Dunn Index Research Articles

Performance Analysis of Hard and Soft Clustering Approaches For Gene Expression Data

Mining gene expression data is growing rapidly to predict gene expression patterns and assist clinicians in early diagnosis of tumor formation. Clustering gene expression data is the most important phase, helps in finding group of genes that are highly expressed and suppressed. This paper analyses the performance of most representative hard and soft off-line clustering algorithms: K-Means, Fuzzy C-Means, Self Organizing Maps (SOM) based clustering and Genetic Algorithm (GA) based clustering for brain tumor gene expression dataset. Clusters produced by the clustering algorithms are the indications of the cellular processes. Clustering results are evaluated using clustering indices such as Xie-Beni index (XB), Davies-Bouldin index (DB), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE) and Dunn's Index (DI) along with the time taken to find the compactness and separation of clusters. Experimental results prove soft clustering approaches works well to predict clusters of highly expressed and suppressed genes.

An optimal rough fuzzy clustering algorithm using particle swarm optimisation

Rough fuzzy hybrid models are widely used for handling uncertain and vague data and are very efficient in handling real life applications. Particle swarm optimisation (PSO) has been found to be a useful tool to optimise and find the best out of a set of solutions. In this paper, we propose a computational algorithm by embedding PSO in rough fuzzy hybrid clustering, which forms overlapping clusters with optimised partition. The proposed algorithm uses rough fuzzy C-means to formulate fuzzy lower and fuzzy boundary region of the clusters based on membership of objects with respect to their prototypes. This method has been applied to a swarm of clusters to get the best partitions at local and global levels qualified by Davies Bouldin (DB) and Dunn (D) indexes as fitness measures. This algorithm generates clusters dynamically and its superiority over other existing clustering techniques is established experimentally by taking several real world datasets.

Self-Optimal Clustering Technique Using Optimized Threshold Function

This paper presents a self-optimal clustering (SOC) technique which is an advanced version of improved mountain clustering (IMC) technique. The proposed clustering technique is equipped with major changes and modifications in its previous versions of algorithm. SOC is compared with some of the widely used clustering techniques such as K-means, fuzzy C-means, Expectation and Maximization, and K-medoid. Also, the comparison of the proposed technique is shown with IMC and its last updated version. The quantitative and qualitative performances of all these well-known clustering techniques are presented and compared with the aid of case studies and examples on various benchmarked validation indices. SOC has been evaluated via cluster compactness within itself and separation with other clusters. The optimizing factor in the threshold function is computed via interpolation and found to be effective in forming better quality clusters as verified by visual assessment and various standard validation indices like the global silhouette index, partition index, separation index, and Dunn index.

Assessment and application of clustering techniques to atmospheric particle number size distribution for the purpose of source apportionment

Abstract. Long-term measurements of particle number size distribution (PNSD) produce a very large number of observations and their analysis requires an efficient approach in order to produce results in the least possible time and with maximum accuracy. Clustering techniques are a family of sophisticated methods that have been recently employed to analyse PNSD data; however, very little information is available comparing the performance of different clustering techniques on PNSD data. This study aims to apply several clustering techniques (i.e. K means, PAM, CLARA and SOM) to PNSD data, in order to identify and apply the optimum technique to PNSD data measured at 25 sites across Brisbane, Australia. A new method, based on the Generalised Additive Model (GAM) with a basis of penalised B-splines, was proposed to parameterise the PNSD data and the temporal weight of each cluster was also estimated using the GAM. In addition, each cluster was associated with its possible source based on the results of this parameterisation, together with the characteristics of each cluster. The performances of four clustering techniques were compared using the Dunn index and Silhouette width validation values and the K means technique was found to have the highest performance, with five clusters being the optimum. Therefore, five clusters were found within the data using the K means technique. The diurnal occurrence of each cluster was used together with other air quality parameters, temporal trends and the physical properties of each cluster, in order to attribute each cluster to its source and origin. The five clusters were attributed to three major sources and origins, including regional background particles, photochemically induced nucleated particles and vehicle generated particles. Overall, clustering was found to be an effective technique for attributing each particle size spectrum to its source and the GAM was suitable to parameterise the PNSD data. These two techniques can help researchers immensely in analysing PNSD data for characterisation and source apportionment purposes.

Optimal Feature Selection from VMware ESXi 5.1 Feature Set

A study of VMware ESXi 5.1 server has been carried out to find the optimal set of parameters which suggest usage of different resources of the server. Feature selection algorithms have been used to extract the optimum set of parameters of the data obtained from VMware ESXi 5.1 server using esxtop command. Multiple virtual machines (VMs) are running in the mentioned server. K-means algorithm is used for clustering the VMs. The goodness of each cluster is determined by Davies Bouldin index and Dunn index respectively. The best cluster is further identified by the determined indices. The features of the best cluster are considered into a set of optimal parameters.

Optimal Feature Selection from VMware ESXi 5.1 Feature Set

A study of VMware ESXi 5.1 server has been carried out to find the optimal set of parameters which suggest usage of different resources of the server. Feature selection algorithms have been used to extract the optimum set of parameters of the data obtained from VMware ESXi 5.1 server using esxtop command. Multiple virtual machines (VMs) are running in the mentioned server. K-means algorithm is used for clustering the VMs. The goodness of each cluster is determined by Davies Bouldin index and Dunn index respectively. The best cluster is further identified by the determined indices. The features of the best cluster are considered into a set of optimal parameters.

Intensity drift removal in LC/MS metabolomics by common variance compensation

Liquid chromatography coupled to mass spectrometry (LC/MS) has become widely used in Metabolomics. Several artefacts have been identified during the acquisition step in large LC/MS metabolomics experiments, including ion suppression, carryover or changes in the sensitivity and intensity. Several sources have been pointed out as responsible for these effects. In this context, the drift effects of the peak intensity is one of the most frequent and may even constitute the main source of variance in the data, resulting in misleading statistical results when the samples are analysed. In this article, we propose the introduction of a methodology based on a common variance analysis before the data normalization to address this issue. This methodology was tested and compared with four other methods by calculating the Dunn and Silhouette indices of the quality control classes. The results showed that our proposed methodology performed better than any of the other four methods. As far as we know, this is the first time that this kind of approach has been applied in the metabolomics context. The source code of the methods is available as the R package intCor at http://b2slab.upc.edu/software-and-downloads/intensity-drift-correction/. Supplementary data are available at Bioinformatics online.

A novel utility-based model for identifying the customer value in online shopping

This study focuses on identifying customer's utility in online shopping. The utility is defined as the level of customer satisfaction in the online shopping experience. Our study is consisted of three phases: In the first phase, customers are segmented by K-means algorithm according to some demographic and preference properties. The optimal number of cluster is determined by DUNN index. In the second phase, one-dimensional utility functions are identified according to each significant factor in online context. By testing the utility independency, the multiplicative utility functions are used for identifying the global customer's utility. In the third phase, a novel customer value model is developed with utility usage. The proposed RFMU model can identify customer value better than RFM model and can resolve the main drawback of RFM model in predicting the value of new customers. This model is tested in one electronic retailer that provides flower and plant products and services.

Spatial Data Clustering and Zonation of Earthquake Building Damage Hazard Area

Research conducted with the aim to develop spatial data cluster and analyse the characteristics of each cluster of data in order to develop spatial zonation of building damage hazard caused by the earthquake in the city of Banda Aceh. The data used consists of the data peak ground acceleration (PGA), lithology and topographic zone data with the four phases of the study consisted of data normalization with min-max method, determination of optimum data group with the connectivity index, Dunn index and the Silhouette index, clustering of data with the k-Means algorithm and the data interpolation using kriging algorithm to construct the zonation of hazard area. The optimum numbers of clusters used in these researches are two, with the first 170 data largely concentrated at a distance of less than 0.1 to 0.5 from the cluster centre and the second 55 others data concentrated at a distance of 0.3 - 0.5 from the cluster centre. Banda Aceh and surrounding areas can be spatially divided into two classes of potential building damage caused by the earthquake with high hazard class building damage are generally located near the coastline.

Quality Assessment on Satellite Images based on Internal Criterion Techniques

Segmentation of digital image plays a major role in computer visualization. It is used to extract meaningful objects that exist on the images. Region based clustering is done to extract objects based on the colors present in the satellite images. The principle of clustering is to identify the similar domains from a huge data set to produce an accurate representation of the image. In this paper, k-means, fuzzy c means and kernel fuzzy c means clustering algorithms are used to partition an image data set into number clusters. The images are clustered into four and six categories for which the qualities of the images are compared through the internal criterion techniques Davies–Bouldin index and Dunn index. For this paper, experiment is carried out with more than 100 satellite images. Finally the PASCO Satellite Ortho (PSO) satellite image is selected, which covers the areas around Mt. Kaimondake in Kagoshima, Japan. The experimental results reveal that the quality of the clustered partitions based on the internal criterion conclude, kernel fuzzy c means clustering algorithm performs better than fuzzy c means and k-means clustering methods.

Comparison of clustering algorithms on generalized propensity score in observational studies: a simulation study

In observational studies, unbalanced observed covariates between treatment groups often cause biased inferences on the estimation of treatment effects. Recently, generalized propensity score (GPS) has been proposed to overcome this problem; however, a practical technique to apply the GPS is lacking. This study demonstrates how clustering algorithms can be used to group similar subjects based on transformed GPS. We compare four popular clustering algorithms: k-means clustering (KMC), model-based clustering, fuzzy c-means clustering and partitioning around medoids based on the following three criteria: average dissimilarity between subjects within clusters, average Dunn index and average silhouette width under four various covariate scenarios. Simulation studies show that the KMC algorithm has overall better performance compared with the other three clustering algorithms. Therefore, we recommend using the KMC algorithm to group similar subjects based on the transformed GPS.

A Comparative Study of Color Image Segmentation Using Hard, Fuzzy,Rough Set Based Clustering Techniques

Image segmentation is the process of subdividing an image into its constituent parts and extracting these parts of interest, which are the objects. Colour image segmentation emerges as a new area of research. It can solve many contemporary problems in medical imaging, mining and mineral imaging, bioinformatics, and material sciences. Naturally, color image segmentation demands well defined borders of different objects in an image. So, there is a fundamental demand of accuracy. The segmented regions or components should not be further away from the true object than one or a few pixels. So, there is a need for improved image segmentation technique that can segment different components precisely. Image data may have corrupted values due to the usual limitations or artifacts of imaging devices. Noisy data, data sparsity, and high dimensionality of data create difficulties in image pixel clustering. As a result, image pixel clustering becomes a harder problem than other form of data. Taking into account all the above considerations we propose an unsupervised image segmentation method using Rough-Fuzzy C-Mean a hybrid model for segmenting RGB image by reducing cluster centers using rough sets and Fuzzy C-Means Method, and also compare the effectiveness of the clustering methods such as Hard C Means (HCM), Fuzzy C Means (FCM), Fuzzy K Means (FKM), Rough C Means (RCM) with cluster validity index such as DB Index, XB Index and Dunn Index. A good clustering procedure should make the value of DB index as low as possible, for Dunn Index high value, and for XB Index low value.

A proposed IPC-based clustering method for exploiting expert knowledge and its application to strategic planning

In order to exploit the professional knowledge of the patent office examiners (implied in the IPC assignment) in the clustering process, a modified method (IPC-based clustering) has been proposed and applied to strategic planning. The performance of the proposed method was evaluated by comparison with two existing methods: K-Means and TwoStep of SPSS Clementine using the DB index and Dunn index. Afterwards, the IPC-based clustering (accompanied by link analysis) was applied to a practical domain (strategic planning) using the patent data of thin-film solar cell, so as to understand the possibility of implementing it in the management areas. According to the experimental results, the technical topics have been identified, and suggested strategies for companies have been generated for assisting the decision-making of top management. Finally, in future work the proposed method will be employed to other kinds of patent data to test its performance and applied to other practical domains to examine its feasibility in different management areas.

Mining Spatio-Temporal Data of Fatal Accident

accidents are an important concern of today's governments and societies, due to the high cost of human and economical resources involved. Data mining has been proven able to significantly help in improving traffic safety. Among several data mining tasks, clustering technique is mostly applied on spatio-temporal data, especially for the traffic data. A number of traffic related works proposed different clustering techniques for mining the spatio-temporal of traffic accident. However, some difficulties appeared when analyzing these datasets, such as the size of data, the lack of statistical evaluation methods, and interpreting the valuable patterns. With regard to solving this problem, this paper proposes a clustering approach for mining spatio-temporal data of fatal accident using local triangular kernel clustering (LTKC) algorithm. LTKC is kernel-density-based clustering algorithm that has the ability to determine the number of clusters automatically. We also propose three visualization techniques for use to interpret and present the optimal clustering result in an easy-understanding form. From the experimental results, LTKC approach was found to be able to discover responsible clusters within fatal accident data, which had proven by silhouette and Dunn index values close to 1. In addition, using visual techniques, we can state that the clustering results were well-separated and compact clusters.

On the Application of Clustering Techniques for Office Buildings' Energy and Thermal Comfort Classification

The aim of this paper is to develop and propose an integrated classification method for the determination of office buildings' energy and thermal comfort rating classes. The applications of five clustering techniques: Hierarchical, K-Means, Gaussian Mixture Models, Fuzzy, and Neural algorithms to a large building dataset are tested in order to investigate the appropriate method for establishing energy and thermal comfort classifications. For the clustering results testing, three internal validity indices: the Silhouette, the Davies Bouldin, and the Dunn Index have been applied, in order to select the appropriate number of clusters and the most efficient algorithm for each case. The proposed classification approach is also evaluated through comparisons with the methodologies that are recommended by the European standards. The classification results are used for a parametric study of common buildings' characteristics in each rating class, in order to provide with a tool for adopting improvement recommendations for buildings' energy efficiency.

강수지역 구분을 위한 최적 자료 전처리 기법 분석

본 연구에서는 우리나라 강수지역 구분을 위한 군집해석시 최적 자료 전처리 기법에 대하여 파악하고자 하였다. 이를 위하여 전국 기상청 관할의 75개 관측소의 지형 및 기상자료를 활용하였다. 적용된 자료 전처리 기법은 4가지로 일반 정규화 방법, 수정 정규화 방법, 표준화 방법 및 요인분석이다. 전처리된 자료를 K-means 군집분석을 통하여 군집을 구분한 후 유효성 측도인 Dunn 지수 및 Silhouette 지수를 통하여 효율성을 분석하였다. 군집수를 3개에서 9개까지 1개씩 늘려가며 분석한 결과 모든 경우에서 요인분석을 통한 자료가 최적의 효율성을 나타내었으나, 최적 군집개수의 산정에는 다소 부족한 것으로 나타났다. In this study, the data preprocessing methods were analyzed to obtain the optimal clustering solution in South Korea. The geographic data and weather data in 75 stations of Korea Meteorological Administration are applied. The applied data preprocessing methods are general normalization, modified normalization, standardization and factor analysis. After the clustering analysis were conducted by K-mean method with preprocessing data, the efficiency of data preprocessing methods are estimated using the clustering index, such as Dunn index and Silhouette index. The clustering analysis are carried out as the cluster number changes from 3 to 9. Among the data preprocessing methods, the data by factor analysis shows the best efficiency for clustering analysis. However, it is not enough to find the optimal cluster number.

Validation of Clustering Techniques for Student Grouping in Intelligent E-learning Systems

An intelligent e-learning system should be enhanced with personalization features that enable it to be tailored to different students' needs. The individual requirements of learners may depend on their characteristic traits, such as dominant learning styles. Finding groups of students with similar preferences can help when systems are being adjusted for individual requirements. The performance of personalized educational systems is dependant upon the number and quality of student clusters obtained. In this chapter the application of clustering techniques for grouping students according to their learning style preferences is considered. Such groups are evaluated by disparate validation criteria and the usage of different validation techniques is discussed. Experiments were conducted for different sets of real and artificially generated data on students' learning styles and the indices: Dunn's Index, Davies-Bouldin Index, SD Validity Index as well as the S_Dbw Validity Index are compared. From the experiment results some indications concerning the best validating criteria, as well as optimal clustering schema, are presented.

A Density Based Dynamic Data Clustering Algorithm based on Incremental Dataset

Problem statement: Clustering and visualizing high-dimensional dynamic data is a challenging problem. Most of the existing clustering algorithms are based on the static statistical relationship among data. Dynamic clustering is a mechanism to adopt and discover clusters in real time environments. There are many applications such as incremental data mining in data warehousing applications, sensor network, which relies on dynamic data clustering algorithms. Approach: In this work, we present a density based dynamic data clustering algorithm for clustering incremental dataset and compare its performance with full run of normal DBSCAN, Chameleon on the dynamic dataset. Most of the clustering algorithms perform well and will give ideal performance with good accuracy measured with clustering accuracy, which is calculated using the original class labels and the calculated class labels. However, if we measure the performance with a cluster validation metric, then it will give another kind of result. Results: This study addresses the problems of clustering a dynamic dataset in which the data set is increasing in size over time by adding more and more data. So to evaluate the performance of the algorithms, we used Generalized Dunn Index (GDI), Davies-Bouldin index (DB) as the cluster validation metric and as well as time taken for clustering. Conclusion: In this study, we have successfully implemented and evaluated the proposed density based dynamic clustering algorithm. The performance of the algorithm was compared with Chameleon and DBSCAN clustering algorithms. The proposed algorithm performed significantly well in terms of clustering accuracy as well as speed.

A Comparison Study of Validity Indices on Swarm-Intelligence-Based Clustering

Swarm intelligence has emerged as a worthwhile class of clustering methods due to its convenient implementation, parallel capability, ability to avoid local minima, and other advantages. In such applications, clustering validity indices usually operate as fitness functions to evaluate the qualities of the obtained clusters. However, as the validity indices are usually data dependent and are designed to address certain types of data, the selection of different indices as the fitness functions may critically affect cluster quality. Here, we compare the performances of eight well-known and widely used clustering validity indices, namely, the Caliński-Harabasz index, the CS index, the Davies-Bouldin index, the Dunn index with two of its generalized versions, the I index, and the silhouette statistic index, on both synthetic and real data sets in the framework of differential-evolution-particle-swarm-optimization (DEPSO)-based clustering. DEPSO is a hybrid evolutionary algorithm of the stochastic optimization approach (differential evolution) and the swarm intelligence method (particle swarm optimization) that further increases the search capability and achieves higher flexibility in exploring the problem space. According to the experimental results, we find that the silhouette statistic index stands out in most of the data sets that we examined. Meanwhile, we suggest that users reach their conclusions not just based on only one index, but after considering the results of several indices to achieve reliable clustering structures.

효모 마이크로어레이 유전자 발현 데이터에 대한 유전자 선별 및 군집분석

마이크로어레이 유전자 발현 데이터인 yeast cdc15에 대해 시계열 데이터의 특성을 반영한 푸리에 계수를 이용한 검정통계량과 FDR 다중비교법을 이용하여 차별화된 유전자를 선별한 후 선별된 유전자들에 대해 모형기반 군집방법, K-평균법, PAM, SOM, 계층적 Ward 군집방법과 Fuzzy 군집방법을 실시하였다. 군집방법에 따른 특성을 알아보고 군집화 결과와 내부유효성 측도로 연결성 측도, Dunn 지수와 실루엣 값을 살펴본다. 또한 GO분석을 통한 생물학적 의미도 파악해본다. We accomplish clustering analyses for yeast cell cycle microarray expression data. To reflect the characteristics of a time-course data, we screen the genes using the test statistics with Fourier coefficients applying a FDR procedure. We compare the results done by model-based clustering, K-means, PAM, SOM, hierarchical Ward method and Fuzzy method with the yeast data. As the validity measure for clustering results, connectivity, Dunn index and silhouette values are computed and compared. A biological interpretation with GO analysis is also included.