Appropriate Number Of Clusters Research Articles

Dialectometry-based classification of the Central–Southern Italian dialects

Abstract This paper provides a new classification of Central–Southern Italian dialects using dialectometric methods. All varieties considered are analyzed and cast in a data set where homogeneous areas are evaluated according to a selected list of phonetic features. Using numerical evaluation of these features and the Manhattan distance, a linguistic distance rule is defined. On this basis, the classification problem is formulated as a clustering problem, and a k-means algorithm is used. Additionally, an ad-hoc rule is set to identify transitional areas, and silhouette analysis is used to select the most appropriate number of clusters. While meaningful results are obtained for each number of clusters, a nine-group classification emerges as the most appropriate. As the results suggest, this classification is less subjective, more precise, and more comprehensive than traditional ones based on selected isoglosses.

Symbolic Aggregate Approximation-Based Clustering of Monthly Natural Gas Consumption

Natural gas is an indispensable non-renewable energy source for many countries. It is used in many different areas such as heating and kitchen appliances in homes, and heat treatment and electricity generation in industry. Natural gas is an essential component of the transportation sector, providing a cleaner alternative to traditional fuels in vehicles and fleets. Moreover, natural gas plays a vital role in boosting energy efficiency through the development of combined heat and power systems. These systems produce electricity and useful heat concurrently. As nations move towards more sustainable energy solutions, natural gas has gained prominence as a transitional fuel. This is due to its lower carbon emissions when compared to coal and oil, thus making it an essential component of the global energy framework. In this study, monthly natural gas consumption data of 28 different European countries between 2014 and 2022 are used. Symbolic Aggregate Approximation method is used to analyse the data. Analyses are made with different numbers of segments and numbers of alphabet sizes, and alphabet vectors of each country are created. These letter vectors are used in hierarchical clustering and dendrogram graphs are created. Furthermore, the elbow method is used to determine the appropriate number of clusters. Clusters of countries are created according to the determined number of clusters. In addition, it is interpreted according to the consumption trends of the countries in the determined clusters.

Ensemble CART surrogate-assisted automatic multi-objective rough fuzzy clustering algorithm for unsupervised image segmentation

Multi-objective clustering algorithms (MOCAs) are popular in unsupervised image segmentation due to their merit of meeting multiple segmentation requirements and the prospect of automatically estimating the number of clusters. However, most of them suffer from high time costs and are easily to be influenced by the uncertainty when handling real complex images. To address these issues, we propose an ensemble classification and regression tree (CART) surrogate-assisted automatic multi-objective rough fuzzy clustering (ECS-AMRFC) algorithm for unsupervised image segmentation. Firstly, a cluster medoid-based encoding scheme is employed to represent solutions with different number of clusters and meanwhile lessen the length of encoding. Then, we design an ensemble CART as the surrogate model to significantly reduce the computational burden. Moreover, a surrogate model management strategy is proposed to accelerate the optimization and enhance the quality of surrogate modeling. To handle the uncertainty in data, we extend the rough fuzzy clustering into MOCAs and construct three complementary objective functions to seek proper cluster medoids from multiple perspectives. In addition, the Gaussian kernel is introduced into the objective functions to handle image pixels that cannot separate linearly in the feature space. Finally, a kernelized rough fuzzy clustering validity index is defined to automatically select the optimal solution with no requirements of any prior knowledge. Experiments show that ECS-AMRFC not only identifies appropriate number of clusters on different kinds of images, but also obtains better segmentation results than state-of-the-art rough fuzzy clustering algorithms and automatic MOCAs.

Study and methodology exploration of high-potassium glass and lead-barium glass classification patterns based on cluster analysis and decision tree

This study aims to analyze the classification patterns of high-potassium glass and lead-barium glass. It involves preprocessing the data through cluster analysis and employing machine learning decision trees and K-means clustering models for in-depth analysis. In the clustering analysis model, we start by performing a cluster difference analysis on the feature attributes of high-potassium glass and lead-barium glass to obtain initial classification results. Subsequently, we use machine learning decision tree models to partition the data into training and testing sets to explore the classification patterns. Construct a K-means clustering model by iteratively determining the initial cluster centroids' positions using an algorithm and calculating the silhouette coefficient for different numbers of clusters.This process aids in determining the appropriate number of clusters and the initial cluster centroids' positions. The results indicate significant differences in various features between high-potassium glass and lead-barium glass, and the employment of decision trees and K-means models successfully classifies artifacts. In conclusion, this study provides a robust method for the classification of high-potassium glass and lead-barium glass, offering valuable insights for research and application in related fields.

Segmenting the Higher Education Market: An Analysis of Admissions Data Using K-Means Clustering

One of the affecting factors of marketing strategy in educational institutions is determining clear marketing objectives including suitable segmentation. This study develops a market segmentation for private HEIs considering the potential academic records of targeting schools and geographic factors. K-Means clustering method is exploited to cluster around 260 data with eight attributes. The elbow method and silhouette coefficient are used to determine the appropriate number of clusters. Findings suggest that schools within Cluster 1 and Cluster 4, with approximately 42% market share, are the primary market segment for deploying a robust and targeted marketing strategy.

A novel clustering based method for characterizing household electricity consumption profiles

A new methodology based on expert knowledge and data mining is proposed to obtain data-driven models that characterize household consumption profiles. These profiles are useful for electricity marketers to understand their customers’ consumption. They could then adjust their electricity purchases in the market and provide recommendations to their customers to manage their consumption. The novelty of this research work is proposing a new procedure to determine an adequate number of clusters for a clustering task. Therefore, the proposed new methodology includes this novel procedure to build the models in two phases. In the first phase, clustering algorithms are used to group the data using different numbers of clusters. For the second phase, a new procedure (k-ISAC_TLP) is proposed and used to select the most appropriate number of clusters. This methodology allows the inclusion of domain information. In the case of household electricity consumption, where only groups with a significant number are relevant as long as the error is small, it allows the use of metrics like the mean absolute error and the number of observations (daily electricity consumption profiles). According to experts, the results achieved in two real datasets (from Spain and Ireland), with millions of observations support the methodology and reveal novel knowledge. In both cases, two and a half million observations have been analyzed and around twenty electricity consumption profiles have been detected. The methodology is easily extensible to problems of any domain where clustering algorithms are applicable. A software solution has been implemented and made freely available.

Feature-based clustering of the left ventricular strain curve for cardiovascular risk stratification in the general population

ObjectiveIdentifying individuals with subclinical cardiovascular (CV) disease could improve monitoring and risk stratification. While peak left ventricular (LV) systolic strain has emerged as a strong prognostic factor, few studies have analyzed the whole temporal profiles of the deformation curves during the complete cardiac cycle. Therefore, in this longitudinal study, we applied an unsupervised machine learning approach based on time-series-derived features from the LV strain curve to identify distinct strain phenogroups that might be related to the risk of adverse cardiovascular events in the general population.MethodWe prospectively studied 1,185 community-dwelling individuals (mean age, 53.2 years; 51.3% women), in whom we acquired clinical and echocardiographic data including LV strain traces at baseline and collected adverse events on average 9.1 years later. A Gaussian Mixture Model (GMM) was applied to features derived from LV strain curves, including the slopes during systole, early and late diastole, peak strain, and the duration and height of diastasis. We evaluated the performance of the model using the clinical characteristics of the participants and the incidence of adverse events in the training dataset. To ascertain the validity of the trained model, we used an additional community-based cohort (n = 545) as external validation cohort.ResultsThe most appropriate number of clusters to separate the LV strain curves was four. In clusters 1 and 2, we observed differences in age and heart rate distributions, but they had similarly low prevalence of CV risk factors. Cluster 4 had the worst combination of CV risk factors, and a higher prevalence of LV hypertrophy and diastolic dysfunction than in other clusters. In cluster 3, the reported values were in between those of strain clusters 2 and 4. Adjusting for traditional covariables, we observed that clusters 3 and 4 had a significantly higher risk for CV (28% and 20%, P ≤ 0.038) and cardiac (57% and 43%, P ≤ 0.024) adverse events. Using SHAP values we observed that the features that incorporate temporal information, such as the slope during systole and early diastole, had a higher impact on the model's decision than peak LV systolic strain.ConclusionEmploying a GMM on features derived from the raw LV strain curves, we extracted clinically significant phenogroups which could provide additive prognostic information over the peak LV strain.

Dimensionality reduction model based on integer planning for the analysis of key indicators affecting life expectancy

Abstract Purpose Exploring a dimensionality reduction model that can adeptly eliminate outliers and select the appropriate number of clusters is of profound theoretical and practical importance. Additionally, the interpretability of these models presents a persistent challenge. Design/methodology/approach This paper proposes two innovative dimensionality reduction models based on integer programming (DRMBIP). These models assess compactness through the correlation of each indicator with its class center, while separation is evaluated by the correlation between different class centers. In contrast to DRMBIP-p, the DRMBIP-v considers the threshold parameter as a variable aiming to optimally balances both compactness and separation. Findings This study, getting data from the Global Health Observatory (GHO), investigates 141 indicators that influence life expectancy. The findings reveal that DRMBIP-p effectively reduces the dimensionality of data, ensuring compactness. It also maintains compatibility with other models. Additionally, DRMBIP-v finds the optimal result, showing exceptional separation. Visualization of the results reveals that all classes have a high compactness. Research limitations The DRMBIP-p requires the input of the correlation threshold parameter, which plays a pivotal role in the effectiveness of the final dimensionality reduction results. In the DRMBIP-v, modifying the threshold parameter to variable potentially emphasizes either separation or compactness. This necessitates an artificial adjustment to the overflow component within the objective function. Practical implications The DRMBIP presented in this paper is adept at uncovering the primary geometric structures within high-dimensional indicators. Validated by life expectancy data, this paper demonstrates potential to assist data miners with the reduction of data dimensions. Originality/value To our knowledge, this is the first time that integer programming has been used to build a dimensionality reduction model with indicator filtering. It not only has applications in life expectancy, but also has obvious advantages in data mining work that requires precise class centers.

A cluster analysis on the potential of livestock farming: Türkiye in a global context.

This study aims to rank, and cluster countries in terms of some essential livestock indicators, and evaluate the subject with specific attention to the conditions existing in Türkiye. The study material covers 142 countries whose 2020 data were fully reported by the World Food and Agriculture Organization, the World Trade Organization, and the World Bank. It was determined that the most appropriate number of clusters would be 4 and significant differences were found between these clusters in terms of medium and high effect size for all indicators (P < 0.01). The cluster of 31 countries, according to the Ward algorithm, and the cluster of 37 countries according to the K-Means algorithm, both including Türkiye, were found to have higher averages than the other clusters in terms of related indicators (P < 0.01). The common elements in both clusters were determined: Türkiye, USA, Germany, Argentina, Brazil, Ethiopia, Morocco, France, India, the Netherlands, England, Spain, Italy, Canada, Kazakhstan, Kenya, Colombia, Pakistan, Peru, Poland, and Russia. Taking into account the geographical proximity and economic relations, Türkiye should examine the livestock models followed by these countries and evaluate the possible areas of cooperation that can be developed and competition that could be faced by these countries.

Comparative Analysis of the Clustering Quality in Self-Organizing Maps for Human Posture Classification.

The objective of this article is to develop a methodology for selecting the appropriate number of clusters to group and identify human postures using neural networks with unsupervised self-organizing maps. Although unsupervised clustering algorithms have proven effective in recognizing human postures, many works are limited to testing which data are correctly or incorrectly recognized. They often neglect the task of selecting the appropriate number of groups (where the number of clusters corresponds to the number of output neurons, i.e., the number of postures) using clustering quality assessments. The use of quality scores to determine the number of clusters frees the expert to make subjective decisions about the number of postures, enabling the use of unsupervised learning. Due to high dimensionality and data variability, expert decisions (referred to as data labeling) can be difficult and time-consuming. In our case, there is no manual labeling step. We introduce a new clustering quality score: the discriminant score (DS). We describe the process of selecting the most suitable number of postures using human activity records captured by RGB-D cameras. Comparative studies on the usefulness of popular clustering quality scores-such as the silhouette coefficient, Dunn index, Calinski-Harabasz index, Davies-Bouldin index, and DS-for posture classification tasks are presented, along with graphical illustrations of the results produced by DS. The findings show that DS offers good quality in posture recognition, effectively following postural transitions and similarities.

An advanced ensemble clustering approach for data partitioning and mining to optimize performance in variable refrigerant flow systems

This study presents a data mining-based approach to develop clustering ensemble models for data partitioning of variable refrigerant flow (VRF) system, with the aim of improving the quality of pattern detection and laying a solid foundation for further data mining. This approach mainly includes three parts. First, data preprocessing combines handling outliers, feature filtering, stable data filtering and data normalization. Secondly, consensus clustering is used to obtain an appropriate number of clusters. To generate base clusterings, we applied three clustering algorithms - k-means, self-organizing maps, and fuzzy C-means - in a 1:1:1 ratio. These base clusterings were selected based on the adjusted rand index as the underlying selection criterion. For clustering ensemble, we utilized three integration methods, namely K-modes, latent class analysis, and linkage clustering ensemble. Finally, analyze the metric difference and time consumption of the integration clustering results of different methods, and obtain a suitable data partitioning scheme for VRF system. This case study examines the utilization of the proposed method to analyze the operation data of a VRF system in an office building. The results indicate that the quality of the clustering derived by the ensemble clustering model is notably superior to that of the individual base clustering. Moreover, the latent class analysis method demonstrates remarkable advantages in achieving top-quality clustering outcomes. These findings suggest that the proposed method can be effective in optimizing VRF system operation while leveling up the accuracy of data analysis. Ensemble models have considerable merit in devising fault identification and diagnosis techniques, optimizing operation, and exploring the links between VRF systems and smart grids.

A Granularity-Based Clustering Method for Reducing Write Amplification in Solid-State Drives

In recent years, solid-state drives (SSDs) that adopt NAND flash memory have been widely used as the main storage devices. In particular, NAND flash memory has a special feature of “out-of-place” updates to write the up-to-date data to a free page, and the corresponding old page will become invalid. When the number of free pages in SSDs is insufficient, garbage collection (GC) will be executed to reclaim the invalid pages in a block by erasing the block. Many studies have shown that a good hot/cold data separation (i.e., clustering) can greatly reduce the overhead of GC so as to improve the SSD performance. However, previous clustering methods usually use a static number of clusters or a fixed size of granularity (i.e., a fine-grained or a coarse-grained granularity), so they may not always perform well for different kinds of workloads. Therefore, we propose a granularity-based clustering method to adaptively adjust the size of granularity groups for an appropriate number of clusters at runtime according to the update distances of logical addresses. According to the experimental results, we can improve SSD performance by reducing the overhead of GC and decrease the write amplification. Furthermore, we can show that the proposed method can utilize a fine-grained granularity to retain the record accuracy of update distances and also utilize a coarse-grained granularity to reduce the space required to record update distances.

K-Means Clustering of 51 Geospatial Layers Identified for Use in Continental-Scale Modeling of Outdoor Acoustic Environments

Applying machine learning methods to geographic data provides insights into spatial patterns in the data as well as assists in interpreting and describing environments. This paper investigates the results of k-means clustering applied to 51 geospatial layers, selected and scaled for a model of outdoor acoustic environments, in the continental United States. Silhouette and elbow analyses were performed to identify an appropriate number of clusters (eight). Cluster maps are shown and the clusters are described, using correlations between the geospatial layers and clusters to identify distinguishing characteristics for each cluster. A subclustering analysis is presented in which each of the original eight clusters is further divided into two clusters. Because the clustering analysis used geospatial layers relevant to modeling outdoor acoustics, the geospatially distinct environments corresponding to the clusters may aid in characterizing acoustically distinct environments. Therefore, the clustering analysis can guide data collection for the problem of modeling outdoor acoustic environments by identifying poorly sampled regions of the feature space (i.e., clusters which are not well-represented in the training data).

Exploring the heterogeneities of factors affecting e-bicyclist severities in delivery e-scooter crashes

Delivery e-bicyclists are vulnerable traffic participants, and delivery e-scooter crashes annually cause great losses. There are limited empirical analyses performed to characterize the endogenous and exogenous influences of potential factors on delivery e-scooter crash severities. This study focused on identifying the heterogeneous impacts of contributing factors. Based on 3064 police-reported delivery e-scooter crashes, different potential factors selected from seven perspectives were examined. Combining the latent class clustering analysis and the partial proportional odds model, an unsupervised learning approach was developed to modeling the heterogeneities as well as the corresponding marginal effects. According to the AIC, BIC, and entropy-based approach, the most appropriate number of clusters was identified as three. The model results revealed that the top six factors significantly influencing the injury severities were running red light, reverse riding, speeding, bike lane, changing lane, and e-bicyclist age. Their maximum absolute values of the marginal effects were more than 29%. The sub-models owned a better goodness of fit in characterizing heterogeneities and avoiding the model bias. It was easy to find the remarkable heterogeneities within each factor and across different clusters. The findings could provide insightful guidance and effective recommendations for alleviating the crash losses and promoting rider safety.

Grouping Matrix Based Graph Pooling with Adaptive Number of Clusters

Graph pooling is a crucial operation for encoding hierarchical structures within graphs. Most existing graph pooling approaches formulate the problem as a node clustering task which effectively captures the graph topology. Conventional methods ask users to specify an appropriate number of clusters as a hyperparameter, then assuming that all input graphs share the same number of clusters. In inductive settings where the number of clusters could vary, however, the model should be able to represent this variation in its pooling layers in order to learn suitable clusters. Thus we propose GMPool, a novel differentiable graph pooling architecture that automatically determines the appropriate number of clusters based on the input data. The main intuition involves a grouping matrix defined as a quadratic form of the pooling operator, which induces use of binary classification probabilities of pairwise combinations of nodes. GMPool obtains the pooling operator by first computing the grouping matrix, then decomposing it. Extensive evaluations on molecular property prediction tasks demonstrate that our method outperforms conventional methods.

Blysmo compressi-Eriophoretum latifoliae ass. nova, a new association of the Caricion fuscae alliance from the Sharri Mountains

The sedge-moss vegetation of the moderately to low calcium-rich slightly acidic fens of the Caricion fuscae alliance depends on a very specific combination of ecological and climatic conditions to thrive. Until recently, the classification of this vegetation group was complicated by its rarity on the southern edges of its range in Europe. As part of a larger database of phytocenological relevés carried out in Mt. Luboten, we came across an interesting group of 15 relevés on fen vegetation sites. We were curious to know if this plant community was a previously known association or if it might represent something new within this alliance. We compiled a separate dataset at JUICE that includes four plant communities from this alliance, along with our 15 original releves. The classification was based on modified TWINSPAN and beta-flexible clustering as a numerical classification method, with OPTIMCLASS determining the appropriate number of clusters. Five associations were clearly delineated, with the four associations taken from the literature sources clearly grouped individually and a new, fifth association appearing as separate, with completely unique characteristics. This new association: Blysmo compressi-Eriophoretum latifoliae occurs at elevations of ~ 1650 m a.s.l. on NE and NW slopes of the mountain. With this work we offer the description of a new high-mountain fen association. These associations may play an important syntaxonomic role as more Balkan data become available on this alliance. The sedge-moss and fen vegetation in the Balkans is particularly rare and characterised by a very diverse and specific vegetation, so it rightly deserves more attention from vegetation scientists and conservation authorities.

Clustering of football players based on performance data and aggregated clustering validity indexes

Abstract We analyse football (soccer) player performance data with mixed type variables from the 2014-15 season of eight European major leagues. We cluster these data based on a tailor-made dissimilarity measure. In order to decide between the many available clustering methods and to choose an appropriate number of clusters, we use the approach by Akhanli and Hennig (2020. “Comparing Clusterings and Numbers of Clusters by Aggregation of Calibrated Clustering Validity Indexes.” Statistics and Computing 30 (5): 1523–44). This is based on several validation criteria that refer to different desirable characteristics of a clustering. These characteristics are chosen based on the aim of clustering, and this allows to define a suitable validation index as weighted average of calibrated individual indexes measuring the desirable features. We derive two different clusterings. The first one is a partition of the data set into major groups of essentially different players, which can be used for the analysis of a team’s composition. The second one divides the data set into many small clusters (with 10 players on average), which can be used for finding players with a very similar profile to a given player. It is discussed in depth what characteristics are desirable for these clusterings. Weighting the criteria for the second clustering is informed by a survey of football experts.

Typology of Indian Domestic Tourists: Clustering Based on Motives to Visit

The study aims to segment domestic tourists and understand the differences across these segments. It adopts an empirical approach and seeks to provide implications relevant to marketers. The literature review indicates that research on the motivational factors of domestic tourists needs to be more comprehensive. The study was carried out on a sample frame of domestic tourist respondents. Data were collected from 456 respondents by using a survey approach. An adapted questionnaire has been used to collect the data. The study uses the SPSS software to apply the K-mean cluster analysis to determine the most appropriate number of clusters, and travel motivation scores were calculated. The results indicate three prime segments among domestic tourists: self-enhancers, pleasure tourists and sensation seekers. The motivational factors driving these segments hold far-reaching marketing implications for tourism marketers. The study’s findings will help tourism marketers design an appropriate marketing strategy to attract tourists.

A new efficient method for solving the multiple ellipse detection problem

In this paper, we consider the multiple ellipse detection problem based on data points coming from a number of ellipses in the plane not known in advance. In so doing, data points are usually contaminated with some noisy errors. In this paper, the multiple ellipse detection problem is solved as a center-based problem from cluster analysis. Therefore, an ellipse is considered a Mahalanobis circle. In this way, we easily determine a distance from a point to the ellipse and also an ellipse as the cluster center. In the case when the number of ellipses is known in advance, an optimal partition is searched for on the basis of the k-means algorithm that is modified for this case. Hence, a good initial approximation for M-circle-centers is searched for as unit circles with the application of a few iterations of the well-known DIRECT algorithm for global optimization. In the case when the number of ellipses is not known in advance, optimal partitions with 1,2,… clusters for the case when cluster-centers are ellipses are determined by using an incremental algorithm. Among them, the partition with the most appropriate number of clusters is selected. For that purpose, a new Geometrical Objects-index (GO-index) is defined. Numerous test-examples point to high efficiency of the proposed method. Many algorithms can be found in the literature that recognize ellipses with clear edges well, but that do not recognize ellipses with unclear or noisy edges. On the other hand, our algorithm is specifically used for recognition of ellipses with unclear or noisy edges.

Sparse tree-based clustering of microbiome data to characterize microbiome heterogeneity in pancreatic cancer.

There is a keen interest in characterizing variation in the microbiome across cancer patients, given increasing evidence of its important role in determining treatment outcomes. Here our goal is to discover subgroups of patients with similar microbiome profiles. We propose a novel unsupervised clustering approach in the Bayesian framework that innovates over existing model-based clustering approaches, such as the Dirichlet multinomial mixture model, in three key respects: we incorporate feature selection, learn the appropriate number of clusters from the data, and integrate information on the tree structure relating the observed features. We compare the performance of our proposed method to existing methods on simulated data designed to mimic real microbiome data. We then illustrate results obtained for our motivating data set, a clinical study aimed at characterizing the tumor microbiome of pancreatic cancer patients.