It is highly likely that there is a partition that is judged by a stability measure as a bad one while it contains one (or more) high quality cluster(s); and then it is totally neglected. So, inspiring from the evaluation of partitions, researchers turn to define measures for evaluation of clusters. Many stability measures have been proposed such as Normalized Mutual Information to validate a partition. The defined measures are based on Normalized Mutual Information. The drawback of the commonly used approach will be discussed in this paper and a criterion is proposed to assess the association between a cluster and a partition which is called Edited Normalized Mutual Information, ENMI criterion. The ENMI criterion compensates the drawback of the common Normalized Mutual Information (NMI) measure. Also, a clustering ensemble method that is based on aggregating a subset of primary clusters is proposed. The proposed method uses the Average ENMI as fitness measure to select a number of clusters. The clusters that satisfy a predefined threshold of the mentioned measure are selected to participate in the final ensemble. To combine the chosen clusters a set of consensus function methods are employed. One class of the used consensus functions is the co-association based consensus functions. Since the Evidence Accumulation Clustering, EAC, method can’t derive the co-association matrix from a subset of clusters, Extended EAC, EEAC, is employed to construct the co-association matrix from the chosen subset of clusters. The second class of the used consensus functions is based on hyper graph partitioning algorithms. The other class of the used consensus functions considers the chosen clusters as a new feature space and uses a simple clustering algorithm to extract the consensus partitioning. The empirical studies show that the proposed method outperforms other well-known ensembles.

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Clustering ensemble selection considering quality and diversity

For obtaining the more robust, novel, stable, and consistent clustering result, clustering ensemble has been emerged. There are two approaches in clustering ensemble frameworks: (a) the approaches that focus on creation or preparation of a suitable ensemble, called as ensemble creation approaches, and (b) the approaches that try to find a suitable final clustering (called also as consensus clustering) out of a given ensemble, called as ensemble aggregation approaches. The first approaches try to solve ensemble creation problem. The second approaches try to solve aggregation problem. This paper tries to propose an ensemble aggregator, or a consensus function, called as Robust Clustering Ensemble based on Sampling and Cluster Clustering (RCESCC).RCESCC algorithm first generates an ensemble of fuzzy clusterings generated by the fuzzy c-means algorithm on subsampled data. Then, it obtains a cluster-cluster similarity matrix out of the fuzzy clusters. After that, it partitions the fuzzy clusters by applying a hierarchical clustering algorithm on the cluster-cluster similarity matrix. In the next phase, the RCESCC algorithm assigns the data points to merged clusters. The experimental results comparing with the state of the art clustering algorithms indicate the effectiveness of the RCESCC algorithm in terms of performance, speed and robustness.

A fuzzy clustering ensemble based on cluster clustering and iterative Fusion of base clusters

Clustering ensemble indicates to an approach in which a number of (usually weak) base clusterings are performed and their consensus clustering is used as the final clustering. Knowing democratic decisions are better than dictatorial decisions, it seems clear and simple that ensemble (here, clustering ensemble) decisions are better than simple model (here, clustering) decisions. But it is not guaranteed that every ensemble is better than a simple model. An ensemble is considered to be a better ensemble if their members are valid or high-quality and if they participate according to their qualities in constructing consensus clustering. In this paper, we propose a clustering ensemble framework that uses a simple clustering algorithm based on kmedoids clustering algorithm. Our simple clustering algorithm guarantees that the discovered clusters are valid. From another point, it is also guaranteed that our clustering ensemble framework uses a mechanism to make use of each discovered cluster according to its quality. To do this mechanism an auxiliary ensemble named reference set is created by running several kmeans clustering algorithms.

An Ensemble of Locally Reliable Cluster Solutions

The low frequency oscillations have always been the main problem of power system and can lead to power angle instability, limiting the maximum power to be transmitted on tie-lines and system separation. For boosting power system stability limits, the most effectiveness way is to install supplementary excitation control, power system stabilizer (PSS) to add a supplementary feedback stabilizing signal into the automatic voltage regulator (AVR). This article investigates the coordination and optimization of fuzzy controllers for designing PSS and STATCOM controllers for more attenuation of power system fluctuations. The designed fuzzy controller replaces the STATCOM AC voltage regulator. Moreover, for more damping a fuzzy power system stabilizer (FPSS) is placed on all machines. Coordination between Fuzzy Based STATCOM (FSTATCOM) and FPSS is achieved by Self-Adaptive Learning Bat Algorithm (SALBA) in two stages. At first, scaling factors and then fuzzy sets of membership functions (MFs) will be tuned based on a performance index. To indicate the effectiveness of the proposed scheme, the coordinated optimized FPSS and FSTATCOM are compared with conventional design approaches like conventional PSS (CPSS) and proportional-integral controller based STATCOM (PISTATCOM). The simulations clearly demonstrate the effectiveness of the coordinated fuzzy controllers in terms of transient and dynamic stability.

Simultaneous design of fuzzy PSS and fuzzy STATCOM controllers for power system stability enhancement

Clustering ensemble (CE) takes multiple clustering solutions into consideration in order to effectively improve the accuracy and robustness of the final result. To reduce redundancy as well as noise, a CE selection (CES) step is added to further enhance performance. Quality and diversity are two important metrics of CES. However, most of the CES strategies adopt heuristic selection methods or a threshold parameter setting to achieve tradeoff between quality and diversity. In this paper, we propose a transfer CES (TCES) algorithm which makes use of the relationship between quality and diversity in a source dataset, and transfers it into a target dataset based on three objective functions. Furthermore, a multiobjective self-evolutionary process is designed to optimize these three objective functions. Finally, we construct a transfer CE framework (TCE-TCES) based on TCES to obtain better clustering results. The experimental results on 12 transfer clustering tasks obtained from the 20newsgroups dataset show that TCE-TCES can find a better tradeoff between quality and diversity, as well as obtaining more desirable clustering results.

Transfer Clustering Ensemble Selection

Clustering as a major task in data mining is responsible for discovering hidden patterns in unlabeled datasets. Finding the best clustering is also considered as one of the most challenging problems in data mining. Due to the problem complexity and the weaknesses of primary clustering algorithm, a large part of research has been directed toward ensemble clustering methods. Ensemble clustering aggregates a pool of base clusterings and produces an output clustering that is also named consensus clustering. The consensus clustering is usually better clustering than the output clusterings of the basic clustering algorithms. However, lack of quality in base clusterings makes their consensus clustering weak. In spite of some researches in selection of a subset of high quality base clusterings based on a clustering assessment metric, cluster-level selection has been always ignored. In this paper, a new clustering ensemble framework has been proposed based on cluster-level weighting. The certainty amount that the given ensemble has about a cluster is considered as the reliability of that cluster. The certainty amount that the given ensemble has about a cluster is computed by the accretion amount of that cluster by the ensemble. Then by selecting the best clusters and assigning a weight to each selected cluster based on its reliability, the final ensemble is created. After that, the paper proposes cluster-level weighting co-association matrix instead of traditional co-association matrix. Then, two consensus functions have been introduced and used for production of the consensus partition. The proposed framework completely overshadows the state-of-the-art clustering ensemble methods experimentally.

Ahmad Reza Nazari

Papers

A comprehensive study of clustering ensemble weighting based on cluster quality and diversity