some important concepts and properties of information systems using some relational matrices. The relational matrix is then introduced into multi-scale information systems, and used to describe some main concepts in systems, including the lower and upper approximate sets and the consistence of systems. Furthermore, from the view of the relation matrix, the scale significance is defined to describe the global optimal scale and the local optimal scale of multi-scale information systems. Finally, the relational matrix is used to compute the scale significance and to construct the optimal scale selection algorithms. The efficiency of these algorithms is examined by several practical examples and experiments.

A vast amount of time-series data is generated from multiple fields. Mining these data can uncover hidden patterns and behavior characteristics. The analysis of such data is complex because they are voluminous and have high dimensions. Clustering can provide a preprocessing step to extract insights. However, clustering such data poses challenges, as many existing algorithms are not efficient enough to handle them. In addition, many traditional and modern clustering algorithms need help with parameter-tuning problems. Ensemble clustering, an amalgamation of clustering algorithms, has emerged as a promising method for improving the accuracy, stability, and robustness of clustering solutions. This study presents Ensemble clustering using Affinity Propagation (ECAP). AP is efficient because it does not require the number of clusters to be specified a priori, allowing the data to reveal its structure. When used in an ensemble framework, the inherent strengths of AP are amplified by integrating multiple clustering results. This aggregation mitigates the influence of any single, potentially suboptimal clustering outcome, leading to more stable and reliable clusters. Extensive experiments were performed on four real-world datasets for rand index, homogeneity, completeness, and V-measure to determine the efficacy of the proposed approach. The results show that the proposed method outperforms AP, Kmeans, and spectral clustering.

Relationship between fuzzy sets and crisp partitions defined on the same finite set of objects X is studied. Granular structure of a fuzzy set is described by rough fuzzy sets and the quality of approximation of a fuzzy set by a crisp partition is evaluated. Measure of rough dissimilarity between clusters from a crisp partition of X with respect to a fuzzy set A defined on X is introduced. Properties of this measure are explored and some applications are provided. Classification of membership grades of A into linguistic categories is discussed.

This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse' framework that we call cluster ensembles. The cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information. In addition to a direct maximization approach, we propose three effective and efficient techniques for obtaining high-quality combiners (consensus functions). The first combiner induces a similarity measure from the partitionings and then reclusters the objects. The second combiner is based on hypergraph partitioning. The third one collapses groups of clusters into meta-clusters which then compete for each object to determine the combined clustering. Due to the low computational costs of our techniques, it is quite feasible to use a supra-consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation. We evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios: (i) where the original clusters were formed based on non-identical sets of features, (ii) where the original clustering algorithms worked on non-identical sets of objects, and (iii) where a common data-set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution. Promising results are obtained in all three situations for synthetic as well as real data-sets.

Profile-based assessment of diseases affective factors using fuzzy association rule mining approach: A case study in heart diseases