Number Of Clusters In Data Set Research Articles

DEA-based internal validity index for clustering

Internal validity indices are crucial in evaluating the quality of clustering results, serving as valuable tools for comparing various clustering algorithms and determining the optimal number of clusters for datasets. Most existing internal validity indices use the worst-case scenario to represent the overall validity. Moreover, some indices assign equal weights to distances among different clusters, even when these distances might have varying degrees of influence on the overall validity. Data envelopment analysis (DEA) is an effective technique for evaluating the performance of decision-making units through the computation of the ratio of the weighted sum of outputs to the weighted sum of inputs. The weight assigned to each indicator signifies its degree of influence on efficiency. Furthermore, DEA can be viewed as a multiple-criteria evaluation methodology, wherein inputs and outputs are two sets of performance criteria. We propose a DEA-based internal validity index (DEAI) to evaluate the validity of the clustering results. In this approach, intra-cluster compactness and inter-cluster separation are employed for determining the input(s) and output(s). The DEAI is then applied to the artificial datasets and empirical examples. Experimental results illustrate that DEAI outperforms six classic internal validity indices in accurately identifying the optimal cluster across all 10 datasets.

IMI2: A fuzzy clustering validity index for multiple imbalanced clusters

The fuzzy c-means (FCM) clustering algorithm requires the pre-definition of the number of clusters. When used for imbalanced datasets, FCM tends to equalize the sizes of clusters and thus produces bad clustering results. Although clustering validity index (CVI) is commonly employed to determine the number of clusters, it is often ineffective for bad clustering results of FCM. To address this issue, we have previously proposed a fuzzy CVI, namely IMI, for imbalanced datasets. However, IMI encounters issues when the number of clusters exceeds three, as it tends to divide the majority clusters into multiple subclusters. In this paper, a novel CVI, IMI2, is proposed to enhance the performance of IMI. IMI2 adopts a two-step clustering algorithm that merges some clusters from the IMI result based on their separation values. This enhancement overcomes the limitations of IMI, rendering IMI2 an excellent CVI capable of accurately determining the number of clusters for datasets with multiple imbalanced clusters. The performance of IMI2 is evaluated using several synthetic and UCI datasets. The results demonstrate that IMI2 outperforms other methods in terms of its superior performance for multiple imbalanced clusters. IMI2 retains the good performance of IMI for datasets with two or three clusters, while significantly improving it for multiple imbalanced clusters.

Observations of intra-peatland variability using multiple spatially coincident remotely sensed data sources and machine learning

Peatlands are important sites of ecosystem services, particularly as soil carbon stores, and are recognised in many international climate strategies. However, drained peatlands, which have been modified for industrial extraction or agriculture, are responsible for carbon emission. Peatland restoration aims to return these degraded sites to a natural state. Multiple means of remotely monitoring the success of peat restoration are available, ranging from space-based satellite measurements (optical and radar) to airborne geophysical measurements (electro-magnetic and radiometric). This paper integrates multi-band, spatially coincident, remotely sensed data into a single framework, resulting in a comprehensive interpretation of intra-peatland variation of key restoration indicators. It uses a semi-automatic, data driven approach with unsupervised neural network machine learning clustering. A Multi-Cluster Average Standard Deviation metric is introduced which can determine the appropriate number of clusters for any dataset. The method was applied to a site in Ireland, representative of degraded peatlands, where optical satellite and airborne radiometric geophysical measurements were combined. The method was successful at determining the appropriate number of clusters for single and combined datasets, and the resulting cluster signatures provided visually compelling representations of the intra-peatland variation. This resulted in a comprehensive interpretation of intra-peatland variation of several key peatland restoration indicators, namely surface vegetation levels and soil moisture to ∼ 60 cm of the peat surface. The study provides a framework for high spatial and temporal resolution monitoring of peatland restoration using future drone-based platforms.

Investigation of the optimal number of clusters by the adaptive EM algorithm

This paper considers the investigation of the optimal number of clusters for datasets that are modeled as the Gaussian mixture. For that purpose, the adaptive method that is based on the modified Expectation Maximization (EM) algorithm is developed. The modification is conducted within the hidden variable of the standard EM algorithm. Assuming that data are multivariate normally distributed, where each component of the Gaussian mixture corresponds to one cluster, the modification is provided by utilizing the fact that the Mahalanobis distance of samples follows a Chi-square distribution. Besides, the quantity measure is constructed in order to determine number of clusters. The proposed method is presented in several numerical examples.

Kluster: An Efficient Scalable Procedure for Approximating the Number of Clusters in Unsupervised Learning

Abstract The majority of the clinical observation data stored in large-scale Electronic Health Record (EHR) research data networks are unlabeled. Unsupervised clustering can provide invaluable tools for studying patient sub-groups in these data. Many of the popular unsupervised clustering algorithms are dependent on identifying the number of clusters. Multiple statistical methods are available to approximate the number of clusters in a dataset. However, available methods are computationally inefficient when applied to large amounts of data. Scalable analytical procedures are needed to extract knowledge from large clinical datasets. Using both simulated, clinical, and public data, we developed and tested the kluster procedure for approximating the number of clusters in a large clinical dataset. The kluster procedure iteratively applies four statistical cluster number approximation methods to small subsets of data that were drawn randomly with replacements and recommends the most frequent and mean number of clusters resulted from the iterations as the potential optimum number of clusters. Our results showed that the kluster's most frequent product that iteratively applies a model-based clustering strategy using Bayesian Information Criterion (BIC) to samples of 200–500 data points, through 100 iterations, offers a reliable and scalable solution for approximating the number of clusters in unsupervised clustering. We provide the kluster procedure as an R package.

Using the stability of objects to determine the number of clusters in datasets

We introduce a novel method for assessing the robustness of clusters found by partitioning algorithms. First, we show how the stability of individual objects can be estimated based on repeated runs of the K-means and K-medoids algorithms. The quality of the resulting clusterings, expressed by the popular Calinski–Harabasz, Silhouette, Dunn and Davies–Bouldin cluster validity indices, is taken into account when computing the stability estimates of individual objects. Second, we explain how to assess the stability of individual clusters of objects and sets of clusters that are found by partitioning algorithms. Finally, we present a new and effective stability-based algorithm that improves the ability of traditional partitioning methods to determine the number of clusters in datasets. We compare our algorithm to some well-known cluster identification techniques, including X-means, Pvclust, Adegenet, Prediction Strength and Nselectboot. Our experiments with synthetic and benchmark data demonstrate the effectiveness of the proposed algorithm in different practical situations. The R package ClusterStability has been developed to provide applied researchers with new stability estimation tools presented in this paper. It is freely distributed through the Comprehensive R Archive Network (CRAN) and available at: https://cran.r-project.org/web/packages/ClusterStability.

Histogram-based automatic segmentation of images

The segmentation process is defined by separating the objects as clustering in the images. The most used method in the segmentation is k-means clustering algorithm. k-means clustering algorithm needs the number of clusters, the initial central points of clusters as well as the image information. However, there is no preliminary information about the number of clusters in real-life problems. The parameters defined by the user in the segmentation algorithms affect the results of segmentation process. In this study, a general approach performing segmentation without requiring any parameters has been developed. The optimum cluster number has been obtained searching the histogram both vertically and horizontally and recording the local and global maximum values. The quite nearly values have been omitted, since the near local peaks are nearly the same objects. Segmentation processes have been performed with k-means clustering giving the possible centroids of the clusters and the optimum cluster number obtained from the histogram. Finally, thanks to histogram method, the number of clusters of k-means clustering has been automatically found for each image dataset. And also, the histogram-based finding of the number of clusters in datasets could be used prior to clustering algorithm for other signal or image-based datasets. These results have shown that the proposed hybrid method based on histogram and k-means clustering method has obtained very promising results in the image segmentation problems.

Fuzzy Rules for Ant Based Clustering Algorithm

This paper provides a new intelligent technique for semisupervised data clustering problem that combines the Ant System (AS) algorithm with the fuzzyc-means (FCM) clustering algorithm. Our proposed approach, called F-ASClass algorithm, is a distributed algorithm inspired by foraging behavior observed in ant colonyT. The ability of ants to find the shortest path forms the basis of our proposed approach. In the first step, several colonies of cooperating entities, called artificial ants, are used to find shortest paths in a complete graph that we called graph-data. The number of colonies used in F-ASClass is equal to the number of clusters in dataset. Hence, the partition matrix of dataset founded by artificial ants is given in the second step, to the fuzzyc-means technique in order to assign unclassified objects generated in the first step. The proposed approach is tested on artificial and real datasets, and its performance is compared with those ofK-means,K-medoid, and FCM algorithms. Experimental section shows that F-ASClass performs better according to the error rate classification, accuracy, and separation index.

Application of Density Based Clustering to Microarray Data Analysis

Application of Density Based Clustering to Microarray Data AnalysisIn just a few years, gene expression microarrays have rapidly become a standard experimental tool in the biological and medical research. Microarray experiments are being increasingly carried out to address the wide range of problems, including the cluster analysis. The estimation of the number of clusters in datasets is one of the main problems of clustering microarrays. As a supplement to the existing methods we suggest the use of a density based clustering technique DBSCAN that automatically defines the number of clusters. The DBSCAN and other existing methods were compared using the microarray data from two datasets used for diagnosis of leukemia and lung cancer.