Point Symmetry-based Distance Research Articles

Aggregation of multi-objective fuzzy symmetry-based clustering techniques for improving gene and cancer classification

The current work reports about the application of a cluster ensemble approach in combining results produced by some multiobjective-based clustering techniques. Firstly, some multiobjective-based fuzzy clustering techniques are developed using the search capabilities of differential evolution and particle swarm optimization. Both these clustering techniques utilize a recently developed point symmetry-based distance for allocation of points to different clusters. The appropriate partitioning from a data set is identified by optimizing simultaneously two cluster quality measures, namely Xie–Beni index and FSym-index. First objective function uses Euclidean distance as a similarity measure, and the second objective function uses point symmetry-based distance in its computation. A set of trade-off solutions are produced by each of these clustering techniques on the final Pareto optimal front. Finally, this set of solutions are combined using a link-based cluster ensemble technique. The effectiveness of ensemble techniques is illustrated on partitioning some real-life gene expression and cancer data sets where automatic identification of set of genes or set of cancer tissues is a pressing issue. The potency of the ensemble techniques applied on both the multi-objective DE- and PSO-based clustering approaches is shown in comparison with several state-of-the-art techniques.

Enhancing point symmetry-based distance for data clustering

In this paper, at first a new point symmetry-based similarity measurement is proposed which satisfies the closure and the symmetry properties of any distance function. The different desirable properties of the new distance are elaborately explained. Thereafter a new clustering algorithm based on the search capability of genetic algorithm is developed where the newly developed point symmetry-based distance is used for cluster assignment. The allocation of points to different clusters is performed in such a way that the closure property is satisfied. The proposed GA with newly developed point symmetry distance based (GAnPS) clustering algorithm is capable of determining different symmetrical shaped clusters having any sizes or convexities. The effectiveness of the proposed GAnPS clustering technique in identifying the proper partitioning is shown for twenty-one data sets having various characteristics. Performance of GAnPS is compared with existing symmetry-based genetic clustering technique, GAPS, three popular and well-known clustering techniques, K-means, expectation maximization and average linkage algorithm. In a part of the paper, the utility of the proposed clustering technique is shown for partitioning a remote sensing satellite image. The last part of the paper deals with the development of some automatic clustering techniques using the newly proposed symmetry-based distance.

Exploring differential evolution and particle swarm optimization to develop some symmetry-based automatic clustering techniques: application to gene clustering

In the current paper, we have developed two bio-inspired fuzzy clustering algorithms by incorporating the optimization techniques, namely differential evolution and particle swarm optimization. Both these clustering techniques can detect symmetrical-shaped clusters utilizing the established point symmetry-based distance measure. Both the proposed approaches are automatic in nature and can detect the number of clusters automatically from a given dataset. A symmetry-based cluster validity measure, F-Sym-index, is used as the objective function to be optimized in order to automatically determine the correct partitioning by both the approaches. The effectiveness of the proposed approaches is shown for automatically clustering some artificial and real-life datasets as well as for clustering some real-life gene expression datasets. The current paper presents a comparative analysis of some meta-heuristic-based clustering approaches, namely newly proposed two techniques and the already existing automatic genetic clustering techniques, VGAPS, GCUK, HNGA. The obtained results are compared with respect to some external cluster validity indices. Moreover, some statistical significance tests, as well as biological significance tests, are also conducted. Finally, results on gene expression datasets have been visualized by using some visualization tools, namely Eisen plot and cluster profile plot.

ParSymG: a parallel clustering approach for unsupervised classification of remotely sensed imagery

ABSTRACTSymmetry is a common feature in the real world. It may be used to improve a classification by using the point symmetry-based distance as a measure of clustering. However, it is time consuming to calculate the point symmetry-based distance. Although an efficient parallel point symmetry-based K-means algorithm (ParSym) has been propsed to overcome this limitation, ParSym may get stuck in sub-optimal solutions due to the K-means technique it used. In this study, we proposed a novel parallel point symmetry-based genetic clustering (ParSymG) algorithm for unsupervised classification. The genetic algorithm was introduced to overcome the sub-optimization problem caused by inappropriate selection of initial centroids in ParSym. A message passing interface (MPI) was used to implement the distributed master–slave paradigm. To make the algorithm more time-efficient, a three-phase speedup strategy was adopted for population initialization, image partition, and kd-tree structure-based nearest neighbor searching. The advantages of ParSymG over existing ParSym and parallel K-means (PKM) alogithms were demonstrated through case studies using three different types of remotely sensed images. Results in speedup and time gain proved the excellent scalability of the ParSymG algorithm.

Use of Semisupervised Clustering and Feature-Selection Techniques for Identification of Co-expressed Genes.

Studying the patterns hidden in gene-expression data helps to understand the functionality of genes. In general, clustering techniques are widely used for the identification of natural partitionings from the gene expression data. In order to put constraints on dimensionality, feature selection is the key issue because not all features are important from clustering point of view. Moreover some limited amount of supervised information can help to fine tune the obtained clustering solution. In this paper, the problem of simultaneous feature selection and semisupervised clustering is formulated as a multiobjective optimization (MOO) task. A modern simulated annealing-based MOO technique namely AMOSA is utilized as the background optimization methodology. Here, features and cluster centers are represented in the form of a string and the assignment of genes to different clusters is done using a point symmetry-based distance. Six optimization criteria based on several internal and external cluster validity indices are utilized. In order to generate the supervised information, a popular clustering technique, Fuzzy C-mean, is utilized. Appropriate subset of features, proper number of clusters and the proper partitioning are determined using the search capability of AMOSA. The effectiveness of this proposed semisupervised clustering technique, Semi-FeaClustMOO, is demonstrated on five publicly available benchmark gene-expression datasets. Comparison results with the existing techniques for gene-expression data clustering again reveal the superiority of the proposed technique. Statistical and biological significance tests have also been carried out.

K-means algorithm with a novel distance measure

In this paper, we describe an essential problem in data clustering and present some solutions for it. We investigated using distance measures other than Euclidean type for improving the performance of clustering. We also developed an improved point symmetry-based distance measure and proved its efficiency. We developed a k-means algorithm with a novel distance measure that improves the performance of the classical k-means algorithm. The proposed algorithm does not have the worst-case bound on running time that exists in many similar algorithms in the literature. Experimental results shown in this paper demonstrate the effectiveness of the proposed algorithm. We compared the proposed algorithm with the classical k-means algorithm. We presented the proposed algorithm and their performance results in detail along with avenues of future research.

Efficient parallel algorithm for pixel classification in remote sensing imagery

An important approach for image classification is the clustering of pixels in the spectral domain. Fast detection of different land cover regions or clusters of arbitrarily varying shapes and sizes in satellite images presents a challenging task. In this article, an efficient scalable parallel clustering technique of multi-spectral remote sensing imagery using a recently developed point symmetry-based distance norm is proposed. The proposed distributed computing time efficient point symmetry based K-Means technique is able to correctly identify presence of overlapping clusters of any arbitrary shape and size, whether they are intra-symmetrical or inter-symmetrical in nature. A Kd-tree based approximate nearest neighbor searching technique is used as a speedup strategy for computing the point symmetry based distance. Superiority of this new parallel implementation with the novel two-phase speedup strategy over existing parallel K-Means clustering algorithm, is demonstrated both quantitatively and in computing time, on two SPOT and Indian Remote Sensing satellite images, as even K-Means algorithm fails to detect the symmetry in clusters. Different land cover regions, classified by the algorithms for both images, are also compared with the available ground truth information. The statistical analysis is also performed to establish its significance to classify both satellite images and numeric remote sensing data sets, described in terms of feature vectors.

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.

GAPS: A clustering method using a new point symmetry-based distance measure

In this paper, an evolutionary clustering technique is described that uses a new point symmetry-based distance measure. The algorithm is therefore able to detect both convex and non-convex clusters. Kd-tree based nearest neighbor search is used to reduce the complexity of finding the closest symmetric point. Adaptive mutation and crossover probabilities are used. The proposed GA with point symmetry (GAPS) distance based clustering algorithm is able to detect any type of clusters, irrespective of their geometrical shape and overlapping nature, as long as they possess the characteristic of symmetry. GAPS is compared with existing symmetry-based clustering technique SBKM, its modified version, and the well-known K -means algorithm. Sixteen data sets with widely varying characteristics are used to demonstrate its superiority. For real-life data sets, ANOVA and MANOVA statistical analyses are performed.