Cluster Analysis Problem Research Articles

Clustering Analysis of Multivariate Data: A Weighted Spatial Ranks-Based Approach

Determining the right number of clusters without any prior information about their numbers is a core problem in cluster analysis. In this paper, we propose a nonparametric clustering method based on different weighted spatial rank (WSR) functions. The main idea behind WSR is to define a dissimilarity measure locally based on a localized version of multivariate ranks. We consider a nonparametric Gaussian kernel weights function. We compare the performance of the method with other standard techniques and assess its misclassification rate. The method is completely data-driven, robust against distributional assumptions, and accurate for the purpose of intuitive visualization and can be used both to determine the number of clusters and assign each observation to its cluster.

Fuzzy Cluster Analysis: Pseudometrics and Fuzzy Clusters

Introduction. Clustering problems arise in various spheres of human activity. In cases where there are no initial data sufficient for statistical analysis or information obtained from experts is used, fuzzy models are proposed that take into account different types of uncertainty and more argumentatively reflect real situations that model systems of different purposes. Particular attention is drawn to invariance in problems with different types of data measured in different scales according to the classification of S. Stevens. It is known that when solving cluster analysis problems using the transitive closure operation with respect to the equivalence that is obtained, such connections between objects as similarity and dissimilarity are changed. Therefore, it is necessary to take into account the problem of adequacy when developing models and algorithms for solving problems of fuzzy cluster analysis. The purpose of the paper is an analyzing the problem of adequacy of the results of fuzzy cluster analysis on the introduction of metrics and pseudometrics on fuzzy sets in the presence of several qualitative and quantitative characteristics of objects. Propose an approach that ensures the adequacy of pseudometrics, that is, provides invariance with respect to permissible transformations of the values of fuzzy features, and also ensures the division of objects into equivalence classes without distorting the distance between them. Results. Axiomatic definitions of a fuzzy cluster and a fuzzy α level cluster are proposed, which are introduced as fuzzy sets of elements similar to certain elements of a given set, if the condition is met: the dissimilarity ratio must be an invariant pseudometric. This condition is ensured by the use of the linguistic correlation coefficient when calculating fuzzy relations of similarity and dissimilarity. Based on the definition of a fuzzy cluster of α level and threshold conorm, the distance between fuzzy clusters of α level is determined. Conclusions. The proposed approach can be the basis for the development of algorithms for solving cluster analysis problems. This provides a meaningful interpretation of the obtained clusters, and the possibility of clarifying the results in further studies of their structure. Keywords: fuzzy set, conorm, metric, pseudometric, fuzzy similarity relation, fuzzy cluster.

Effectiveness Analysis of Stock KDJ Indicator Method based on K-means Clustering

The application of data mining technology expands various techniques in stock investment. Among them, cluster analysis is one of the common means to study stock technical indicators. There is a problem in the current cluster analysis of stock technical indicators -- the lack of validation of large-scale stock technical indicators data sets. Most of them are suitable for the comprehensive analysis of technical indicators of a single stock or multiple stocks. Aiming at this problem, this paper takes "the validity analysis of the large-scale stock KDJ index set method based on K-means clustering" as the theme. Firstly, the k-means clustering algorithm was used to construct a deep analysis model (KDJ-k-means) for the KDJ index set of the Shenzhen Index component data group. Secondly, the K, D and J index sets of 2697 constituent stocks of Shenzhen Composite Index are analyzed experimentally. Finally, the results of integrated data mining are obtained. The KDJ-k-means model is an optimization scheme based on the KDJ index set using clustering technology, which provides an intuitive and efficient visual application for deep analysis of large-scale stock data groups.

CPSO: Chaotic Particle Swarm Optimization for Cluster Analysis

(Background) To solve the cluster analysis better, we propose a new method based on the chaotic particle swarm optimization (CPSO) algorithm.
 (Methods) In order to enhance the performance in clustering, we propose a novel method based on CPSO. We first evaluate the clustering performance of this model using the Variance Ratio Criterion (VRC) as the evaluation metric. The effectiveness of the CPSO algorithm is compared with that of the traditional Particle Swarm Optimization (PSO) algorithm. The CPSO aims to improve the VRC value while avoiding local optimal solutions. The simulated dataset is set at three levels of overlapping: non-overlapping, partial overlapping, and severe overlapping. Finally, we compare CPSO with two other methods.
 (Results) By observing the comparative results, our proposed CPSO method performs outstandingly. In the conditions of non-overlapping, partial overlapping, and severe overlapping, our method has the best variance ratio criterion values of 1683.2, 620.5, and 275.6, respectively. The mean VRC values in these three cases are 1683.2, 617.8, and 222.6.
 (Conclusion) The CPSO performed better than other SOTA methods for cluster analysis problems. CPSO is effective for cluster analysis.

A New Density Peak Clustering Algorithm With Adaptive Clustering Center Based on Differential Privacy

A new density peak clustering (DPC) algorithm with adaptive clustering center based on differential privacy was proposed to solve the problems of poor adaptability of high-dimensional data, inability to automatically determine clustering centers, and privacy problems in clustering analysis. First, to solve the problem of poor adaptability of high-dimensional data, cosine distance was used to measure the similarity between high-dimensional datasets. Then, aiming at the subjective problem of clustering center selection, from the perspective of ranking graph, the weight <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(i-1)/i$ </tex-math></inline-formula> was introduced creatively, the slope trend of ranking graph was redefined to realize the adaptive clustering center. Finally, aiming at the privacy problem, the Laplacian noise of appropriate privacy budget was added to the core statistic (local density) of the algorithm to achieve the balance between privacy protection and algorithm effectiveness. Experimental results on both the synthetic and UCI datasets show that this algorithm can not only realize the automatic selection of clustering center, but also solve the privacy problem in clustering analysis, and improve the clustering evaluation index greatly, which proves the effectiveness of the algorithm.

On the extended Choquet-Sugeno-like operator

In this short paper, we introduce and discuss the extended Choquet-Sugeno-like operator. It generalizes most of modifications of the Choquet integral on a finite set known in the literature providing a partially positive answer to the question posed by H. Bustince et al. in 2021. It also includes unknown Choquet-like and Sugeno-like operators. The standard optimization problem in cluster analysis is formulated using multivariable extension of the new operator.

Image Forgery Detection via Forensic Similarity Graphs

In the article 'Exposing Fake Images with Forensic Similarity Graphs', O. Mayer and M. C. Stamm introduce a novel image forgery detection method. The proposed method is built on a graph-based representation of images, where image patches are represented as the vertices of the graph, and the edge weights are assigned in order to reflect the forensic similarity between the connected patches. In this representation, forged regions form highly connected subgraphs. Therefore, forgery detection and localization can be cast as a cluster analysis problem on the similarity graph. The authors present two graph clustering methods to detect and localize image forgeries. In this paper, we present briefly the method and offer an online executable version allowing everyone to test it on their own suspicious images. **This is an MLBriefs article, the source code has not been reviewed!**<br> **The original source code is [[available here|https://omayer.gitlab.io/forensicgraph/]] (last checked 2022/11/07).**

Cluster Analysis of the Expenditures for Environmental and Technological Innovations in Sustainable Development Policy Formation

The major task of the present work is to identify the main problems of cluster analysis on environmental and technological innovations in the formation of regional sustainable development policy, as well as modeling the expenditures for technological and environmental innovations. The number of innovative enterprises increases rapidly, and they are developing at a rapid pace. Measures to reduce the impact on the environment, such as improving technological equipment, recycling waste, implementing technologies aimed at preserving natural resources, creating new types of products with long service life and the possibility of recycling, employing advanced purification technologies, etc. will require in the vast majority of cases not only financial expenditures but the implementation of innovative solutions.&#x0D; The authors are intended to study out and optimize this work and improve the research framework.

АЛГОРИТМЫ АГЛОМЕРАТИВНОЙ КЛАСТЕРИЗАЦИИ ПРИМЕНИТЕЛЬНО К ЗАДАЧАМ АНАЛИЗА ЛИНГВИСТИЧЕСКОЙ ЭКСПЕРТНОЙ ИНФОРМАЦИИ

This article discusses and presents the main problems and principles of the data clusteringprocess, in particular, the principles and tasks of clustering text arrays of linguistic expert information.In the course of this work, the main difficulties arising in the design of such systems wereidentified, for example: the need for preprocessing data, reducing the size of the initial sample,etc. To effectively perform the presented tasks, the implemented solution must have an integratedapproach that takes into account the efficiency indicators of methods aimed at solving individualsubtasks, as well as the ability to provide high efficiency indicators for the implementation of eachstage of the clustering process. In the presented work, various groups of hierarchical clusteringalgorithms are considered, in particular, a subgroup of agglomerative clustering algorithms wasconsidered in relation to the problems of clustering linguistic expert information. In the describedwork, a formal statement of the text clustering problem is given, and the main group of implementedsolutions based on the principles of agglomerative clustering is determined: ROCK, CURE,CHAMELEON. A detailed review of each of the presented algorithms is carried out, and the mainadvantages and disadvantages of each of them are formulated. The advantage of this work can beconsidered the totality of the presented data on the algorithms, as well as the results of a comparative analysis, which make it possible to further assess the feasibility and potential probability ofusing these solutions from the presented group of agglomerative clustering algorithms. The noveltyof this work lies in the formation of an overview analysis of existing approaches in the field ofhierarchical clustering for solving the problems of cluster analysis of linguistic expert information,as well as the formation of the results of the comparative analysis of the considered algorithms.

CANet: An Unsupervised Deep Convolutional Neural Network for Efficient Cluster-Analysis-Based Multibaseline InSAR Phase Unwrapping

Multibaseline (MB) phase unwrapping (PU) is a vital processing procedure for MB synthetic aperture radar interferometry (InSAR) signal processing and can improve the traditional InSAR by changing the ill-posed problem to the well-posed problem. The existing research has shown that the MB PU problem can be successfully converted into an unsupervised cluster analysis problem. Using the high feature descriptiveness of the deep learning technique, an unsupervised deep convolutional neural network, referred to as CANet, is proposed to cluster all the pixels into different groups according to the input’s recognizable pattern of the ambiguity number of the MB interferometric phase. Subsequently, we extend our previous two-stage programming-based MB processing approach (TSPA) to processing MB PU on a sparse irregular network, which is established from the clustering result of CANet. Both theoretical analysis and experimental results show that the proposed method is an effective MB PU method, and its execution time is drastically lower than those of many classical MB PU methods.

Hybrid radial basis function DEA and its applications to regression, segmentation and cluster analysis problems

This paper uses a radial basis function (RBF) transformation of data envelopment analysis (DEA) data to perform RBF-DEA. It is shown that the RBF-DEA frontier identifies cases that have average efficiency scores in traditional DEA. The formal identification of average efficiency cases allows decision-makers to use these cases and related information for regression, segmentation and cluster analysis. Additionally, negative inputs and outputs can be used in RBF-DEA and unique ranking of fully efficient cases in traditional DEA can be achieved by further evaluating these fully efficient cases against the average RBF-DEA regression frontier. When compared to traditional cluster analysis, RBF-DEA cluster analysis offers unique advantages in that number of clusters do not need to be mentioned and cluster labels are identified by the RBF-DEA technique. Furthermore, unlike the traditional techniques, RBF-DEA cluster memberships are not sensitive to any initial random starting points.

An evolutionary many-objective approach to multiview clustering using feature and relational data

Many application domains involve the consideration of multiple data sources. Typically, each of these data views provides a different perspective of a given set of entities. Inspired by early work on multiview (supervised) learning, multiview algorithms for data clustering offer the opportunity to consider and integrate all this information in an unsupervised setting. In practice, some complex real-world problems may give rise to a handful or more data views, each with different reliability levels. However, existing algorithms are often limited to the consideration of two views only, or they assume that all the views have the same level of importance. Here, we describe the design of an evolutionary algorithm for the problem of multiview cluster analysis, exploiting recent advances in the field of evolutionary optimization to address settings with a larger number of views. The method is capable of considering views that are represented in the form of distinct feature sets, or distinct dissimilarity matrices, or a combination of the two. Our experimental results on standard (including real-world) benchmark datasets confirm that the adoption of a many-objective evolutionary algorithm addresses limitations of previous work, and can easily scale to settings with four or more data views. The final highlight of our paper is an illustration of the potential of the approach in an application to breast lesion classification.

Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis

Compared to the intuitionistic fuzzy sets, the Pythagorean fuzzy sets (PFSs) can provide the decision makers with more freedom to express their evaluation information. There exist some research results on the correlation coefficient between PFSs, but sometimes they fail to deal with the problems of disease diagnosis and cluster analysis. To tackle the drawbacks of the existing correlation coefficients between PFSs, some novel directional correlation coefficients are put forward to compute the relationship between two PFSs by taking four parameters of the PFSs into consideration, which are the membership degree, non-membership degree, strength of commitment, and direction of commitment. Afterwards, two practical examples are given to show the application of the proposed directional correlation coefficient in the disease diagnosis, and the application of the proposed weighted directional correlation coefficient in the cluster analysis. Finally, they are compared with the previous correlation coefficients that have been developed for PFSs.

A Novel Approach for Gaussian Mixture Model Clustering Based on Soft Computing Method

Determining the number of clusters in a data set is a significant and difficult problem in cluster analysis. In this study, a new model-based clustering approach is proposed for the estimation of the number of clusters. In the proposed method, the number of components in each variable is determined by using univariate Gaussian mixture models. The number of alternative cluster centres and mixture models was determined according to the number of components in heterogeneous variables. In this study, appropriate Gaussian mixture models were determined with the help of "mixture model soft computing method" for the first time. Vector arrays showing the number and addresses of clusters in appropriate Gaussian mixture models were created, and according to the parameter estimations of these models that fit the arrays, the best model was obtained through information criteria. The clustering success achieved with the proposed mixture model soft computing method was compared with the results of Gaussian mixture model clustering methods namely, mclust, clustvarsel, varselLCM, selvarMix and vscc model selection methods in R package. All respective methods analyse and determine the number of clustering for the data sets, synthetic-1, synthetic-2, Iris, and Landsat Satellite Image data sets, respectively and evaluate the correct classification rate. The results revealed that the proposed method shows better results for the determination of number of clustering as well as correct classification rate. The novelty of the study is that a new model-based dimension reduction method is proposed for the estimation of the number of clusters. A deterministic clustering approach is proposed for clustering and classification success on reduced data.

Unsupervised Clustering of Neighborhood Associations and Image Segmentation Applications

Irregular shape clustering is always a difficult problem in clustering analysis. In this paper, by analyzing the advantages and disadvantages of existing clustering analysis algorithms, a new neighborhood density correlation clustering (NDCC) algorithm for quickly discovering arbitrary shaped clusters. Because the density of the center region of any cluster sample dataset is greater than that of the edge region, the data points can be divided into core, edge, and noise data points, and then the density correlation of the core data points in their neighborhood can be used to form a cluster. Further more, by constructing an objective function and optimizing the parameters automatically, a locally optimal result that is close to the globally optimal solution can be obtained. This algorithm avoids the clustering errors caused by iso-density points between clusters. We compare this algorithm with other five clustering algorithms and verify it on two common remote sensing image datasets. The results show that it can cluster the same ground objects in remote sensing images into one class and distinguish different ground objects. NDCC has strong robustness to irregular scattering dataset and can solve the clustering problem of remote sensing image.

Variable Weighting in Fuzzy k-Means Clustering to Determine the Number of Clusters

One of the most significant problems in cluster analysis is to determine the number of clusters in unlabeled data, which is the input for most clustering algorithms. Some methods have been developed to address this problem. However, little attention has been paid on algorithms that are insensitive to the initialization of cluster centers and utilize variable weights to recover the number of clusters. To fill this gap, we extend the standard fuzzy $k$ k -means clustering algorithm. It can automatically determine the number of clusters by iteratively calculating the weights of all variables and the membership value of each object in all clusters. Two new steps are added to the fuzzy $k$ k -means clustering process. One of them is to introduce a penalty term to make the clustering process insensitive to the initial cluster centers. The other one is to utilize a formula for iterative updating of variable weights in each cluster based on the current partition of data. Experimental results on real-world and synthetic datasets have shown that the proposed algorithm effectively determined the correct number of clusters while initializing the different number of cluster centroids. We also tested the proposed algorithm on gene data to determine a subset of important genes.

Interpolating time series based on fuzzy cluster analysis problem

This study proposes the model for interpolating time series to use them to forecast effectively for future. This model is established based on the improved fuzzy clustering analysis problem, which is implemented by the Matlab procedure. The proposed model is illustrated by a data set and tested for many other datasets, especially for 3003 series in M3-Competition data. Comparing to the existing models, the proposed model always gives the best result. We also apply the proposed model in forecasting the salt peak for a coastal province of Vietnam. Examples and applications show the potential of the studied problem.

О геометрических подходах к решению некоторых задач кластеризации данных

Рассматривается геометрический подход к упорядочиванию данных при решении задач кластерного анализа. В ходе решения задачи упорядочивания данные интерпретируются как множество точек декартовой плоскости с введенной Евклидовой метрикой.

A Fuzzy Time Series Model Based on Improved Fuzzy Function and Cluster Analysis Problem

Based on the improvement in establishing the relations of data, this study proposes a new fuzzy time series model. In this model, the suitable number of fuzzy sets and their specific elements are determined automatically. In addition, using the percentage variations of series between consecutive periods of time, we build the fuzzy function. Incorporating all these improvements, we have a new fuzzy time series model that is better than many existing ones through the well-known data sets. The calculation of the proposed model can be performed conveniently and efficiently by a MATLAB procedure . The proposed model is also used in forecasting for an urgent problem in Vietnam. This application also shows the advantages of the proposed model and illustrates its effectiveness in practical application.

VNS-BASED ALGORITHMS FOR THE CENTROID-BASED CLUSTERING PROBLEM

The k-means algorithm with the corresponding problem formulation is one of the first methods that researchers use when solving a new automatic grouping (clus-tering) problem. Its improvement, modification and combination with other algorithms are described in the works of many researchers. In this research, we propose new al-gorithms of the Greedy Heuristic Method, which use an idea of the search in variable neighborhoods for solving the classical cluster analysis problem, and allows us to obtain a more accurate and stable result of solving in comparison with the known algorithms. Our computational experiments show that the new algorithms allow us to obtain re-sults with better values of the objective function value (sum of squared distances) in comparison with classical algorithms such as k-means, j-means and genetic algorithms on various practically important datasets. In addition, we present the first results for the GPU realization of the Greedy Heuristic Method.