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

This paper presents a comparison between external and internal cluster validity indices with a similar bounded index range. F-measure (FM) and Fowlkes-Mallows (FMI) of external validity indices, as well as Silhouette (SIL) of internal validity index, were chosen for this comparative analysis. Ten numerical data sets, namely Haberman, BUPA (liver disorder), Wisconsin Diagnostic Breast Cancer (WDBC), Iris, Seeds, Wine, User Knowledge, Cleveland, Segmentation, and Glass, were deployed to benchmark the clustering outcomes based on Fuzzy C-Mean (FCM) algorithm. Mean, minimum, and maximum scores were calculated to determine the similarities and differences among the indices. Pearson correlation was reported as well. As a result, the index scores displayed a slight difference between the external and internal validity indices. A moderate and positive correlation was noted between the external and internal validity index (r=. 66, r=.65 p<0.01) scores. This correlation signifies a similar graph pattern between the cluster validity indices. This comparative analysis revealed that the external and internal cluster validity indices with similar bounded index ranges and slightly different index scores generate a moderate and positive correlation with a similar graph pattern.

Procedures that evaluate the results of clustering algorithms are known as clustering validation (CV) indexes. There are several (CV) indexes usually classified into two broad classes namely external and internal clustering validation indexes depending on whether on ground truth or optimal clustering are known in advance or not respectively. Traditional cluster validation indexes are even impossible to perform especially when the size of the data set is very large. In this paper, we are interested in external validation of clustering large data sets. To solve the issue of CV in a big data context, we propose in this paper a parallel external clustering validation especially F-measure (MR_F-measure) model that is based on MapReduce. The experimental results reveal that MR_F-measure scales very well with increasing data set sizes.

Procedures that evaluate the results of clustering algorithms are known as cluster validation (CV) indexes. There exist several CV indexes usually classified into two broad classes namely external and internal clustering validation indexes depending on whether ground truth or optimal clustering solutions are known in advance or not respectively. Traditional cluster validation indexes are even impossible to perform especially when the size of the data set is very large. To solve the issue of CV indexes in such contexts, we propose parallel and distributed external clustering validation models based on MapReduce for three indexes namely: F-measure, Normalized Mutual Information and Variation of Information. The experimental results reveal that these models scale very well with increasing size of dataset and provide accurate results.

Purpose – The most commonly used approaches for cluster validation are based on indices but the majority of the existing cluster validity indices do not work well on data sets of different complexities. The purpose of this paper is to propose a new cluster validity index (ARSD index) that works well on all types of data sets. Design/methodology/approach – The authors introduce a new compactness measure that depicts the typical behaviour of a cluster where more points are located around the centre and lesser points towards the outer edge of the cluster. A novel penalty function is proposed for determining the distinctness measure of clusters. Random linear search-algorithm is employed to evaluate and compare the performance of the five commonly known validity indices and the proposed validity index. The values of the six indices are computed for all nc ranging from (nc min, nc max) to obtain the optimal number of clusters present in a data set. The data sets used in the experiments include shaped, Gaussian-like and real data sets. Findings – Through extensive experimental study, it is observed that the proposed validity index is found to be more consistent and reliable in indicating the correct number of clusters compared to other validity indices. This is experimentally demonstrated on 11 data sets where the proposed index has achieved better results. Originality/value – The originality of the research paper includes proposing a novel cluster validity index which is used to determine the optimal number of clusters present in data sets of different complexities.

There are two notoriously hard problems in cluster analysis, estimating the number of clusters, and checking whether the population to be clustered is not actually homogeneous. Given a dataset, a clustering method and a cluster validation index, this paper proposes to set up null models that capture structural features of the data that cannot be interpreted as indicating clustering. Artificial datasets are sampled from the null model with parameters estimated from the original dataset. This can be used for testing the null hypothesis of a homogeneous population against a clustering alternative. It can also be used to calibrate the validation index for estimating the number of clusters, by taking into account the expected distribution of the index under the null model for any given number of clusters. The approach is illustrated by three examples, involving various different clustering techniques (partitioning around medoids, hierarchical methods, a Gaussian mixture model), validation indexes (average silhouette width, prediction strength and BIC), and issues such as mixed type data, temporal and spatial autocorrelation.

Fusion of evolvable genome structure and multi-objective optimization for subspace clustering

PDBI: A partitioning Davies-Bouldin index for clustering evaluation

Determining the most proper number of cluster in fuzzy clustering by using artificial neural networks

This study presents the discovery of meaningful patterns (groups) from the obese samples of health and nutritional survey data by applying various clustering techniques. Due to the mixed nature of the data (qualitative and quantitative variables) in the data set, the best-suited clustering techniques with appropriate dissimilarity metrics were chosen to interpret the meaningful results. The relationships between obesity and the lifestyle affecting factors like demography, socio-economic status, physical activity, and dietary behavior were assessed using four cluster techniques namely Two-Step clustering, Partition Around Medoids (PAM), Agglomerative Hierarchical clustering and, Kohonen Self Organizing Maps (SOMs). The solutions generated by these techniques were analyzed and validated by the help of cluster validity (CV) indices and later on their associations were determined with the obesity classes to discover the pattern from the obese sample. Two-Step clustering and hierarchical clustering outperformed the other applied techniques in identifying the subgroups based on the underlying hidden patterns in the data. Based on the CV indices values and the association analysis (obesity factor with the cluster solutions), two subgroups were generated and profiles of these groups have been reported. The first group belonged to the middle-aged individuals who seem to take care of their lifestyle while the other group belonged to young-aged individuals who in contrast to the first group presented a careless lifestyle factor (i.e., physical activity and dietary behavior). The salient features of these subgroups have been reported and can be proposed for the betterment in the health care industry. The research helped in identifying the interesting subsets/groups within survey data demonstrating similar characteristics and health status (i.e., prevalence of obesity with respect to lifestyle factors like physical activity, dietary behavior etc.) which will help to suggest appropriate measures/steps to be taken by the concerned departments to counter them and prevent in the population.

Transmissions in the mmWave spectrum benefit from a-priori knowledge of radio channel propagation models. This paper is concerned with one important task that helps provide a more accurate channel model, namely, the clustering of all multipath components arriving at the receiver. Our work focuses on directive transmissions in urban outdoor scenarios and shows the importance of the correct estimation of the number of clusters for mmWave radio channels simulated with a software ray-tracer tool. We investigate the effectiveness of k-means and k-power-means clustering algorithms in predicting the number of clusters through the use of cluster validity indices (CVIs) and score fusion techniques. Our investigation shows that clustering is a difficult task because the optimal number of clusters is not always given by one or by a combination of more CVIs. However, using score fusion methods, we find the optimal partitioning for the k-means algorithm based on the power and time of arrival of the multipath rays or based on their angle of arrival. When the k-power-means algorithm is used, the power of each arriving ray is the most important clustering factor, making the dominant received paths pull the other ones around them, to form a cluster. Thus, the number of clusters is smaller and the decision based on CVIs or score fusion factors easier to be taken.

Missing data are unavoidable in the real-world application of unsupervised machine learning, and their nonoptimal processing may decrease the quality of data-driven models. Imputation is a common remedy for missing values, but directly estimating expected distances have also emerged. Because treatment of missing values is rarely considered in clustering related tasks and distance metrics have a central role both in clustering and cluster validation, we developed a new toolbox that provides a wide range of algorithms for data preprocessing, distance estimation, clustering, and cluster validation in the presence of missing values. All these are core elements in any comprehensive cluster analysis methodology. We describe the methodological background of the implemented algorithms and present multiple illustrations of their use. The experiments include validating distance estimation methods against selected reference methods and demonstrating the performance of internal cluster validation indices. The experimental results demonstrate the general usability of the toolbox for the straightforward realization of alternate data processing pipelines. Source code, data sets, results, and example macros are available on GitHub. <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/markoniem/nanclustering_toolbox</uri>

A measurement of cluster quality is often needed for DNA microarray data analysis. In this paper, we introduce a new cluster validity index, which measures geometrical features of the data. The essential concept of this index is to evaluate the ratio between the squared total length of the data eigen-axes with respect to the between-cluster separation. We show that this cluster validity index works well for data that contain clusters closely distributed or with different sizes. We verify the method using three simulated data sets, two real world data sets and two microarray data sets. The experiment results show that the proposed index is superior to five other cluster validity indices, including partition coefficients (PC), General silhouette index (GS), Dunn’s index (DI), CH Index and I-Index. Also, we have given a theorem to show for what situations the proposed index works well.

Fuzzy C-Means (FCM) algorithm has been widely used in cluster analysis of gene expression data. It can converge rapidly and provide more information regarding relationships within the data thanks to the usage of fuzzy sets to represent the degrees of cluster membership for every data point. However, FCM has a shortcoming in that it requires a priori specification of cluster number and cluster validation. Most cluster validity indices are based on the data themselves and may not be applicable for gene expression data. In this paper, we propose a Bayesian method using Gene Ontology (GO) annotations for gene expression cluster validation. We show that our method outperforms popular validity indices on gene expression datasets.

Several cluster validity measures have been proposed for evaluating clustering results. However, existing methods may not work well for the following two kinds of data sets. The first one is that the data set contains cluster groups with different densities. The second one is that some of the cluster groups are closely positioned. In this paper, we introduce a new cluster validity index. In this method, we define the index as the ratio between the squared total length of the data eigen-axes and the between-cluster separation. Compared with existing cluster validity indices, the proposed index produces more accurate results and is able to handle the two kinds of data sets mentioned above.

Social learning differential evolution