Fuzzy Cluster Validity Index Research Articles

Artificial immune multi-objective SAR image segmentation with fused complementary features

Artificial immune systems (AIS) are the computational systems inspired by the principles and processes of the vertebrate immune system. AIS-based algorithms typically mimic the human immune system’s characteristics of learning and adaptability to solve some complicated problems. Here, an artificial immune multi-objective optimization framework is formulated and applied to synthetic aperture radar (SAR) image segmentation. The important innovations of the framework are listed as follows: (1) an efficient and robust immune, multi-objective optimization algorithm is proposed, which has the features of adaptive rank clones and diversity maintenance by K-nearest-neighbor list; (2) besides, two conflicting, fuzzy clustering validity indices are incorporated into this framework and optimized simultaneously and (3) moreover, an effective, fused feature set for texture representation and discrimination is constructed and researched, which utilizes both the Gabor filter’s ability to precisely extract texture features in low- and mid-frequency components and the gray level co-occurrence probability’s (GLCP) ability to measure information in high-frequency. Two experiments with synthetic texture images and SAR images are implemented to evaluate the performance of the proposed framework in comparison with other five clustering algorithms: fuzzy C-means (FCM), single-objective genetic algorithm (SOGA), self-organizing map (SOM), wavelet-domain hidden Markov models (HMTseg), and spectral clustering ensemble (SCE). Experimental results show the proposed framework has obtained the better performance in segmenting SAR images than other five algorithms and behaves insensitive to the speckle noise.

Unsupervised and Supervised Learning Approaches Together for Microarray Analysis

In this article, a novel concept is introduced by using both unsupervised and supervised learning. For unsupervised learning, the problem of fuzzy clustering in microarray data as a multiobjective optimization is used, which simultaneously optimizes two internal fuzzy cluster validity indices to yield a set of Pareto-optimal clustering solutions. In this regards, a new multiobjective differential evolution based fuzzy clustering technique has been proposed. Subsequently, for supervised learning, a fuzzy majority voting scheme along with support vector machine is used to integrate the clustering information from all the solutions in the resultant Pareto-optimal set. The performances of the proposed clustering techniques have been demonstrated on five publicly available benchmark microarray data sets. A detail comparison has been carried out with multiobjective genetic algorithm based fuzzy clustering, multiobjective differential evolution based fuzzy clustering, single objective versions of differential evolution and genetic algorithm based fuzzy clustering as well as well known fuzzy c-means algorithm. While using support vector machine, comparative studies of the use of four different kernel functions are also reported. Statistical significance test has been done to establish the statistical superiority of the proposed multiobjective clustering approach. Finally, biological significance test has been carried out using a web based gene annotation tool to show that the proposed integrated technique is able to produce biologically relevant clusters of coexpressed genes.

Fuzzy clustering algorithms for unsupervised change detection in remote sensing images

In this paper, we propose a context-sensitive technique for unsupervised change detection in multitemporal remote sensing images. The technique is based on fuzzy clustering approach and takes care of spatial correlation between neighboring pixels of the difference image produced by comparing two images acquired on the same geographical area at different times. Since the ranges of pixel values of the difference image belonging to the two clusters ( changed and unchanged) generally have overlap, fuzzy clustering techniques seem to be an appropriate and realistic choice to identify them (as we already know from pattern recognition literatures that fuzzy set can handle this type of situation very well). Two fuzzy clustering algorithms, namely fuzzy c-means (FCM) and Gustafson–Kessel clustering (GKC) algorithms have been used for this task in the proposed work. For clustering purpose various image features are extracted using the neighborhood information of pixels. Hybridization of FCM and GKC with two other optimization techniques, genetic algorithm (GA) and simulated annealing (SA), is made to further enhance the performance. To show the effectiveness of the proposed technique, experiments are conducted on two multispectral and multitemporal remote sensing images. A fuzzy cluster validity index (Xie–Beni) is used to quantitatively evaluate the performance. Results are compared with those of existing Markov random field (MRF) and neural network based algorithms and found to be superior. The proposed technique is less time consuming and unlike MRF does not require any a priori knowledge of distributions of changed and unchanged pixels.

A novel hybrid algorithm for creating self-organizing fuzzy neural networks

A novel hybrid algorithm based on a genetic algorithm and particle swarm optimization to design a fuzzy neural network, named self-organizing fuzzy neural network based on GA and PSO (SOFNNGAPSO), to implement Takagi–Sugeno (TS) type fuzzy models is proposed in this paper. The proposed algorithm, as a new hybrid algorithm, consists of two phases. A tuning based on TS's fuzzy model is applied to identify the fuzzy structure, and also a fuzzy cluster validity index is utilized to determine the optimal number of clusters. To obtain a more precision model, GA and PSO are performed to conduct fine tuning for the obtained parameter set of the premise parts and consequent parts in the aforementioned fuzzy model. The proposed algorithm is successfully applied to three tested examples.

A Selection Model for Optimal Fuzzy Clustering Algorithm and Number of Clusters Based on Competitive Comprehensive Fuzzy Evaluation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Fuzzy <formula formulatype="inline"><tex Notation="TeX">$c$</tex></formula>-means (FCM) and its variants suffer from two problems---local minima and cluster validity---which have a direct impact on the formation of final clustering. There are two strategies---optimization and center initialization strategies---that address the problem of local minima. This paper proposes a center initialization approach based on a minimum spanning tree to keep FCM from local minima. With regard to cluster validity, various strategies have been proposed. On the basis of the fuzzy cluster validity index, this paper proposes a selection model that combines multiple pairs of a fuzzy clustering algorithm and cluster validity index to identify the number of clusters and simultaneously selects the optimal fuzzy clustering for a dataset. The promising performance of the proposed center-initialization method and selection model is demonstrated by experiments on real datasets. </para>

Combining Pareto-optimal clusters using supervised learning for identifying co-expressed genes

BackgroundThe landscape of biological and biomedical research is being changed rapidly with the invention of microarrays which enables simultaneous view on the transcription levels of a huge number of genes across different experimental conditions or time points. Using microarray data sets, clustering algorithms have been actively utilized in order to identify groups of co-expressed genes. This article poses the problem of fuzzy clustering in microarray data as a multiobjective optimization problem which simultaneously optimizes two internal fuzzy cluster validity indices to yield a set of Pareto-optimal clustering solutions. Each of these clustering solutions possesses some amount of information regarding the clustering structure of the input data. Motivated by this fact, a novel fuzzy majority voting approach is proposed to combine the clustering information from all the solutions in the resultant Pareto-optimal set. This approach first identifies the genes which are assigned to some particular cluster with high membership degree by most of the Pareto-optimal solutions. Using this set of genes as the training set, the remaining genes are classified by a supervised learning algorithm. In this work, we have used a Support Vector Machine (SVM) classifier for this purpose.ResultsThe performance of the proposed clustering technique has been demonstrated on five publicly available benchmark microarray data sets, viz., Yeast Sporulation, Yeast Cell Cycle, Arabidopsis Thaliana, Human Fibroblasts Serum and Rat Central Nervous System. Comparative studies of the use of different SVM kernels and several widely used microarray clustering techniques are reported. Moreover, statistical significance tests have been carried out to establish the statistical superiority of the proposed clustering approach. Finally, biological significance tests have been carried out using a web based gene annotation tool to show that the proposed method is able to produce biologically relevant clusters of co-expressed genes.ConclusionThe proposed clustering method has been shown to perform better than other well-known clustering algorithms in finding clusters of co-expressed genes efficiently. The clusters of genes produced by the proposed technique are also found to be biologically significant, i.e., consist of genes which belong to the same functional groups. This indicates that the proposed clustering method can be used efficiently to identify co-expressed genes in microarray gene expression data.Supplementary Website The pre-processed and normalized data sets, the matlab code and other related materials are available at .

On fuzzy cluster validity indices

Cluster analysis aims at identifying groups of similar objects, and helps to discover distribution of patterns and interesting correlations in large data sets. Especially, fuzzy clustering has been widely studied and applied in a variety of key areas and fuzzy cluster validation plays a very important role in fuzzy clustering. This paper introduces the fundamental concepts of cluster validity, and presents a review of fuzzy cluster validity indices available in the literature. We conducted extensive comparisons of the mentioned indices in conjunction with the Fuzzy C-Means clustering algorithm on a number of widely used data sets, and make a simple analysis of the experimental results.

A novel hybrid algorithm for function approximation

This paper introduces a novel hybrid algorithm for function approximation. The proposed algorithm consists of a hybrid approach to develop Takagi and Sugeno's fuzzy model for function approximation. In this paper, a coarse tuning based on Takagi and Sugeno's fuzzy model is applied to identify the fuzzy structure, and also a fuzzy cluster validity index is utilized to determine the optimal number of clusters. To obtain a more precision model, genetic algorithm (GA) and particle swarm optimization (PSO) are performed to conduct fine-tuning for the obtained parameter set of the premise parts and consequent parts in the aforementioned fuzzy model. The proposed algorithm is successfully applied to three tested examples. Compared with other existing approaches in the literature, the proposed algorithm is very useful for modeling function approximation.

An objective approach to cluster validation

Cluster validation is a major issue in cluster analysis. Many existing validity indices do not perform well when clusters overlap or there is significant variation in their covariance structure. The contribution of this paper is twofold. First, we propose a new validity index for fuzzy clustering. Second, we present a new approach for the objective evaluation of validity indices and clustering algorithms. Our validity index makes use of the covariance structure of clusters, while the evaluation approach utilizes a new concept of overlap rate that gives a formal measure of the difficulty of distinguishing between overlapping clusters. We have carried out experimental studies using data sets containing clusters of different shapes and densities and various overlap rates, in order to show how validity indices behave when clusters become less and less separable. Finally, the effectiveness of the new validity index is also demonstrated on a number of real-life data sets.

A study of some fuzzy cluster validity indices, genetic clustering and application to pixel classification

In this article, the effectiveness of variable string length genetic algorithm along with a recently developed fuzzy cluster validity index ( PBMF) has been demonstrated for clustering a data set into an unknown number of clusters. The flexibility of a variable string length Genetic Algorithm (VGA) is utilized in conjunction with the fuzzy indices to determine the number of clusters present in a data set as well as a good fuzzy partition of the data for that number of clusters. A comparative study has been performed for different validity indices, namely, PBMF, XB, PE and PC. The results of the fuzzy VGA algorithm are compared with those obtained by the well known FCM algorithm which is applicable only when the number of clusters is fixed a priori. Moreover, another genetic clustering scheme, that also requires fixing the value of the number of clusters, is implemented. The effectiveness of the PBMF index as the optimization criterion along with a genetic fuzzy partitioning technique is demonstrated on a number of artificial and real data sets including a remote sensing image of the city of Kolkata.

A cluster validity index for fuzzy clustering

Cluster validity indexes have been used to evaluate the fitness of partitions produced by clustering algorithms. This paper presents a new validity index for fuzzy clustering called a partition coefficient and exponential separation (PCAES) index. It uses the factors from a normalized partition coefficient and an exponential separation measure for each cluster and then pools these two factors to create the PCAES validity index. Considerations involving the compactness and separation measures for each cluster provide different cluster validity merits. In this paper, we also discuss the problem that the validity indexes face in a noisy environment. The efficiency of the proposed PCAES index is compared with several popular validity indexes. More information about these indexes is acquired in series of numerical comparisons and also three real data sets of Iris, Glass and Vowel. The results of comparative study show that the proposed PCAES index has high ability in producing a good cluster number estimate and in addition, it provides a new point of view for cluster validity in a noisy environment.