Multiobjective Clustering Technique Research Articles

A Multi-Objective Clustering for Better Data Management in Connected Environment

Over the past decade, the rapid increase in connected devices has enabled the emergence of new digital ecosystems to provide new opportunities for monitoring and managing systems to optimize overall performance. With these connected environments, data collection and management become increasingly challenging. A significant number of works in the literature have addressed data collection and management based on different contexts (e.g., mobile ad hoc, Peer-2-Peer, and IoT networks). Today, a wired network uses all of these protocols simultaneously, thus highlighting the need to build a standard data collection and management framework that considers all potential user preferences. For this purpose, multi-objective clustering has been utilized as a promising solution to ensure the stability of connected devices during the collection and management of data. In this paper, we introduce a new multi-objective clustering (MOC) technique based on various criteria for cluster construction and head selection in connected environments. More precisely, the proposed solution is based hypergraphs to represent the connected environment and clusters according to similarities between heterogeneous devices. Then, a cross-sectional hypergraph algorithm is applied to select the cluster heads. Experiments conducted show that our solution outperforms the pioneering literature methods in terms of performance and effectiveness.

Multimodal Web Page Segmentation Using Self-organized Multi-objective Clustering

Web page segmentation (WPS) aims to break a web page into different segments with coherent intra- and inter-semantics. By evidencing the morpho-dispositional semantics of a web page, WPS has traditionally been used to demarcate informative from non-informative content, but it has also evidenced its key role within the context of non-linear access to web information for visually impaired people. For that purpose, a great deal of ad hoc solutions have been proposed that rely on visual, logical, and/or text cues. However, such methodologies highly depend on manually tuned heuristics and are parameter-dependent. To overcome these drawbacks, principled frameworks have been proposed that provide the theoretical bases to achieve optimal solutions. However, existing methodologies only combine few discriminant features and do not define strategies to automatically select the optimal number of segments. In this article, we present a multi-objective clustering technique called MCS that relies on \( K \) -means, in which (1) visual, logical, and text cues are all combined in a early fusion manner and (2) an evolutionary process automatically discovers the optimal number of clusters (segments) as well as the correct positioning of seeds. As such, our proposal is parameter-free, combines many different modalities, does not depend on manually tuned heuristics, and can be run on any web page without any constraint. An exhaustive evaluation over two different tasks, where (1) the number of segments must be discovered or (2) the number of clusters is fixed with respect to the task at hand, shows that MCS drastically improves over most competitive and up-to-date algorithms for a wide variety of external and internal validation indices. In particular, results clearly evidence the impact of the visual and logical modalities towards segmentation performance.

Distributed clustering in peer to peer networks using multi-objective whale optimization

Multi-objective clustering algorithms have superiority over its single objective counterparts as they include additional knowledge on properties of data in the form of objectives to discover the underlying clusters present in various datasets. This paper proposes a distributed clustering algorithm using multi-objective whale optimization (DMOWOA) for peer to peer network. The algorithm minimizes two objective functions to perform clustering, namely : Total Euclidean Deviation and Total Symmetrical Deviation. Both objective values are shared using diffusion method of cooperation to obtain correct partitioning at each peer. A single solution from the non-dominated solutions is selected as final solution based on its minimum distance to origin in the normalized objective space. The proposed algorithm’s performance is evaluated on four synthetic and five real-life wireless sensor network datasets (Canada weather station dataset, Delhi air pollution content dataset, Intel laboratory dataset, Washington cook agronomy farm dataset and Thames river water quality dataset). The comparison is carried out with multi-objective distributed particle swarm optimization (DMOPSO), distributed K-Means (DK-Means) and other seven recently developed nature inspired multi-objective clustering techniques. The proposed algorithm in most of the cases outperforms the existing techniques in terms of statistical measures Minkowski Score, Dunn index and Silhouette index. The average rank of the proposed algorithm is also better in Kruskal–Wallis statistical test.

Multi-view clustering for multi-omics data using unified embedding

In real world applications, data sets are often comprised of multiple views, which provide consensus and complementary information to each other. Embedding learning is an effective strategy for nearest neighbour search and dimensionality reduction in large data sets. This paper attempts to learn a unified probability distribution of the points across different views and generates a unified embedding in a low-dimensional space to optimally preserve neighbourhood identity. Probability distributions generated for each point for each view are combined by conflation method to create a single unified distribution. The goal is to approximate this unified distribution as much as possible when a similar operation is performed on the embedded space. As a cost function, the sum of Kullback-Leibler divergence over the samples is used, which leads to a simple gradient adjusting the position of the samples in the embedded space. The proposed methodology can generate embedding from both complete and incomplete multi-view data sets. Finally, a multi-objective clustering technique (AMOSA) is applied to group the samples in the embedded space. The proposed methodology, Multi-view Neighbourhood Embedding (MvNE), shows an improvement of approximately 2−3% over state-of-the-art models when evaluated on 10 omics data sets.

Data Forecasting and Storage Sizing for PV Battery System Using Fuzzy Markov Chain Model

Although photovoltaic (PV) power is a green energy source, the high output variability of PV power generation leads to lags in network availability. To increase PV power plant reliability, an energy storage system can be incorporated. However, improper selection of storage size increases system cost or decreases network availability due to over- or under-sizing of the storage capacity, respectively. For this reason, we develop a generalized Markov chain-based battery charging–discharging procedure for determining proper storage size. In this work, multi-objective clustering and fuzzy decision-making (FDM) techniques for selecting the most optimal storage size with optimal availability are also proposed to avoid issues associated with conventional selection procedures. The reliability of our approach is analyzed based on forecasted data. As better prediction yields more dispatchable storage sizing, thereby improving system reliability, a first-order fuzzy time-series, Markov chain-based prediction method is used owing to its high prediction efficiency. To explore PV power generation performance in both cool and hot, sunny conditions, the temperature effect is considered in the storage sizing–availability analysis.

Automatic Scientific Document Clustering Using Self-organized Multi-objective Differential Evolution

Document clustering is the partitioning of a given collection of documents into various K- groups based on some similarity/dissimilarity criterion. This task has applications in scope detection of journals/conferences, development of some automated peer-review support systems, topic-modeling, latest cognitive-inspired works on text summarization, and classification of documents based on semantics, etc. In the current paper, a cognitive-inspired multi-objective automatic document clustering technique is proposed which is a fusion of self-organizing map (SOM) and multi-objective differential evolution approach. The variable number of cluster centers are encoded in different solutions of the population to determine the number of clusters from a data set in an automated way. These solutions undergo various genetic operations during evolution. The concept of SOM is utilized in designing new genetic operators for the proposed clustering technique. In order to measure the goodness of a clustering solution, two cluster validity indices, Pakhira-Bandyopadhyay-Maulik index, and Silhouette index, are optimized simultaneously. The effectiveness of the proposed approach, namely self-organizing map based multi-objective document clustering technique (SMODoc_clust) is shown in automatic classification of some scientific articles and web-documents. Different representation schemas including tf, tf-idf and word-embedding are employed to convert articles in vector-forms. Comparative results with respect to internal cluster validity indices, namely, Dunn index and Davies-Bouldin index, are shown against several state-of-the-art clustering techniques including three multi-objective clustering techniques namely MOCK, VAMOSA, NSGA-II-Clust, single objective genetic algorithm (SOGA) based clustering technique, K-means, and single-linkage clustering. Results obtained clearly show that our approach is better than existing approaches. The validation of the obtained results is also shown using statistical significant t tests.

Sophisticated SOM based genetic operators in multi-objective clustering framework

Multi-objective clustering refers to the partitioning of a given collection of objects into various K-groups based on some similarity/dissimilarity criterion while optimizing different partition quality measures simultaneously. The current paper proposes an automated decomposition based multi-objective clustering technique, SOMDEA_clust, which is a fusion of self-organizing map (SOM) and multi-objective differential evolution. A novel reproduction operator is designed where the ensemble of multiple neighborhoods extracted using self-organizing map is used for constructing the variable mating pool size. The probabilities of selecting different sizes of the neighborhood are updated based on their performances in generating new improved solutions in the last few generations. Decomposition based selection scheme is also utilized in our paper which divides the multi-objective optimization (MOO) problem into a number of single objective subproblems. The objective functions corresponding to these subproblems are optimized in a collaborative manner by the use of MOO. The potentiality of the proposed framework is shown for clustering four real-life data sets and five artificial data sets in comparison to some existing multi-objective based clustering techniques, namely MOCK, SMEA_clust, MEA_clust, a single objective based genetic clustering technique, SOGA and a traditional clustering technique, K-means. To show the utility of SOM based reproduction operators, another decomposition based multi-objective clustering technique (MDEA_clust) without the use of SOM based operators is also developed in this paper. In order to show the efficacy of the proposed clustering technique in handling large data sets, two large scale datasets having more than 5000 data points are also utilized. As a real-life application, the proposed clustering technique is applied for scientific/web document clustering where a set of scientific/web documents are partitioned based on their content-similarities. Semantic representation is utilized to covert the text document into a real vector. Experimental results clearly illustrate the effectiveness of fusion of SOM and DE in developing an effective clustering technique.

Reference point based archived many objective simulated annealing

Recent research in optimization theory focuses on developing algorithms for the many objective optimization problems. These problems require careful attention to efficiently handle the increasing number of objectives and also to address the various challenges associated with these types of problems. The present study introduces a new unconstrained many-objective optimization algorithm called reference point based many objective simulated annealing algorithm (RSA). The algorithm is an amalgamation of several new modules including a reference point based clustering technique to control the size of the archive which stores the solutions, a novel mutation strategy termed as mutation-switching and a new acceptance probability function. Unlike the existing simulated annealing based multiobjective optimization techniques, the current work explores the use of archive-to-archive transition rather than point-to-point transition. The performance of RSA is validated and compared with many other state-of-the-art algorithms on a number of unconstrained benchmark problems of DTLZ and WFG test suites with up to 15 objectives. The experimental results show that RSA outperforms AMOSA, NSGA-III, MOEA/D-PBI and θ-DEA in terms of two well-known performance metrics, namely inverse generational distance (IGD) and hyper-volume (HV), for a majority of the test cases considered . It has also been shown that RSA usually requires fewer number of function evaluations compared to other algorithms for equal or better performance and might thus be more useful for MaOO problems which are expensive in terms of computational time. To illustrate some real-life applications of RSA, in a part of the paper, we have developed a multiobjective clustering technique utilizing RSA as the underlying optimization mechanism which is then used for segmenting satellite images.Obtained results prove the efficacy of RSA in solving the segmentation task.

Multi-objective clustering technique based on [formula omitted]-nodes update policy and similarity matrix for mining communities in social networks

This paper proposes a relatively all-purpose network clustering technique based on the framework of multi-objective evolutionary algorithms, which can effectively dispose the issue of community detection in unsigned social networks, as well as in signed social networks. Firstly, we formulate a generalized similarity function to construct a similarity matrix, and then a pre-partitioning strategy is projected according to the similarity matrix. The pre-partitioning strategy merely considers nodes with high similarity values, which avoids the interference of noise nodes during the label update phase. In this way, at the initial phase of the algorithm, nodes with strong connections are fleetly gathered into sub-communities. Secondly, we elaborately devise a crossover operator, called cross-merging operator, to merge sub-communities generated by the pre-partitioning technique. Moreover, a special mutation operator, based on the similarity matrix of nodes, is implemented to adjust boundary nodes connecting different communities. Finally, to handle different types of networks, we, therefore, have presented the novel multi-objective optimization models for this issue. Through a bulk of rigorous experiments on both unsigned and signed social networks, the preeminent clustering performance illustrate that the proposed algorithm is capable of mining communities effectively.

Bio-inspired multiobjective clustering optimization: A survey and a proposal

Multiobjective clustering techniques have been used to simultaneously consider several complementary aspects of clustering quality. They optimize two or more cluster validity indices simultaneously, they lead to high-quality results, and have emerged as attractive and robust alternatives for solving clustering problems. This paper provides a brief review of bio-Inspired multiobjective clustering, and proposes a bee-inspired multiobjective optimization (MOO) algorithm, named cOptBees-MO, to solve multiobjective data clustering problems. In its survey part, a brief tutorial on MOO and multiobjective clustering optimization (MOCO) is presented, followed by a review of the main works in the area. Particular attention is given to the many objective functions used in MOCO. To evaluate the performance of the algorithm it was executed for various datasets and the results presented high quality clusters, diverse solutions an the automatic determination of a suitable number of clusters.

A multi-objective genetic algorithm with fuzzy c-means for automatic data clustering

This article presents a multi-objective genetic algorithm which considers the problem of data clustering. A given dataset is automatically assigned into a number of groups in appropriate fuzzy partitions through the fuzzy c-means method. This work has tried to exploit the advantage of fuzzy properties which provide capability to handle overlapping clusters. However, most fuzzy methods are based on compactness and/or separation measures which use only centroid information. The calculation from centroid information only may not be sufficient to differentiate the geometric structures of clusters. The overlap-separation measure using an aggregation operation of fuzzy membership degrees is better equipped to handle this drawback. For another key consideration, we need a mechanism to identify appropriate fuzzy clusters without prior knowledge on the number of clusters. From this requirement, an optimization with single criterion may not be feasible for different cluster shapes. A multi-objective genetic algorithm is therefore appropriate to search for fuzzy partitions in this situation. Apart from the overlap-separation measure, the well-known fuzzy Jm index is also optimized through genetic operations. The algorithm simultaneously optimizes the two criteria to search for optimal clustering solutions. A string of real-coded values is encoded to represent cluster centers. A number of strings with different lengths varied over a range correspond to variable numbers of clusters. These real-coded values are optimized and the Pareto solutions corresponding to a tradeoff between the two objectives are finally produced. As shown in the experiments, the approach provides promising solutions in well-separated, hyperspherical and overlapping clusters from synthetic and real-life data sets. This is demonstrated by the comparison with existing single-objective and multi-objective clustering techniques.

An enriched game-theoretic framework for multi-objective clustering

The framework of multi-objective clustering can serve as a competent technique in nowadays human issues ranging from decision making process to machine learning and pattern recognition problems. Multi-objective clustering basically aims at placing similar objects into the same groups based on some conflicting objectives, which substantially supports the use of game theory to come to a resolution. Based on these understandings, this paper suggests Enriched Game Theory K-means, called EGTKMeans, as a novel multi-objective clustering technique based on the notion of game theory. EGTKMeans is specially designed to optimize two intrinsically conflicting objectives, named, compaction and equi-partitioning. The key contributions of the proposed approach are three folds. First, it formulates an elegant and novel payoff definition which considers both objectives with equal priority. The presented payoff function incorporates a desirable fairness into the final clustering results. Second, EGTKMeans performs better off by utilizing the advantages of mixed strategies as well as those of pure ones, considering the existence of mixed Nash Equilibrium in every game. The last but not the least is that EGTKMeans approaches the optimal solution in a very promising manner by optimizing both objectives simultaneously. The experimental results suggest that the proposed approach significantly outperforms other rival methods across real world and synthetic data sets with reasonable time complexity.

A generalized automatic clustering algorithm in a multiobjective framework

In this paper a new multiobjective (MO) clustering technique (GenClustMOO) is proposed which can automatically partition the data into an appropriate number of clusters. Each cluster is divided into several small hyperspherical subclusters and the centers of all these small sub-clusters are encoded in a string to represent the whole clustering. For assigning points to different clusters, these local sub-clusters are considered individually. For the purpose of objective function evaluation, these sub-clusters are merged appropriately to form a variable number of global clusters. Three objective functions, one reflecting the total compactness of the partitioning based on the Euclidean distance, the other reflecting the total symmetry of the clusters, and the last reflecting the cluster connectedness, are considered here. These are optimized simultaneously using AMOSA, a newly developed simulated annealing based multiobjective optimization method, in order to detect the appropriate number of clusters as well as the appropriate partitioning. The symmetry present in a partitioning is measured using a newly developed point symmetry based distance. Connectedness present in a partitioning is measured using the relative neighborhood graph concept. Since AMOSA, as well as any other MO optimization technique, provides a set of Pareto-optimal solutions, a new method is also developed to determine a single solution from this set. Thus the proposed GenClustMOO is able to detect the appropriate number of clusters and the appropriate partitioning from data sets having either well-separated clusters of any shape or symmetrical clusters with or without overlaps. The effectiveness of the proposed GenClustMOO in comparison with another recent multiobjective clustering technique (MOCK), a single objective genetic algorithm based automatic clustering technique (VGAPS-clustering), K-means and single linkage clustering techniques is comprehensively demonstrated for nineteen artificial and seven real-life data sets of varying complexities. In a part of the experiment the effectiveness of AMOSA as the underlying optimization technique in GenClustMOO is also demonstrated in comparison to another evolutionary MO algorithm, PESA2.

Gene expression data analysis using multiobjective clustering improved with SVM based ensemble.

Microarray technology facilitates the monitoring of the expression levels of thousands of genes over different experimental conditions simultaneously. Clustering is a popular data mining tool which can be applied to microarray gene expression data to identify co-expressed genes. Most of the traditional clustering methods optimize a single clustering goodness criterion and thus may not be capable of performing well on all kinds of datasets. Motivated by this, in this article, a multiobjective clustering technique that optimizes cluster compactness and separation simultaneously, has been improved through a novel support vector machine classification based cluster ensemble method. The superiority of MOCSVMEN (MultiObjective Clustering with Support Vector Machine based ENsemble) has been established by comparing its performance with that of several well known existing microarray data clustering algorithms. Two real-life benchmark gene expression datasets have been used for testing the comparative performances of different algorithms. A recently developed metric, called Biological Homogeneity Index (BHI), which computes the clustering goodness with respect to functional annotation, has been used for the comparison purpose.

Automatic MR brain image segmentation using a multiseed based multiobjective clustering approach

In this paper, the automatic segmentation of a multispectral magnetic resonance image of the brain is posed as a clustering problem in the intensity space. The automatic clustering problem is thereafter modelled as solving a multiobjective optimization (MOO) problem, optimizing a set of cluster validity indices simultaneously. A multiobjective clustering technique, named MCMOClust, is used to solve this problem. MCMOClust utilizes a recently developed simulated annealing based multiobjective optimization method as the underlying optimization strategy. Each cluster is divided into several small hyperspherical subclusters and the centers of all these small sub-clusters are encoded in a string to represent the whole clustering. For assigning points to different clusters, these local sub-clusters are considered individually. For the purpose of objective function evaluation, these sub-clusters are merged appropriately to form a variable number of global clusters. Two cluster validity indices, one based on the Euclidean distance, XB-index, and another recently developed point symmetry distance based cluster validity index, Sym-index, are optimized simultaneously to automatically evolve the appropriate number of clusters present in MR brain images. A semi-supervised method is used to select a single solution from the final Pareto optimal front of MCMOClust. The present method is applied on several simulated T1-weighted, T2-weighted and proton density normal and MS lesion magnetic resonance brain images. Superiority of the present method over Fuzzy C-means, Expectation Maximization clustering algorithms and a newly developed symmetry based fuzzy genetic clustering technique (Fuzzy-VGAPS), are demonstrated quantitatively. The automatic segmentation obtained by multiseed based multiobjective clustering technique (MCMOClust) is also compared with the available ground truth information.

A new multiobjective clustering technique based on the concepts of stability and symmetry

Most clustering algorithms operate by optimizing (either implicitly or explicitly) a single measure of cluster solution quality. Such methods may perform well on some data sets but lack robustness ...

A new multiobjective simulated annealing based clustering technique using symmetry

In this paper, we have proposed a multiobjective clustering technique which optimizes simultaneously two objectives, one reflecting the total ‘goodness’ present in the data set in terms of total compactness (measured using Euclidean distance) of the clusters, and the other reflecting the total symmetry present in the clusters of the data set. The proposed algorithm uses a simulated annealing based multiobjective optimization method as the underlying optimization criterion. Center based encoding is used. The proposed multiobjective clustering technique is able to suitably evolve these cluster centers in such a way so that the two objectives are optimized ‘simultaneously’. Assignment of points to different clusters is done based on the newly developed point symmetry based distance rather than the Euclidean distance. Results on eight artificial and six real-life data sets show that the proposed technique is well-suited to detect true partitioning from data sets with clusters having either the hyperspherical shape or point symmetric structure. Results are compared with those obtained by five existing clustering techniques, one multiobjective clustering technique, MOCK, average linkage clustering algorithm, expectation maximization clustering algorithm, well-known genetic algorithm based K-means clustering technique (GAK-means) and a newly developed genetic algorithm with point symmetry based clustering technique (GAPS).

A symmetry based multiobjective clustering technique for automatic evolution of clusters

In this paper the problem of automatic clustering a data set is posed as solving a multiobjective optimization (MOO) problem, optimizing a set of cluster validity indices simultaneously. The proposed multiobjective clustering technique utilizes a recently developed simulated annealing based multiobjective optimization method as the underlying optimization strategy. Here variable number of cluster centers is encoded in the string. The number of clusters present in different strings varies over a range. The points are assigned to different clusters based on the newly developed point symmetry based distance rather than the existing Euclidean distance. Two cluster validity indices, one based on the Euclidean distance, XB-index, and another recently developed point symmetry distance based cluster validity index, Sym-index, are optimized simultaneously in order to determine the appropriate number of clusters present in a data set. Thus the proposed clustering technique is able to detect both the proper number of clusters and the appropriate partitioning from data sets either having hyperspherical clusters or having point symmetric clusters. A new semi-supervised method is also proposed in the present paper to select a single solution from the final Pareto optimal front of the proposed multiobjective clustering technique. The efficacy of the proposed algorithm is shown for seven artificial data sets and six real-life data sets of varying complexities. Results are also compared with those obtained by another multiobjective clustering technique, MOCK, two single objective genetic algorithm based automatic clustering techniques, VGAPS clustering and GCUK clustering.

A new multiobjective clustering technique based on the concepts of stability and symmetry

Most clustering algorithms operate by optimizing (either implicitly or explicitly) a single measure of cluster solution quality. Such methods may perform well on some data sets but lack robustness with respect to variations in cluster shape, proximity, evenness and so forth. In this paper, we have proposed a multiobjective clustering technique which optimizes simultaneously two objectives, one reflecting the total cluster symmetry and the other reflecting the stability of the obtained partitions over different bootstrap samples of the data set. The proposed algorithm uses a recently developed simulated annealing-based multiobjective optimization technique, named AMOSA, as the underlying optimization strategy. Here, points are assigned to different clusters based on a newly defined point symmetry-based distance rather than the Euclidean distance. Results on several artificial and real-life data sets in comparison with another multiobjective clustering technique, MOCK, three single objective genetic algorithm-based automatic clustering techniques, VGAPS clustering, GCUK clustering and HNGA clustering, and several hybrid methods of determining the appropriate number of clusters from data sets show that the proposed technique is well suited to detect automatically the appropriate number of clusters as well as the appropriate partitioning from data sets having point symmetric clusters. The performance of AMOSA as the underlying optimization technique in the proposed clustering algorithm is also compared with PESA-II, another evolutionary multiobjective optimization technique.

MR Brain Image Segmentation Using A Multi-seed Based Automatic Clustering Technique

In this paper, the automatic segmentation of multispectral magnetic resonance image of the brain is posed as a clustering problem in the intensity space. Thereafter an automatic clustering technique is proposed to solve this problem. The proposed real-coded variable string length genetic clustering technique (MCVGAPS clustering) is able to evolve the number of clusters present in the data set automatically. Each cluster is divided into several small hyperspherical subclusters and the centers of all these small sub-clusters are encoded in a string to represent the whole clustering. For assigning points to different clusters, these local sub-clusters are considered individually. For the purpose of objective function evaluation, these sub-clusters are merged appropriately to form a variable number of global clusters. A recently developed point symmetry distance based cluster validity index, Sym-index, is optimized to automatically evolve the appropriate number of clusters present in an MR brain image. The proposed method is applied on several simulated T1-weighted, T2- weighted and proton density normal and MS lesion magnetic resonance brain images. Superiority of the proposed method over Fuzzy C-means, Expectation Maximization clustering algorithms are demonstrated quantitatively. The automatic segmentation obtained by multiseed based multiobjective clustering technique (MCVGAPS) is also compared with the available ground truth information.