Rand Statistic Research Articles

A Comparative Analysis of Data Stream Clustering Algorithms

This study compares the performance of stream clustering algorithms (DenStream, CluStream, ClusTree) on Massive Online Analysis (MOA) using synthetic and real-world datasets. The algorithms are compared in the presence on noise level [0%, 10%, 30%] on the synthetic data. DenStream epsilon parameter was tune to 0.01 and 0.03 to improve its performance. We use the performance evaluation metrics CMM, F1-P, F1-R, Purity, Silhouette Coefficient, and Rand statistic. On synthetic data, our results show that ClusTree outperformed CluStream and DenStream on the almost all the metrics except in Purity and Silhouette were DenStream performs better at noise levels (10% and 30%). ClusTree outperform CluStream and DenStream on Forest Cover type dataset on metrics CMM, F1-P, F1-R, Silhouette Coefficient, and Rand statistic with 90%, 74%, 77% and 89% respectively. However, the tune DenStream epsilon parameter shows some improvements. On electricity data, DenStream outperform CluStream and ClusTree at epsilon parameter (0.03 and 0.05) on metrics F1-P, F1-R, and Purity. The investigation of DenStream epsilon parameter (0.03 and 0.05) on RandomBRF Generator with noise level [0%, 10%, 30%] shows that DenStream with epsilon 0.03 outperform other parameter adjustment.

Discovering communities of malapps on Android-based mobile cyber-physical systems

Android-based devices like smartphones have become ideal mobile cyber-physical systems (MCPS) due to their powerful processors and variety of sensors. In recent years, an explosively and continuously growing number of malicious applications (malapps) have posed a great threat to Android-based MCPS as well as users’ privacy. The effective detection of malapps is an emerging yet crucial task. How to establish relationships among malapps, discover their potential communities, and explore their evolution process has become a challenging issue in effective detection of malapps. To deal with this issue, in this work, we are motivated to propose an automated community detection method for Android malapps by building a relation graph based on their static features. First, we construct a large feature set to profile the behaviors of malapps. Second, we propose an E-N algorithm for graph construction by combining epsilon graph and k-nearest neighbor (k-NN) graph. It solves the problem of an incomplete graph led by epsilon method and the problem of noise generated by k-NN graph. Finally, a community detection method, Infomap, is employed to explore the underlying structures of the relation graph, and obtain the communities of malapps. We evaluate our community detection method with 3996 malapp samples. Extensive experimental results show that our method outperforms the traditional clustering methods and achieves the best performance with rand statistic of 94.93% and accuracy of 79.53%.

Radiomic feature clusters and prognostic signatures specific for Lung and Head & Neck cancer.

Radiomics provides a comprehensive quantification of tumor phenotypes by extracting and mining large number of quantitative image features. To reduce the redundancy and compare the prognostic characteristics of radiomic features across cancer types, we investigated cancer-specific radiomic feature clusters in four independent Lung and Head & Neck (H∓N) cancer cohorts (in total 878 patients). Radiomic features were extracted from the pre-treatment computed tomography (CT) images. Consensus clustering resulted in eleven and thirteen stable radiomic feature clusters for Lung and H & N cancer, respectively. These clusters were validated in independent external validation cohorts using rand statistic (Lung RS = 0.92, p < 0.001, H & N RS = 0.92, p < 0.001). Our analysis indicated both common as well as cancer-specific clustering and clinical associations of radiomic features. Strongest associations with clinical parameters: Prognosis Lung CI = 0.60 ± 0.01, Prognosis H & N CI = 0.68 ± 0.01; Lung histology AUC = 0.56 ± 0.03, Lung stage AUC = 0.61 ± 0.01, H & N HPV AUC = 0.58 ± 0.03, H & N stage AUC = 0.77 ± 0.02. Full utilization of these cancer-specific characteristics of image features may further improve radiomic biomarkers, providing a non-invasive way of quantifying and monitoring tumor phenotypic characteristics in clinical practice.

Comparison of methods for identifying phenotype subgroups using categorical features data with application to autism spectrum disorder

We evaluate the performance of the Dirichlet process mixture (DPM) and the latent class model (LCM) in identifying autism phenotype subgroups based on categorical autism spectrum disorder (ASD) diagnostic features from the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition Text Revision. A simulation study is designed to mimic the diagnostic features in the ASD dataset in order to evaluate the LCM and DPM methods in this context. Likelihood based information criteria and DPM partitioning are used to identify the best fitting models. The Rand statistic is used to compare the performance of the methods in recovering simulated phenotype subgroups. Our results indicate excellent recovery of the simulated subgroup structure for both methods. The LCM performs slightly better than DPM when the correct number of latent subgroups is selected a priori. The DPM method utilizes a maximum a posteriori (MAP) criterion to estimate the number of classes, and yielded results in fair agreement with the LCM method. Comparison of model fit indices in identifying the best fitting LCM showed that adjusted Bayesian information criteria (ABIC) picks the correct number of classes over 90% of the time. Thus, when diagnostic features are categorical and there is some prior information regarding the number of latent classes, LCM in conjunction with ABIC is preferred.

A method of predicting the number of clusters using Rand's statistic

Distributional and asymptotic results on the moment of Rand's C k statistic were derived by DuBien and Warde [1981. Some distributional results concerning a comparative statistic used in cluster analysis. ASA Proceedings of the Social Statistics Section, 309–313.]. Based on those results, a method to predict the number of clusters is suggested by applying various agglomerative clustering algorithms. In the procedure, the methods using different indexes are examined and compared based on the concept of agreement (or, disagreement) between clusterings generated by different clustering algorithms on the set of data. Our method having practical generality works better than the other methods and assigns statistical meaning to C k values in determining the number of clusters from the comparison.

Comparison of Chernoff-type face and non-graphical methods for clustering multivariate observations

During the past few years the use of Chernoff-type faces (a technique of representing points in k-dimensional space graphically) has been accelerating for discovering clusters and outliers present in a set of multivariate observations. However, their validation for clustering multivariate data seems to be few. The present study deals with evaluating the efficiency of Chernoff-type faces (Flury and Riedwyl) and four non-graphical algorithms, viz., ‘Single linkage’, ‘Complete linkage’, ‘Group average’ and Ward's methods for recovering true cluster structures. Four different data sets have been used, which were based on samples from mixtures of multivariate normal populations with varying variance-covariance matrix and different levels of separation factor. In order to account for the variability between the subjects, experiments with 30 subjects were conducted and they were asked to group all those faces together which look alike. The recovery of hierarchical cluster structure through Chernoff-type faces has been measured using the agreement score which is simply the number of subjects classifying the pair of faces together just by merely looking at the gestalt of a face. In all the four populations considered, the recovery of cluster structure through Chernoff-type faces using the perception matrix based on the classification of faces done by 30 subjects was more similar to that obtained by complete linkage method as evaluated by adjusted Rand statistic and Jaccard index. The efficacy of Chernoff-type faces in recovering true cluster structure seems to be poor when the classification is done by one subject only. The present study revealed that none of the subjects gave a true partitions in all the four populations considered. However, the recovery values (both adjusted Rand and Jaccard) had improved substantially when the clusters were obtained from perception matrix presenting the number of subjects who identified any two faces more similar in their gestalt.

A Comparison of Two Approaches to Beta-Flexible Clustering.

We introduce a UPGMA based counterpart to the Lance and Williams (1966) p-flexible clustering strategy. This new method is compared with the original p-flexible technique based on WPGMA for a range of fl values from -0.8 to +0.1. Recovery of the known cluster structure from simulated data was evaluated using the Hubert and Arabie (1985) version of the Rand statistic. The algorithm used to generate the simulated clusters in the study included error-free data as well as three other error conditions. The simulated data also varied the number of clusters, the underlying dimensionality, and the density distribution of points to the clusters. Results showed that the flexible UPGMA gives the best recovery for all generated data configurations. Further, the flexible UPGMA method with a small negative β value performed better than the standard UPGMA method where β is set equal to zero. The flexible UPGMA strategy, employed with a narrow β range, is recommended based upon its ability to recover cluster structure over all error conditions.

The adjusted rand statistic: A SAS macro

A macro for calculating the Hubert and Arabie (1985) adjusted Rand statistic is presented. The adjusted Rand statistic gives a measure of classification agreement between two partitions of the same set of objects. The macro is written in the SAS macro language and makes extensive use of SAS/IML software (SAS Institute, 1985a, 1985b). The macro uses two different methods of handling missing values. The default method assumes that each object that has a missing value for the classification category is in its own separate category or cluster for that classification. The optional method places all objects with a missing value for the classification category into the same category for that classification.

Differences between ward's and UPGMA methods of cluster analysis: Implications for school psychology

This investigation compares the efficacy of two methods of cluster analysis, the unweighted pair-groups method using arithmetic averages (UPGMA) and Ward's method. Two hundred students who were referred by their classroom teachers for psychological evaluations were grouped together on the basis of measures of intelligence, achievement, and social adjustment by both clustering methods. Evaluation of the adjusted Rand statistic indicated that the two solutions had little in common. The comparison suggested that the UPGMA method yielded the more efficacious groupings. This determination was based on evaluation of the output, in the form of a dendogram, or “tree,” with respect to individual children, on a comparison of the cophenetic correlation coefficient generated by each method, and finally on the results of two separate discriminant analyses using the grouping solution of each method as the criterion and the original variables that entered into the cluster analysis as the predictors. The UPGMA solution was judged more appropriate with respect to how indicidual children were grouped. UPGMA yielded a higher cophenetic correlation than Ward's method, indicating less distortion between the input into the clustering method and the output. The two separate discriminant analyses indicated that the groups formed by UPGMA were statistically more distinct than those formed by Ward's method. Implications, both specific and general, for the praxis of school psychology are discussed.

The Measurement of Classification Agreement: An Adjustment to the Rand Statistic for Chance Agreement

Investigators examining empirically derived classifications are often concerned with the replicability of an obtained classification. However, most available statistics which allow replication comparison suffer from various limitations. This paper proposes an adjustment to one of these statistics, the Rand statistic, which will allow comparison across different levels for number of clusters found within a classification. This adjustment permits the user to compare several different classifications with respect to classification agreement, while correcting for the contribution of chance to any observed agreement.

Hierarchical Cluster Analysis Using Intraclass Correlations: A Mixture Model Study.

Sixteen hierarchical clustering algorithms were compared on their ability to resolve 20 multivariate normal mixtures (Blashfield, 1976) and 12 multivariate gamma mixtures (Mojena, 1977). The 16 algorithms represented a 4 x 4 (amalgamation rule x similarity measure) design. The amalgamation rules were single, complete, average, and centroid linkage. The similarity measures were Euclidean distance, correlation, and the one-way and two-way intraclass correlations. Accuracy was calculated using both kappa as a function of coverage (Edelbrock, 1979) and Rand's statistic. Comparisons were also made with Ward's minimum variance technique. Conclusions based on kappa and Rand's statistic were identical. A subset of algorithms was found to be highly accurate in solving both types of mixtures. The accurate algorithms were average and centroid linkage using the one-way intraclass correlation and Ward's technique. This suggests that the one-way intraclass correlation may be useful in clustering applications aimed at identifying subtypes differing in profile shape, elevation, and scatter.