Cluster Quality Index Research Articles

Coupled zoning and spatial heterogeneity of human activities and natural endowments based on self-organizing map and random forest: A case study of the agro-pastoral ecotone in Gansu, China

Regional zoning is an important way for humans to understand geographical space，but the existing research on regional zoning focuses on natural conditions, ignoring the interdependent characteristics of human and nature, and the driving mechanism of regional differentiation is not sufficiently explained. In this study, using algorithms such as self-organizing feature map, clustering quality index, structural similarity index measure (SSIM) and random forest, the human activity (HA)–natural endowment (NE) coupled zoning in the agro-pastoral ecotone in Gansu, China (AEGC), was conducted to explore the driving mechanism of regional differentiation. Results show the following: (1) The HA-NE coupled zoning has the best clustering effect when implementing the partitioning scheme with a classification number of 4. Accordingly, the AEGC can be divided into four regions with significant differences between HAs and NEs. (2) From the perspective of spatial distribution, HA–NE coupled zoning, climate zoning, geographic zoning, and vegetation zoning are similar, whereas HA zoning is different. The results of SSIM showed that HA–NE coupled zoning takes all types of factors into consideration (SSIM mean 0.708), and the zoning results are better than single type zonings. HAs have strong independence (SSIM mean 0.576), and geographic conditions are closely related to all other factors (SSIM mean 0.671). (3) Elevation is the most important driver of regional differentiation in the AEGC, with a contribution degree of 22.36%; other important drivers include land use intensity, precipitation, and normalized difference vegetation index, with contribution degree distributions of 17.38%, 16.34%, and 15.79%. Furthermore, the dominant factors of regional differentiation in each sub-region are different. This study emphasizes that regional characteristic factors and uneven spatial distribution factors are important drivers of regional differentiation, and land use intensity has become an important force influencing geographic space. Policy recommendations for zonal governance are made based on the inherent conditions of different regions. This study may provide a reference for scientific regional zoning and cognitive regional differentiation.

Combining Cluster Quality Index and Supervised Learning to Predict Students’ Academic Performance

Combining Cluster Quality Index and Supervised Learning to Predict Students’ Academic Performance

Water Quality Assessment on Physicochemical and Biological Parameters of Selected Lentic Ecosystem in Aboh Mbaise Local Government Area, Imo State, Nigeria

The aim of this study is to determine the suitability of the ponds in Aboh Mbaise Local Government Area, Imo State, Nigeria for domestic use. A cross-sectional study was carried out for the study. Composite sampling method was used, where three water samples were collected randomly from each station to ensure that the samples were representative of the entire station. Samples were collected during the rainy season, given that the ponds always dry up during the dry season. Physicochemical and microbial analyses were carried out on water samples of selected lentic aquatic ecosystems in randomly identified ponds in five communities of Aboh Mbaise. These ponds are used by the residents of these villages for various domestic and anthropogenic activities. Statistical analyses include: descriptive statistics, Analysis of Variance, Parallel coordinate plot, Pearson correlation, Agglomerative Hierarchical Clustering (AHC) and Water Quality Index (WQI) were carried out. Results indicate that pond water within the study area did not fall within the bracket of good water quality, as per the WQI range of 0 to 50, thereby affirming the poor quality of water. The WQI for the five ponds ranges from 1338.71 - 3322.81. There is a direct correlation between the presence of Total Bacterial Counts from Shigella and Salmonella counts and the presence of fecal contamination from both human and animal wastes. Given the poor quality of the pond water, it is unhealthy for the inhabitants in the study area to use pond water for food preparation and other household tasks, except if it is treated.

Identification of pre-synaptic density networks using [11C]UCB-J PET imaging and ICA in mice

BackgroundSynaptic vesicle glycoprotein 2A (SV2A) is a vesicle glycoprotein involved in neurotransmitter release. SV2A is located on the pre-synaptic terminals of neurons and visualized using the radioligand [11C]UCB-J and positron emission tomography (PET) imaging. Thus, SV2A PET imaging can provide a proxy for pre-synaptic density in health and disease. This study aims to apply independent component analysis (ICA) to SV2A PET data acquired in mice to identify pre-synaptic density networks (pSDNs), explore how ageing affects these pSDNs, and determine the impact of a neurological disorder on these networks. MethodsWe used [11C]UCB-J PET imaging data (n = 135) available at different ages (3, 7, 10, and 16 months) in wild-type (WT) C57BL/6J mice and in diseased mice (mouse model of Huntington's disease, HD) with reported synaptic deficits. First, ICA was performed on a healthy dataset after it was split into two equal-sized samples (n = 36 each) and the analysis was repeated 50 times in different partitions. We tested different model orders (8, 12, and 16) and identified the pSDNs. Next, we investigated the effect of age on the loading weights of the identified pSDNs. Additionally, the identified pSDNs were compared to those of diseased mice to assess the impact of disease on each pSDNs. ResultsModel order 12 resulted in the preferred choice to provide six reliable and reproducible independent components (ICs) as supported by the cluster-quality index (IQ) and regression coefficients (β) values. Temporal analysis showed age-related statistically significant changes on the loading weights in four ICs. ICA in an HD model revealed a statistically significant disease-related effect on the loading weights in several pSDNs in line with the progression of the disease. ConclusionThis study validated the use of ICA on SV2A PET data acquired with [11C]UCB-J for the identification of cerebral pre-synaptic density networks in mice in a rigorous and reproducible manner. Furthermore, we showed that different pSDNs change with age and are affected in a disease condition. These findings highlight the potential value of ICA in understanding pre-synaptic density networks in the mouse brain.

Comparison and application of SOFM, fuzzy c-means and k-means clustering algorithms for natural soil environment regionalization in China

Soil attributes and their environmental drivers exhibit different patterns in different geographical directions, along with distinct regional characteristics, which may have important effects on substance migration and transformation such as organic matter and soil elements or the environmental impacts of pollutants. Therefore, regional soil characteristics should be considered in the process of regionalization for environmental management. However, no comprehensive evaluation or systematic classification of the natural soil environment has been established for China. Here, we established an index system for natural soil environmental regionalization (NSER) by combining literature data obtained based on bibliometrics with the analytic hierarchy process (AHP). Based on the index system, we collected spatial distribution data for 14 indexes at the national scale. In addition, three clustering algorithms—self-organizing feature mapping (SOFM), fuzzy c-means (FCM) and k-means (KM)—were used to classify and define the natural soil environment. We imported four cluster validity indexes (CVI) to evaluate different models: Davies-Bouldin index (DB), Silhouette index (Sil) and Calinski-Harabasz index (CH) for FCM and KM, clustering quality index (CQI) for SOFM. Analysis and comparison of the results showed that when the number of clusters was 13, the FCM clustering algorithm achieved the optimal clustering results (DB = 1.16, Sil = 0.78, CH = 6.77 × 106), allowing the natural soil environment of China to be divided into 12 regions with distinct characteristics. Our study provides a set of comprehensive scientific research methods for regionalization research based on spatial data, it has important reference value for improving soil environmental management based on local conditions in China.

Resilient electrical distribution grid planning against seismic waves using distributed energy resources and sectionalizers: An Indian's urban grid case study

The urban and suburban advancement has increased the consumption of energy per capita gradually. Electrical distribution companies have expanded their network to cater to the demand, making the system more vulnerable to low probability high impact events. The extreme events occurred in last five year had shown us complete to partial blackout, which calls for resiliency enhancement. The presented study concentrates on the Dehradun, India, which listed as the most earthquake-prone region by Union Nations Development Programme. Hence, this paper proposes three main strategies to make a resilient distribution grid against an earthquake; (i) Hardening approach at grid side and demand side against earthquake disaster (ii) Monte-Carlo methodology for earthquake hazard model (iii) K-means algorithm with clustering quality index to identify the multiple vulnerable zones. Grid side hardening is performed using the optimal unit placement of the Solar PV plant (SPP) with storage and parallel cables with sectionalizers. For demand-side hardening, electric vehicles are considered storage after an event, duly taking their future growth rate into account. Furthermore, a Mixed Integer non-linear problem is formulated to identify the optimal sizing and sitting of SPP with storage. The proposed methodology is developed and applied to the distribution system (156-bus) of Dehradun, India.

A space-structure based dissimilarity measure for categorical data

The development of analysis methods for categorical data begun in 90's decade, and it has been booming in the last years. On the other hand, the performance of many of these methods depends on the used metric. Therefore, determining a dissimilarity measure for categorical data is one of the most attractive and recent challenges in data mining problems. However, several similarity/dissimilarity measures proposed in the literature have drawbacks due to high computational cost, or poor performance. For this reason, we propose a new distance metric for categorical data. We call it: Weighted pairing (W-P) based on feature space-structure, where the weights are understood like a degree of contribution of an attribute to the compact cluster structure. The performance of W-P metric was evaluated in the unsupervised learning framework in terms of cluster quality index. We test the W-P in six real categorical datasets downloaded from the public UCI repository, and we make a comparison with the distance metric (DM3) method and hamming metric (H-SBI). Results show that our proposal outperforms DM3 and H-SBI in different experimental configurations. Also, the W-P achieves highest rand index values and a better clustering discriminant than the other methods.

Алгоритм формирования базы правил нечёткого классификатора на основе алгоритма кластеризации K-средних и метаэвристического алгоритма «китов»

The article presents a description of the algorithm for generating fuzzy rules for a fuzzy classifier using data clustering, metaheuristic, and the clustering quality index, as well as the results of performance testing on real data sets.

OsamorSoft: clustering index for comparison and quality validation in high throughput dataset

The existence of some differences in the results obtained from varying clustering k-means algorithms necessitated the need for a simplified approach in validation of cluster quality obtained. This is partly because of differences in the way the algorithms select their first seed or centroid either randomly, sequentially or some other principles influences which tend to influence the final result outcome. Popular external cluster quality validation and comparison models require the computation of varying clustering indexes such as Rand, Jaccard, Fowlkes and Mallows, Morey and Agresti Adjusted Rand Index (ARIMA) and Hubert and Arabie Adjusted Rand Index (ARIHA). In literature, Hubert and Arabie Adjusted Rand Index (ARIHA) has been adjudged as a good measure of cluster validity. Based on ARIHA as a popular clustering quality index, we developed OsamorSoft which constitutes DNA_Omatrix and OsamorSpreadSheet as a tool for cluster quality validation in high throughput analysis. The proposed method will help to bridge the yawning gap created by lesser number of friendly tools available to externally evaluate the ever-increasing number of clustering algorithms. Our implementation was tested alongside with clusters created with four k-means algorithms using malaria microarray data. Furthermore, our results evolved a compact 4-stage OsamorSpreadSheet statistics that our easy-to-use GUI java and spreadsheet-based tool of OsamorSoft uses for cluster quality comparison. It is recommended that a framework be evolved to facilitate the simplified integration and automation of several other cluster validity indexes for comparative analysis of big data problems.

Hybrid of Hierarchical and Partitional Clustering Algorithm for Gene Expression Data

Microarray analysis able to monitor thousands of gene expression data, however, to elucidate the hidden patterns in the data is a complex process. These gene expression data show its imprecision, noise and vagueness due to its high dimensional properties. There are a handful of clustering algorithms have been proposed to extract the important information from the gene expression data. However, identifying the underlying biological knowledge of the data is still hard. To acknowledge these issues, clustering algorithms are used to reduce the data complexity. In this article, hybrid of agglomerative hierarchical clustering and modified k-medoids (partitional clustering) are proposed. Application of the proposed of clustering algorithms to group the genes that have similar functionality which might assist pre-processing procedures. In order to emphasize the quality of the clustering results, cluster quality index (CQI) is determined. Lung and ovary data sets used and the method retrieved a fair clustering with CQI, 0.37 and 0.48 respectively. This research contributes by avoiding biasness toward genes and provide true sense of clustering output using the advantage of hierarchical and partitional clustering methods.

Comparison of dimensional reduction using the Singular Value Decomposition Algorithm and the Self Organizing Map Algorithm in clustering result of text documents

Dimension reduction has two methods namely feature selection and feature extraction. Dimension reduction using the feature selection method has a better influence than the feature extraction method on the cluster results. However, there is still a need for feature extraction methods to reduce dimensions. For this reason, an alternative algorithm is needed from the feature extraction method. Self Organizing Map (SOM) is one of the artificial neural network models that has a special nature that is effectively able to create spatial internal representations of input data, or in general to create smaller data dimensions. This research was examining the capability of SOM compared to Singular Value Decomposition (SVD) in reducing data dimension of text documents before there were clustered by k-Means. Results show that SVD still better than SOM in cluster quality index but SOM faster than SVD in computation times.

Comparison analysis of K-Means and K-Medoid with Ecluidience Distance Algorithm, Chanberra Distance, and Chebyshev Distance for Big Data Clustering

This study aims to analyze the comparison of object clustering results in big data using K-Means method and K-Medoid method. Combination testing using three algorithms namely Ecludiance Distance, Canberra Distance, and Chebyshev Distance respectively for both methods. The sample of the research is the data set of students of three classes with six variables with a total of 147,679 data. The test results found that K-Means method is more optimal in data clustering than K-Medoid method, both in Ecluid Distance, Chanberra Distance and Chebyshev Distance algorithms which in overall comparison of clustering process with 1: 110.7 rationality. The results also suggested not to useChanberra Distance algorithms for both K-Means and K-Medoid methods because the cluster quality index in the Davies Bouldin test was undefined (∞). The best level of accuracy and quality of cloning is to use K-Means with Chebyshev Distance method, which is to produce five clusters with 0.1 second processing time

A multi-objective gene clustering algorithm guided by apriori biological knowledge with intensification and diversification strategies

BackgroundBiologists aim to understand the genetic background of diseases, metabolic disorders or any other genetic condition. Microarrays are one of the main high-throughput technologies for collecting information about the behaviour of genetic information on different conditions. In order to analyse this data, clustering arises as one of the main techniques used, and it aims at finding groups of genes that have some criterion in common, like similar expression profile. However, the problem of finding groups is normally multi dimensional, making necessary to approach the clustering as a multi-objective problem where various cluster validity indexes are simultaneously optimised. They are usually based on criteria like compactness and separation, which may not be sufficient since they can not guarantee the generation of clusters that have both similar expression patterns and biological coherence.MethodWe propose a Multi-Objective Clustering algorithm Guided by a-Priori Biological Knowledge (MOC-GaPBK) to find clusters of genes with high levels of co-expression, biological coherence, and also good compactness and separation. Cluster quality indexes are used to optimise simultaneously gene relationships at expression level and biological functionality. Our proposal also includes intensification and diversification strategies to improve the search process.ResultsThe effectiveness of the proposed algorithm is demonstrated on four publicly available datasets. Comparative studies of the use of different objective functions and other widely used microarray clustering techniques are reported. Statistical, visual and biological significance tests are carried out to show the superiority of the proposed algorithm.ConclusionsIntegrating a-priori biological knowledge into a multi-objective approach and using intensification and diversification strategies allow the proposed algorithm to find solutions with higher quality than other microarray clustering techniques available in the literature in terms of co-expression, biological coherence, compactness and separation.

A Bi-Objective Clustering Algorithm for Gene Expression Data

Clustering algorithms are a common method for data analysis in many science field. They have become popular among biologists because of ease to discovery similar cellular functions in gene expression data. Most approaches consider the gene clustering as an optimization problem, where an ad-hoc cluster quality index is optimized which can be defined regarding gene expression data or biological information. However, these approaches may not be sufficient since they cannot guarantee to generate clusters with similar expression patterns and biological coherence. In this paper, we propose a bi-objective clustering algorithm to discover clusters of genes with high levels of co-expression and biological coherence. Our approach uses a multi-objective evolutionary algorithm (MOEA) that optimizes two index based on gene expression level and biological functional classes. The algorithm is tested on three real-life gene expression datasets. Results show that the proposed model yields gene clusters with higher levels of co-expression and biological coherence than traditional approaches.

Combining affinity propagation clustering and mutual information network to investigate key genes in fibroid.

The aim of the present study was to investigate key genes in fibroids based on the multiple affinity propogation-Krzanowski and Lai (mAP-KL) method, which included the maxT multiple hypothesis, Krzanowski and Lai (KL) cluster quality index, affinity propagation (AP) clustering algorithm and mutual information network (MIN) constructed by the context likelihood of relatedness (CLR) algorithm. In order to achieve this goal, mAP-KL was initially implemented to investigate exemplars in fibroid, and the maxT function was employed to rank the genes of training and test sets, and the top 200 genes were obtained for further study. In addition, the KL cluster index was applied to determine the quantity of clusters and the AP clustering algorithm was conducted to identify the clusters and their exemplars. Subsequently, the support vector machine (SVM) model was selected to evaluate the classification performance of mAP-KL. Finally, topological properties (degree, closeness, betweenness and transitivity) of exemplars in MIN constructed according to the CLR algorithm were assessed to investigate key genes in fibroid. The SVM model validated that the classification between normal controls and fibroid patients by mAP-KL had a good performance. A total of 9 clusters and exemplars were identified based on mAP-KL, which were comprised of CALCOCO2, COL4A2, COPS8, SNCG, PA2G4, C17orf70, MARK3, BTNL3 and TBC1D13. By accessing the topological analysis for exemplars in MIN, SNCG and COL4A2 were identified as the two most significant genes of four types of methods, and they were denoted as key genes in the progress of fibroid. In conclusion, two key genes (SNCG and COL4A2) and 9 exemplars were successfully investigated, and these may be potential biomarkers for the detection and treatment of fibroid.

A novel automatic picture fuzzy clustering method based on particle swarm optimization and picture composite cardinality

Fuzzy clustering plays an important role in pattern recognition and knowledge discovery. Recently, there has been a great interest of developing fuzzy clustering algorithms on advanced fuzzy sets such as Picture Fuzzy Clustering (FC-PFS) which is an extension of Fuzzy C-Means on Picture Fuzzy Set. A major disadvantage of FC-PFS is how to define a prior number of clusters before clustering. Because each dataset has distinctive features and distributions of patterns, determining such the number for a clustering algorithm would result in good quality. In this paper, we propose a method called Automatic Picture Fuzzy Clustering (AFC-PFS) for determining the most suitable number of clusters for FC-PFS. It is a hybrid method between Particle Swarm Optimization (PSO) and FC-PFS where combined solutions consisting of the number of clusters and equivalent clustering centers and membership matrices are packed and optimized in PSO. A new term namely Picture Composite Cardinality is also given to determine a suitable number of clusters. AFC-PFS is empirically validated on benchmark datasets of UCI Machine Learning Repository by different clustering quality indices. The results show that AFC-PFS has better performance than the relevant methods.

Statistical treatment of 2D NMR COSY spectra in metabolomics: data preparation, clustering-based evaluation of the Metabolomic Informative Content and comparison with 1H-NMR

Compared with the widely used 1H-NMR spectroscopy, two-dimensional NMR experiments provide more sophisticated spectra which should facilitate the identification of relevant spectral zones or biomarkers in metabolomics. This paper focuses on 1H-1H COrrelation SpectroscopY (COSY) spectral data. In spite of longer inherent acquisition times, it is commonly accepted by users (biologists, healthcare professionals) that the introduction of an additional dimension probably represents a huge qualitative step for investigations in terms of metabolites identification. Moreover, it seems natural that more information leads to more predictive power. But, until now, very few statistical studies clearly proved this assumption. Therefore a fundamental question is “Is this supplementary information relevant?”. In order to extend the statistical properties developed for 1D spectroscopy to the challenges raised by 2D spectra, a rigorous study of the performances of COSY spectra is needed as a prerequisite. Having introduced new pre-processing concepts, such as the Global Peak List or an ad hoc 2D “bucketing”, this paper presents an innovative methodology based on multivariate clustering algorithms to evaluate this question. Numerical clustering quality indexes and graphical results are proposed, based both on the spectral presence or absence of peaks (binary position vectors) and on peak intensities, and through different levels of spectral resolution. The second goal of this paper is to compare clustering performances obtained on COSY and on 1H-NMR spectra, with the aim of understanding to what extent the COSY spectra carry more Metabolomic Informative Content about the signal than 1D ones. The methodology is applied to two real experimental designs involving different groups of spectra (which define the signal): a 4-mixture cell culture media containing various supervised metabolites and a complex human serum based design. It is shown that COSY spectra appear to be statistically powerful and, in addition, provide better clustering results than corresponding 1H-NMR when using unlabeled information. Consequently, additional information appears to be relevant for metabolomics applications.

Delineation of Seismic Sources in Probabilistic Seismic‐Hazard Analysis Using Fuzzy Cluster Analysis and Monte Carlo Simulation

Abstract Determination of seismic sources is the first step in probabilistic seismic‐hazard analysis (PSHA); however, this step, especially in low seismic regions, is often controversial. In conventional PSHA procedure, determination of seismic sources is merely based on the subjective judgments of experts, and in many cases, there are great differences among proposed seismic models in a specific region. As a result, one important source of uncertainty in PSHA is due to determination of seismic sources. In this article, by combination of fuzzy clustering analysis and Monte Carlo simulation, an objective method for determination and probabilistic modeling of seismic sources is presented. By clustering spatial locations of earthquakes, it is possible to specify the extent of each seismic source in an objective way. A cluster quality index is used to identify the optimum number of clusters. The density and spread of events in each cluster determines the geometrical shape of seismic sources. Moreover, in this article a method is proposed to construct spatial probability density functions (PDFs) of earthquake locations based on the results of fuzzy clustering analysis. The spatial PDF of earthquakes can be used for the generation of synthetic events in Monte Carlo simulation. The Azarbaijan region, with its varied seismotectonics and generally high seismicity, is used as an important area of seismicity in which to develop and demonstrate the application and capability of fuzzy clustering analysis in specifying seismic sources. The PSHA is performed for the city of Tabriz, and a comprehensive comparison is made between the results of conventional PSHA, ordinary Monte Carlo hazard analysis, and the proposed method. The results indicate there is an objective relationship between observed seismicity and seismotectonic evidences in the region. Moreover, the distribution of synthetic events is highly correlated with the observed seismicity, seismotectonic, and geological information of the region.

Inducing Decision Trees based on a Cluster Quality Index

Decision trees are popular classifiers in data mining, artificial intelligence, and pattern recognition, because they are accurate and easy to comprehend. In this paper, we introduce a new procedure for inducing decision trees, to obtain trees that are more accurate, more compact, and more balanced. Each candidate split is evaluated using Rand Statistics, a quality index based on external measures, because it is considered by many authors as the best existing index. Our method was compared with other state-of-the-art methods and the results over 30 databases from the UCI Repository prove our claims. We also introduce a new equation to measure the balance of a binary tree.

Federating clustering and cluster labelling capabilities with a single approach based on feature maximization: French verb classes identification with IGNGF neural clustering

Classifications which group together verbs and a set of shared syntactic and semantic properties have proven to be useful in both linguistics and Natural Language Processing tasks. However, most existing approaches for automatically acquiring verb classes fail to associate the verb classes produced with an explicit characterisation of the syntactic and semantic properties shared by the class elements. We propose a novel approach to verb clustering which addresses this shortcoming and permits building verb classifications whose classes group together verbs, subcategorisation frames and thematic grids. Our approach involves the use of a recent neural clustering method called IGNGF (Incremental Growing Neural Gas with Feature maximization). The use of a standard distance measure for determining a winner is replaced in IGNGF by feature maximisation measure relying on the features of the data that are associated with clusters during learning. A main advantage of the method is that maximised features used by IGNGF during learning can also be exploited in a final step for accurately labelling the resulting clusters. In this paper, we exploit IGNGF for the unsupervised classification of French verbs and evaluate the obtained clusters (i.e., verb classes) in two different ways. The first way is a quantitative analysis of the clustering process relying on a usual gold standard and on complementary unbiased clustering quality indexes. The second way is a qualitative analysis of the cluster labelling process. Relying on an adapted gold standard, we evaluate the capacity of the IGNGF clusters labels (i.e., subcategorisation frames and thematic grids) to be exploited for bootstraping a VerbNet-like classification for French. Both analyses clearly highlight the advantages of the approach.