Internal Cluster Validity Research Articles

Feature selection and semi-supervised clustering using multiobjective optimization.

In this paper we have coupled feature selection problem with semi-supervised clustering. Semi-supervised clustering utilizes the information of unsupervised and supervised learning in order to overcome the problems related to them. But in general all the features present in the data set may not be important for clustering purpose. Thus appropriate selection of features from the set of all features is very much relevant from clustering point of view. In this paper we have solved the problem of automatic feature selection and semi-supervised clustering using multiobjective optimization. A recently created simulated annealing based multiobjective optimization technique titled archived multiobjective simulated annealing (AMOSA) is used as the underlying optimization technique. Here features and cluster centers are encoded in the form of a string. We assume that for each data set for 10% data points class level information are known to us. Two internal cluster validity indices reflecting different data properties, an external cluster validity index measuring the similarity between the obtained partitioning and the true labelling for 10% data points and a measure counting the number of features present in a particular string are optimized using the search capability of AMOSA. AMOSA is utilized to detect the appropriate subset of features, appropriate number of clusters as well as the appropriate partitioning from any given data set. The effectiveness of the proposed semi-supervised feature selection technique as compared to the existing techniques is shown for seven real-life data sets of varying complexities.

Summer temperature extremes in northeastern Spain: spatial regionalization and links to atmospheric circulation (1960–2006)

A procedure for classifying daily summer temperature extremes in northeastern Spain into homogenous regions has been presented and evaluated. This procedure employed daily temperature series from a dense network of 128 weather stations spanning the period from 1960 to 2006. Characteristics of temperature extremes included temperature frequency (e.g., warm days), intensity (e.g., warmest day), and duration (e.g., maximum length of hot spell). Following the results of the principal components analysis and Ward's method of clustering, the study area was divided into four homogenous sub-regions in terms of both the geographic and climatic meanings: the Mediterranean region, the mainland and the Cantabrian region, the moderately elevated areas westward and southward, and the mountainous region. Based on an internal cluster validation measure (Silhouette width), the quality of clustering was evaluated and ensured. The temporal evolution of the long-term (1960–2006) temperature extremes clearly showed a different behavior amongst these sub-regions. The Mediterranean and the highly elevated regions revealed the strongest signals in both daytime and nighttime extremes. For mainland areas, considerable differences in the behavior of the daytime and nighttime temperature extremes were evident. The influence of atmospheric circulation on spatial and temporal variability of temperature extremes was also explored. The variability of summer temperature extremes in NE Spain appears to be mainly driven by the Scandinavian (SCA), the Western Mediterranean Oscillation (WeMO), and the East Atlantic (EA) patterns, with a tendency toward increasing during the positive (negative) phases of the EA (WeMO and SCA) circulation modes. In such a region with complex geography and climate, regionalization of summer temperature extremes can be advantageous for extracting finer-scale information, which may prove useful for the vulnerability assessments and the development of local adaptation strategies in areas such as health, ecosystems and agriculture.

A comparative study of novel robust clustering algorithms

Both parametric Bayesian mixture and non-parametric Dirichlet process mixture modelling DPM approaches for density estimation and clustering allow for automatic model selection. It is interesting to study which approach can better fit the data. In this paper, we focus on robust clustering taking the Student t-distribution as the building block. We develop two novel robust clustering algorithms, one using Type-IV Student t-distribution mixture modelling SMM and one robust DPM RDPM, and explain them in detail. The new algorithms are compared using controlled experiment settings and benchmark UCI datasets, in terms of commonly-used internal and external cluster validity indices. Experimental results show that Type-IV SMM shows comparable performance to Type-II SMM, while additionally identifying outliers, and that RDPM outperforms conventional DPM. When comparing the two new algorithms with each other, they are found to perform comparably, but Type-IV SMM is less sensitive to initialisation and has a better generalisation ability. Hence, it is recommended to use Type-IV SMM for robust clustering and model selection.

Understanding and Enhancement of Internal Clustering Validation Measures

Clustering validation has long been recognized as one of the vital issues essential to the success of clustering applications. In general, clustering validation can be categorized into two classes, external clustering validation and internal clustering validation. In this paper, we focus on internal clustering validation and present a study of 11 widely used internal clustering validation measures for crisp clustering. The results of this study indicate that these existing measures have certain limitations in different application scenarios. As an alternative choice, we propose a new internal clustering validation measure, named clustering validation index based on nearest neighbors (CVNN), which is based on the notion of nearest neighbors. This measure can dynamically select multiple objects as representatives for different clusters in different situations. Experimental results show that CVNN outperforms the existing measures on both synthetic data and real-world data in different application scenarios.

An extensive comparative study of cluster validity indices

The validation of the results obtained by clustering algorithms is a fundamental part of the clustering process. The most used approaches for cluster validation are based on internal cluster validity indices. Although many indices have been proposed, there is no recent extensive comparative study of their performance. In this paper we show the results of an experimental work that compares 30 cluster validity indices in many different environments with different characteristics. These results can serve as a guideline for selecting the most suitable index for each possible application and provide a deep insight into the performance differences between the currently available indices.

Vinayaka : A Semi-Supervised Projected Clustering Method Using Differential Evolution

Differential Evolution (DE) is an algorithm for evolutionary optimization. Clustering problems have been solved by using DE based clustering methods but these methods may fail to find clusters hidden in subspaces of high dimensional datasets.Subspace and projected clustering methodshave been proposed in literature to find subspace clusters that are present in subspaces of dataset. In this paper we propose VINAYAKA, a semi-supervised projected clustering method based on DE. In this method DE optimizes a hybrid cluster validation index. Subspa ce Clustering Quality Estimate index (SCQE index) is used for internal cluster validation and Gini indexgain is used for external cluster validationin the proposed hybrid cluster validation index.Proposed method is applied on Wisconsin breast cancer dataset.

Vinayaka : A Semi-Supervised Projected Clustering Method Using Differential Evolution

Differential Evolution (DE) is an algorithm for evolutionary optimization. Clustering problems have been solved by using DE based clustering methods but these methods may fail to find clusters hidden in sub-spaces of high dimensional datasets. Subspace and projected clustering methods have been proposed in literature to find subspace clusters that are present in sub-spaces of data set. In this paper we propose VINAYAKA, a semi-supervised projected clustering method based on DE. In this method DE optimizes a hybrid cluster validation index. Subspace Clustering Quality Estimate index (SCQE index) is used for internal cluster validation and Gini index gain is used for external cluster validation in the proposed hybrid cluster validation index. Proposed method is applied on Wisconsin breast cancer data set.

Performance of an Ensemble Clustering Algorithm on Biological Data Sets

Ensemble clustering is a promising approach that combines the results of multiple clustering algorithms to obtain a consensus partition by merging different partitions based upon well-defined rules. In this study, we use an ensemble clustering approach for merging the results of five different clustering algorithms that are sometimes used in bioinformatics applications. The ensemble clustering result is tested on microarray data sets and compared with the results of the individual algorithms. An external cluster validation index, adjusted rand index (C-rand), and two internal cluster validation indices; silhouette, and modularity are used for comparison purposes.

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.

A Survey on Internal Validity Measure for Cluster Validation

Data Clustering is a technique of finding similar characteristics among the data set which are always hidden in nature and grouping them into groups, called as clusters. Different clustering algorithms exhibit different results, since they are very sensitive to the characteristics of original data set especially noise and dimension. The quality of such clustering process determines the purity of cluster and hence it is very important to evaluate the results of the clustering algorithm. Due to this, Cluster validation activity had been a major and challenging task. The major factor which influences cluster validation is the internal cluster validity measure of choosing the optimal number of clusters. The main objective of this article is to present a detailed description of the mathematical working of few cluster validity indices and not all, to classify these indices and to explore the ideas for the future promotion of the work in the domain of cluster validation. In addition to this, a maximization objective function is defined assuming to provide a cluster validation activity.

Towards a standard methodology to evaluate internal cluster validity indices

The evaluation and comparison of internal cluster validity indices is a critical problem in the clustering area. The methodology used in most of the evaluations assumes that the clustering algorithms work correctly. We propose an alternative methodology that does not make this often false assumption. We compared 7 internal cluster validity indices with both methodologies and concluded that the results obtained with the proposed methodology are more representative of the actual capabilities of the compared indices.

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 .