A Novel k'-Means Algorithm for Clustering Analysis

Cluster analysis involves the methodical categorization of data based on the degree of similarity within each group to group data with similar characteristics. This study focuses on classifying poverty data across Indonesian provinces. The methodologies employed include the Fuzzy C-Means (FCM) and Fuzzy Probabilistic C-Means (FPCM) algorithms. The FCM algorithm is a clustering approach where membership values determine the presence of each data point in a cluster. On the other hand, the FPCM algorithm builds upon FCM and Possibilistic C (PCM) algorithms by incorporating probabilistic considerations. This research compares the FCM and FPCM algorithms using local poverty data from Indonesia, specifically examining the Partition Entropy (PE) index value. It aims to identify the optimal number of clusters for provincial-level poverty data in Indonesia. The findings indicate that the FPCM algorithm outperforms the FCM algorithm in categorizing poverty in Indonesia, as evidenced by the PE validity index. Furthermore, the study identifies that the ideal number of clusters for the data is 2.

We report the use of a cluster analysis method based on a multivariate mixture model, known as model‐based clustering, for overcoming the limitations of hierarchical clustering and relocation clustering. Unlike traditional clustering methods in which clusters are formed on the basis of intercluster distances, model‐based clustering classifies observations on the basis of probability estimated from Gaussian mixture modeling, and its statistical basis allows for inference. Three examples are given in which we demonstrate that model‐based clustering gives much better performance for overlapping clusters, a more reliable determination of the number of clusters in data, and better identification of clustering in the presence of outliers than agglomerative hierarchical clustering or iterative relocation clustering using a K‐means criterion. We also show that Markov chain Monte Carlo simulation, as implemented via Gibbs sampling coupled with model‐based clustering, may be used to assess uncertainty of group memberships. Copyright © 2013 John Wiley & Sons, Ltd.

This paper presents a solution for building and implementing data processing models and experimentally evaluates new possibilities for improving ensemble methods based on multilevel data processing models. This study proposes a model to reduce the cost of retraining models when transforming data properties. The research objective is to improve the quality indicators of machine learning models when solving classification problems. The novelty is a method that uses a multilevel architecture of data processing models to determine the current data properties in segments at different levels and assign algorithms with the best quality indicators. This method differs from the known ones by using several model levels that analyze data properties and assign the best models to individual segments of data and training. The improvement consists of using unsupervised clustering of data samples. The resulting clusters are separate subsamples for assigning the best machine-learning models and algorithms. Experimental values of quality indicators for different classifiers on the whole sample and different segments were obtained. The findings show that unsupervised clustering using multilevel models can significantly improve the quality indicators of “weak” classifiers. The quality indicators of individual classifiers improve when the number of data clusters is increased to a certain threshold. The results obtained are applicable to classification when developing models and machine learning methods. The proposed method improved the classification quality indicators by 2–9% due to segmentation and the assignment of models with the best quality indicators in individual segments. Doi: 10.28991/ESJ-2024-08-01-025 Full Text: PDF

Clustering process can make the process of grouping data so that the data in the same cluster have high similarity with the data in the same cluster. One of the clustering algorithm that is widely used is the K-Means because it has advantages such as simple, efficient, easy to understand and easy to apply. Grouping paragraph dealing with similar themes will allow users to find a theme in the Qur'an. This study aims to produce an information system that can perform grouping Quran with K-Means method. This research was conducted with a pre-processing stage process for text data, weighting by TFIDF, grouping data with K-Means clustering, labeling data for keywords. The resulting system is able to display a verse in groups associated with the keyword. The test results by using the index on the silhouette of Surah Al Fatihah generate positive value of 0.336 which means that the data in the right group, while the frequency of keywords versus the amount of data to produce a percentage of 53%, which means the keyword represents half of the data in the cluster. Tests also showed that the test results silhouette will be directly proportional to the number of clusters and inversely proportional to the number of data dimensions. To increase the value of testing required centroid method for early elections, the reduction of data dimensions and methods of measurement of distance and similarity.

Typically clustering algorithms provide clustering solutions with prespecified number of clusters. The lack of a priori knowledge on the true number of underlying clusters in the dataset makes it important to have a metric to compare the clustering solutions with different number of clusters. This article quantifies a notion of persistence of clustering solutions that enables comparing solutions with different number of clusters. The persistence relates to the range of dataresolution scales over which a clustering solution persists; it is quantified in terms of the maximum over two-norms of all the associated cluster-covariance matrices. Thus we associate a persistence value for each element in a set of clustering solutions with different number of clusters. We show that the datasets where natural clusters are a priori known, the clustering solutions that identify the natural clusters are most persistent - in this way, this notion can be used to identify solutions with true number of clusters. Detailed experiments on a variety of standard and synthetic datasets demonstrate that the proposed persistence-based indicator outperforms the existing approaches, such as, gap-statistic method, X-means, Gmeans, PG-means, dip-means algorithms and informationtheoretic method, in accurately identifying the clustering solutions with true number of clusters. Interestingly, our method can be explained in terms of the phase-transition phenomenon in the deterministic annealing algorithm, where the number of distinct cluster centers changes (bifurcates) with respect to an annealing parameter.

A hierarchical Gamma Mixture Model-based method for estimating the number of clusters in complex data

A seed-growing algorithm was proposed in the literature [1] to accurately determine the number of clusters in any arbitrary dataset with reasonably separated clusters and accurately classify the data points into these clusters. Island formation and data bridging were demonstrated and discussed as situations under which the algorithm performs poorly although extremely well otherwise. In this paper, singleton isolation as a pre-processing step in combination with determining and eliminating extremely small-sized clusters during post-processing is proposed as an enhancement to the algorithm. With this enhancement, it is demonstrated that the seed-growing algorithm performs extremely well even in situations where it...

Outlier detection is a part of data analytics that helps users to find discrepancies in working machines by applying outlier detection algorithm on the captured data for every fixed interval. An outlier is a data point that exhibits different properties from other points due to some external or internal forces. These outliers can be detected by clustering the data points. To detect outliers, optimal clustering of data points is important. The problem that arises quite frequently in statistics is identification of groups or clusters of data within a population or sample. The most widely used procedure to identify clusters in a set of observations is k-means using Euclidean distance. Euclidean distance is not so efficient for finding anomaly in multivariate space. This chapter uses k-means algorithm with Mahalanobis distance metric to capture the variance structure of the clusters followed by the application of extreme value analysis (EVA) algorithm to detect the outliers for detecting rare items, events, or observations that raise suspicions from the majority of the data.

This paper purposes a K-means clustering algorithm based on improved filtering process. Thealgorithm improves the filtering process,The two minimum sample points are reasonable initial clustering centers. It makes the probability summary of data in a cluster as large as possible, and the probability summary of data in different clusters as small as possible. Experimental results show that the proposed algorithm can select the proper initial clustering center, and it is more compact and robust than thetraditional K-means clustering algorithm.

One of the most challenging problems in data clustering is to determine the number of clusters. This study intends to propose an improved differential evolution algorithm which integrates automatic clustering based differential evolution (ACDE) algorithm and k-means (ACDE-k-means) algorithm. It requires no prior knowledge about number of clusters. k-means algorithm is employed to tune cluster centroids in order to improve the performance of DE algorithm. To validate the performance of the proposed algorithm, two well-known data sets, Iris and Wine, are employed. The computational results indicate that the proposed ACDE-k-means algorithm is superior to classical DE algorithm.

In view of the considerable applications of data clustering techniques in various fields, such as engineering, artificial intelligence, machine learning, clinical medicine, biology, ecology, disease diagnosis, and business marketing, many data clustering algorithms and methods have been developed to deal with complicated data. These techniques include supervised learning methods and unsupervised learning methods such as density-based clustering, K-means clustering, and K-nearest neighbor clustering. This book reviews recently developed data clustering techniques and algorithms and discusses the development of data clustering, including measures of similarity or dissimilarity for data clustering, data clustering algorithms, assessment of clustering algorithms, and data clustering methods recently developed for insurance, psychology, pattern recognition, and survey data.

The retail business is growing very rapidly with increasing business competition. The application of information technology is one strategy for understanding consumer product purchasing patterns and grouping sales products. This research aims to analyze and compare the K-Means and K-Medoids Clustering techniques for retail data based on the Davies Bouldin Index value and computing time. K-Means is an algorithm that divides data into k clusters based on centroids, while K-Medoids Clustering uses objects with medoids representing clusters as centroid centers. Clustering in both methods produces an optimal number of clusters of 3 clusters. The results of this research show that K-Means produced 358 data in Cluster 1, 292 data in Cluster 2, and 367 data in Cluster 3 with a DBI of 0.7160. Meanwhile, K-Medoids produced 295 data in Cluster 1, 360 data in Cluster 2, and 362 data in Cluster 3 with a DBI of 0.7153. In addition, this study calculated the average computation from 5 experiments, namely K-Means with an average time of 0.024278/s and K-Medoids of 0.05719/s. Based on the lower DBI, K-Medoids have better results in clustering, but the K-Means method is better in terms of computational efficiency. It is hoped that the results of this research will provide valuable insights for retail business people in analyzing sales data.

Data clustering is an important technique for data visualization and statistical data analysis. Using data clustering technique for geo-located data analysis and visualization has been shown to be useful in many practical domains. Although there are numerous studies for data clustering algorithms, the implementations and applications based on these algorithms are rare and inadequate, especially for web-based data visualization services. In this research, a new web-based interactive data clustering prototype is proposed for geo-located data visualization. The necessary web-based infrastructure for geo-located data analysis and visualization is designed and implemented at first. And then the new interactive data clustering prototype using multi-dimensional K-Means algorithm is implemented on the existing infrastructure. In order to assess whether the new prototype can contribute meaningfully to architectural design and urban studies, qualified users with urban study or architectural backgrounds are invited to use the prototype and then make their comments and evaluations. To make it clear how this new prototype might apply in real world settings, an application scenario in which the user might interact with the prototype is provided and analyzed.

The unsupervised clustering analysis of data from temporal or dose-response experiments is one of the most important and challenging tasks of microarray data anlysis. Here we present an extension of CAGED (Cluster Analysis of Gene Expression Dynamics, one of the most commonly used programs) to identify similar gene expression patterns measured in either short time-course or dose-response microarray experiments. Compared to the initial version of CAGED, in which gene expression temporal profiles are modeled by autoregressive equations, this new method uses polynomial models to incorporate time/dosage information into the model, and objective priors to include information about background noise in gene expression data. In its current formulation, CAGED results may change according to the parametrization. In this new formulation, we make the results invariant to reparametrization by using proper prior distributions on the model parameters. We compare the results obtained by our approach with those generated by STEM to show that our method can identify the correct number of clusters and allocate gene expression profiles to the correct clusters in simulated data, and produce more meaningful Gene Ontology enriched clusters in data from real microarray experiments.KeywordsGene Expression DataMicroarray ExperimentPolynomial ModelEase ScoreNatural Logarithmic ScaleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Clustering of big data has received much attention recently. In this paper, we present a new clusiVAT algorithm and compare it with four other popular data clustering algorithms. Three of the four comparison methods are based on the well known, classical batch k -means model. Specifically, we use k -means, single pass k -means, online k -means, and clustering using representatives (CURE) for numerical comparisons. clusiVAT is based on sampling the data, imaging the reordered distance matrix to estimate the number of clusters in the data visually, clustering the samples using a relative of single linkage (SL), and then noniteratively extending the labels to the rest of the data-set using the nearest prototype rule. Previous work has established that clusiVAT produces true SL clusters in compact-separated data. We have performed experiments to show that k -means and its modified algorithms suffer from initialization issues that cause many failures. On the other hand, clusiVAT needs no initialization, and almost always finds partitions that accurately match ground truth labels in labeled data. CURE also finds SL type partitions but is much slower than the other four algorithms. In our experiments, clusiVAT proves to be the fastest and most accurate of the five algorithms; e.g., it recovers 97% of the ground truth labels in the real world KDD-99 cup data (4 292 637 samples in 41 dimensions) in 76 s.