Cluster Validity Research Articles

M-CLUSTER: multistage clustering for unsupervised train wheel condition monitoring

Wheel out-of-roundness (OOR) is a common wheel defect that raises maintenance costs and increases the risk of failure or damage to track components. This paper proposes a novel multistage clustering framework (M-CLUSTER) for unsupervised condition monitoring of train wheels. The framework initially extracts time-domain features from raw acceleration responses collected by rail-mounted sensors. Sensitive features are then selected through an unsupervised feature selection algorithm called local learning-based clustering (LLC). Next, a detector model is trained using density-based spatial clustering of applications with noise (DBSCAN), a data clustering method effective for clusters with similar density. Since this algorithm does not originally involve separate training and testing phases, a new two-step mechanism is introduced: (1) training on a healthy dataset and (2) testing on an unlabelled dataset. Finally, the severity of train wheel defects is classified by K-means, with cluster validity indices (CVI) automatically determining the number of severity clusters (classes). The framework’s efficiency is demonstrated through the detection of defective wheels using the Alfa Pendular passenger model. Results indicate that M-CLUSTER accurately identifies train wheel flats and polygonal wear without labelled data, achieving 98% accuracy by selecting 10 features from the set.

APPLICATION OF AGGLOMERATIVE HIERARCHICAL CLUSTERING IN GROUPING TOURISM INDUSTRY SMES IN EAST JAVA

This study addresses a significant research gap in the classification and evaluation of Small and Medium Enterprises (SMEs) within the tourism industry in East Java, specifically focusing on their marketing performance. The primary objective is to categorize these SMEs based on their marketing effectiveness, a critical factor for their competitiveness in the tourism sector. To achieve this, the research employs cluster analysis, utilizing Agglomerative Hierarchical Clustering techniques. The optimal clustering method was determined using the cophenetic correlation coefficient and cluster validation indices. Data for the analysis were collected through questionnaires, with a sample comprising 30 tourism SMEs across 11 regions in East Java, with responses from three employees per SME. The findings revealed two distinct clusters: SMEs with fairly good marketing performance and those with good marketing performance. The results suggest that while many SMEs in the tourism industry in East Java exhibit competitive marketing capabilities, there remains a subset that requires strategic improvements, particularly in spiritual marketing practices. This study's novelty lies in its approach to classifying tourism SMEs by marketing performance, providing a framework for targeted performance enhancement and industry strengthening in the region.

Prediction and clustering of Alzheimer’s disease by race and sex: a multi-head deep-learning approach to analyze irregular and heterogeneous data

Early detection of Alzheimer’s disease (AD) is crucial to maximize clinical outcomes. Most disease progression analyses include people with diagnoses of cognitive impairment, limiting understanding of AD risk among those with normal cognition. The objective was to establish AD progression models through a deep learning approach to analyze heterogeneous, multi-modal datasets, including clustering analyses of population subsets. A multi-head deep-learning architecture was built to process and learn from biomedical and imaging data from the National Alzheimer’s Coordinating Center. Shapley additive explanation algorithms for feature importance ranking and pairwise correlation analysis were used to identify predictors of disease progression. Four primary disease progression clusters (slow, moderate and rapid converters or non-converters) were subdivided into groups by race and sex, yielding 16 sub-clusters of participants with distinct progression patterns. A multi-head and early-fusion convolutional neural network achieved the most competitive performance and demonstrated superiority over a single-head deep learning architecture and conventional tree-based machine-learning methods, with 97% test accuracy, 96% F1 score and 0.19 root mean square error. From 447 features, 2 sets of 100 predictors of disease progression were extracted. Feature importance ranking, correlation analysis and descriptive statistics further enriched cluster analysis and validation of the heterogeneity of risk factors.

Employing cluster analysis in defining groundwater wells patterns in Rafah

Clustering analysis techniques used in identifying homogeneity of groundwater wells patterns in terms of Chloride, Nitrate, and TDS. Data was collected through the laboratories of Palestinian Water Authority in the Rafah 2020. R-Programming is used for data analysis. Kolmogorov-Smirnov test is used to test data normality. Hierarchical clustering analysis applied to generate a cluster tree (r>0.75) in correlation matrix. Agglomerative Hierarchical Clustering is used to classify with “average” method and found that there are two clusters. First cluster with 28 wells and Second cluster with 9 wells. Test of homogeneity between the two clusters groups using T-test for the hierarchical clustering and found that there are significant differences in means for TDS and for Chloride between first cluster and second cluster with a significant level less than 0.01. While for Nitrates, also, there are significant differences in means between the first cluster and second cluster with a significant level less than 0.05. Different stability validation measures carried out for data concludes that for the APN and ADM measures, hierarchical clustering with two clusters again gives the best score. Three internal cluster validation measures are used. Concludes that Hierarchical clustering with two clusters performs the best in (Connective, Dunn, and Silhouette). Recall that the connectivity should be minimized, while both the Dunn Index and the Silhouette Width should be maximized. Thus, Hierarchical clustering outperforms the other clustering algorithms under each validation measure.

AVERAGE LINKAGE CLUSTERING METHOD AND MOLECULAR DOCKING STUDY ON DATE PALM (PHOENIX DACTYLIFERA L.) AS POTENTIAL ANTI-ANEMIA AGENT

Anemia, characterized by blood hemoglobin (Hb) levels below the World Health Organization's (WHO) normal limit, remains a significant health concern. Date fruit (Phoenix dactylifera L.) stands out as an herbal plant boasting the highest iron content at 13.7 mg, suggesting its potential as an anti-anemia agent. This study aimed to explore the anti-anemia potential of active compounds in date fruit using average linkage clustering and validated using molecular docking. Compounds from dates were gathered via GC-MS analysis and online databases, totaling 145 compounds—50 from GC-MS and 95 from Knapsack and Dr. Duke databases. Additionally, 5 lead compounds served as positive controls for comparison. SwissADME online servers assessed the compounds' properties, serving as materials for the clustering method. The average linkage clustering method was employed, yielding an excellent dendrogram with a cophenetic correlation of 0.711. Notably, a total of 17 date fruit compounds are in the same cluster as the lead compounds. Molecular docking revealed 4 date palm fruit-derived compounds as potential PHD enzyme inhibitors, promising for anemia treatment. In conclusion, the average linkage clustering method and validation using molecular docking approaches highlight date fruit's potential as an alternative anemia treatment, showcasing the significance of interdisciplinary methodologies in drug discovery.

Clustering validation by distribution hypothesis learning

Clustering validation by distribution hypothesis learning

PyCVI: A Python package for internal Cluster Validity Indices, compatible with time-series data

PyCVI: A Python package for internal Cluster Validity Indices, compatible with time-series data

Mixed fuzzy C-means clustering

Clustering analysis becomes challenging when the dataset has mixed data types comprising categorical (nominal or ordinal scale) and numerical (interval scale) features. Mainstream distance metrics cannot handle the information in categorical data about the similarity between the observations and cluster centers, leading to performance loss. Various methods are introduced in the literature to handle the mixed data types in clustering. However, each method has disadvantages in capturing categorical information about similarity, adjusting the contribution of categorical information to clustering, and computational or implementation inefficiency. This study proposes a mixed fuzzy C-means clustering method for mixed data types. Two new distance metrics are developed to handle binary and multi-class nominal features. The scaled entropy of each data type is used to adjust the weight of each data type in the overall similarity metric, providing a lower bias since no user-specified weight is required. A comparative numerical study is conducted with twenty real datasets and seven benchmark methods using five cluster validation statistics. The mixed fuzzy C-means clustering performs better than the benchmark methods and is computationally efficient in practice. Since all the computer codes for implementing mixed fuzzy C-means clustering are given, the proposed method is readily applicable to practical problems.

Internal Purity: A Differential Entropy-Based Internal Validation Index for Crisp and Fuzzy Clustering Validation

Internal Purity: A Differential Entropy-Based Internal Validation Index for Crisp and Fuzzy Clustering Validation

K-PCD: A new clustering algorithm for building energy consumption time series analysis and predicting model accuracy improvement

Clustering algorithms are often applied to building energy consumption data analysis to mine representative patterns of building energy usage. This paper proposes a new clustering algorithm: K-PCD, which is particularly suitable for building energy consumption time series. K-PCD utilizes a Pearson correlation coefficient-based distance measure (PCD), and a novel centroid calculation method that takes into account both the PCD and the traditional Euclidean distance (ED) between time series. This study also proposes a new clustering validity index (CVI) tailored to the predictability of building energy consumption: Energy Prediction Clustering Performance Index (EPCPI). The K-PCD and EPCPI are practically analyzed and validated using one year of data from 29 real buildings. The results indicate that comparing with traditional clustering algorithms, the K-PCD achieves better clustering results. This EPCPI index thoroughly explores building operation patterns, and after adding clustering labels, it can maximize the prediction accuracy of the Back Propagation Neural Network (BPNN) model for building energy consumption.

A 3D approach to understanding heterogeneity in early developing autisms.

Phenotypic heterogeneity in early language, intellectual, motor, and adaptive functioning (LIMA) features are amongst the most striking features that distinguish different types of autistic individuals. Yet the current diagnostic criteria uses a single label of autism and implicitly emphasizes what individuals have in common as core social-communicative and restricted repetitive behavior difficulties. Subtype labels based on the non-core LIMA features may help to more meaningfully distinguish types of autisms with differing developmental paths and differential underlying biology. Unsupervised data-driven subtypes were identified using stability-based relative clustering validation on publicly available Mullen Scales of Early Learning (MSEL) and Vineland Adaptive Behavior Scales (VABS) data (n = 615; age = 24-68months) from the National Institute of Mental Health Data Archive (NDA). Differential developmental trajectories between subtypes were tested on longitudinal data from NDA and from an independent in-house dataset from UCSD. A subset of the UCSD dataset was also tested for subtype differences in functional and structural neuroimaging phenotypes and relationships with blood gene expression. The current subtyping model was also compared to early language outcome subtypes derived from past work. Two autism subtypes can be identified based on early phenotypic LIMA features. These data-driven subtypes are robust in the population and can be identified in independent data with 98% accuracy. The subtypes can be described as Type I versus Type II autisms differentiated by relatively high versus low scores on LIMA features. These two types of autisms are also distinguished by different developmental trajectories over the first decade of life. Finally, these two types of autisms reveal striking differences in functional and structural neuroimaging phenotypes and their relationships with gene expression and may highlight unique biological mechanisms. Sample sizes for the neuroimaging and gene expression dataset are relatively small and require further independent replication. The current work is also limited to subtyping based on MSEL and VABS phenotypic measures. This work emphasizes the potential importance of stratifying autism by a Type I versus Type II distinction focused on LIMA features and which may be of high prognostic and biological significance.

A survey of genetic algorithms for clustering: Taxonomy and empirical analysis

Clustering, an unsupervised learning technique, aims to group patterns into clusters where similar patterns are grouped together, while dissimilar ones are placed in different clusters. This task can present itself as a complex optimization problem due to the extensive search space generated by all potential data partitions. Genetic Algorithms (GAs) have emerged as efficient tools for addressing this task. Consequently, significant advancements and numerous proposals have been developed in this field.This work offers a comprehensive and critical review of state-of-the-art mono-objective Genetic Algorithms (GAs) for partitional clustering. From a more theoretical standpoint, it examines 22 well-known proposals in detail, covering their encoding strategies, objective functions, genetic operators, local search methods, and parent selection strategies. Based on this information, a specific taxonomy is proposed. In addition, from a more practical standpoint, a detailed experimental study is conducted to discern the advantages and disadvantages of approaches. Specifically, 22 different cluster validation indices are considered to compare the performance of clustering techniques. This evaluation is performed across 94 datasets encompassing diverse configurations, including the number of classes, separation between classes, and pattern dimensionality. Results reveal interesting findings, such as the key role of local search in optimizing results and reducing search space. Additionally, representations based on centroids and labels demonstrate greater efficiency and crossover and mutation operators do not prove to be as relevant. Ultimately, while the results are satisfactory, real-world clustering problems introduce additional complexity, especially for algorithms aiming to determine the number of clusters, resulting in diminished performance and the need for new approaches to be explored. Code, datasets and instructions to run algorithms in the LEAL library are available in an associated repository, in order to facilitate future experiments in this environment.

Enhanced Parameter Estimation of DENsity CLUstEring (DENCLUE) Using Differential Evolution

The task of finding natural groupings within a dataset exploiting proximity of samples is known as clustering, an unsupervised learning approach. Density-based clustering algorithms, which identify arbitrarily shaped clusters using spatial dimensions and neighbourhood aspects, are sensitive to the selection of parameters. For instance, DENsity CLUstEring (DENCLUE)—a density-based clustering algorithm—requires a trial-and-error approach to find suitable parameters for optimal clusters. Earlier attempts to automate the parameter estimation of DENCLUE have been highly dependent either on the choice of prior data distribution (which could vary across datasets) or by fixing one parameter (which might not be optimal) and learning other parameters. This article addresses this challenge by learning the parameters of DENCLUE through the differential evolution optimisation technique without prior data distribution assumptions. Experimental evaluation of the proposed approach demonstrated consistent performance across datasets (synthetic and real datasets) containing clusters of arbitrary shapes. The clustering performance was evaluated using clustering validation metrics (e.g., Silhouette Score, Davies–Bouldin Index and Adjusted Rand Index) as well as qualitative visual analysis when compared with other density-based clustering algorithms, such as DPC, which is based on weighted local density sequences and nearest neighbour assignments (DPCSA) and Variable KDE-based DENCLUE (VDENCLUE).

Enhanced motor noise in an autism subtype with poor motor skills

BackgroundMotor difficulties are common in many, but not all, autistic individuals. These difficulties can co-occur with other problems, such as delays in language, intellectual, and adaptive functioning. Biological mechanisms underpinning such difficulties are less well understood. Poor motor skills tend to be more common in individuals carrying highly penetrant rare genetic mutations. Such mechanisms may have downstream consequences of altering neurophysiological excitation-inhibition balance and lead to enhanced behavioral motor noise.MethodsThis study combined publicly available and in-house datasets of autistic (n = 156), typically-developing (TD, n = 149), and developmental coordination disorder (DCD, n = 23) children (age 3–16 years). Autism motor subtypes were identified based on patterns of motor abilities measured from the Movement Assessment Battery for Children 2nd edition. Stability-based relative clustering validation was used to identify autism motor subtypes and evaluate generalization accuracy in held-out data. Autism motor subtypes were tested for differences in motor noise, operationalized as the degree of dissimilarity between repeated motor kinematic trajectories recorded during a simple reach-to-drop task.ResultsRelatively ‘high’ (n = 87) versus ‘low’ (n = 69) autism motor subtypes could be detected and which generalize with 89% accuracy in held-out data. The relatively ‘low’ subtype was lower in general intellectual ability and older at age of independent walking, but did not differ in age at first words or autistic traits or symptomatology. Motor noise was considerably higher in the ‘low’ subtype compared to ‘high’ (Cohen’s d = 0.77) or TD children (Cohen’s d = 0.85), but similar between autism ‘high’ and TD children (Cohen’s d = 0.08). Enhanced motor noise in the ‘low’ subtype was also most pronounced during the feedforward phase of reaching actions.LimitationsThe sample size of this work is limited. Future work in larger samples along with independent replication is important. Motor noise was measured only on one specific motor task. Thus, a more comprehensive assessment of motor noise on many other motor tasks is needed.ConclusionsAutism can be split into at least two discrete motor subtypes that are characterized by differing levels of motor noise. This suggests that autism motor subtypes may be underpinned by different biological mechanisms.

Quantitative evaluation of internal cluster validation indices using binary data sets

AbstractAimsDifferent clustering methods often classify the same data set differently. Selecting the “best” clustering solution from alternatives is possible with cluster validation indices. Because of the large variety of cluster validation indices (CVIs), choosing the most suitable index concerning the data set and clustering algorithms is challenging. We aim to assess different internal clustering validation indices.MethodsArtificial binary data sets with equal‐ and unequal‐sized well‐separated a priori clusters were simulated and three levels of noise were then added. Twenty replications of each of the six types of data sets (two group sizes × three levels of noise) were created and analyzed by three clustering algorithms with Jaccard dissimilarity. Twenty‐seven clustering validation indices are evaluated including both geometric and non‐geometric indices.ResultsAlthough, in theory, all CVIs could differentiate between good and wrong classifications, only a few perform as expected with noisy data. Tau and silhouette widths proved to be the best geometric CVIs both for equal and unequal cluster sizes. Among non‐geometric indices, crispness and OptimClass performed best.ConclusionWe recommend using these best‐performing CVIs. We suggest plotting the CVI value against the number of clusters because the lack of a sharp peak means that the position of the maximum is uncertain.

A Bayesian cluster validity index

Selecting the appropriate number of clusters is a critical step in applying clustering algorithms. To assist in this process, various cluster validity indices (CVIs) have been developed. These indices are designed to identify the optimal number of clusters within a dataset. However, users may not always seek the absolute optimal number of clusters but rather a secondary option that better aligns with their specific applications. This realization has led us to introduce a Bayesian cluster validity index (BCVI), which builds upon existing indices. The BCVI utilizes either Dirichlet or generalized Dirichlet priors, resulting in the same posterior distribution. The proposed BCVI is evaluated using the Calinski-Harabasz, CVNN, Davies–Bouldin, silhouette, Starczewski, and Wiroonsri indices for hard clustering and the KWON2, Wiroonsri–Preedasawakul, and Xie–Beni indices for soft clustering as underlying indices. The performance of the proposed BCVI with that of the original underlying indices has been compared. The BCVI offers clear advantages in situations where user expertise is valuable, allowing users to specify their desired range for the final number of clusters. To illustrate this, experiments classified into three different scenarios are conducted. Additionally, the practical applicability of the proposed approach through real-world datasets, such as MRI brain tumor images are presented. These tools are published as a recent R package ‘BayesCVI’.

Skin Tau Quantification as a Novel Biomarker in Huntington's Disease.

Emerging research implicates tau protein dysregulation in the pathophysiology of Huntington's disease. This study investigated skin tau quantification as a potential biomarker for Huntington's disease and its correlation with disease burden outcomes. In this cross-sectional study, we measured skin tau levels using enzyme-linked immunosorbent assay in 23 Huntington's disease mutations carriers and eight control subjects, examining group discrimination, correlations with genetic markers, clinical assessments, and neuroimaging data. Brain atrophy was quantified by both volumetric measurements from brain segmentation and a voxel-based morphometry approach. Our findings showed elevated skin tau levels in manifest Huntington's disease compared with premanifest and healthy controls. These levels correlated with CAG repeat length, CAG-Age-Product score, composite Unified Huntington's Disease Rating Scale Total Motor Score, cognitive assessments, and disease-related cortical and subcortical volumes, all independent of age and gender. Using skin tau levels in cluster analysis along with genetic and clinical measures led to improved subject stratification, providing enhanced distinction and validity of clusters. This study not only confirms the feasibility of skin tau quantification in Huntington's disease but also establishes its potential as a biomarker for enhancing group classification and assessing disease severity across the Huntington's disease spectrum, opening new directions in biomarker research. © 2024 International Parkinson and Movement Disorder Society.

MST Initialization Based Intuitionistic Fuzzy c Means Clustering Using LINEX Hellinger Distance and Its Applications

Due to the uncertainty and fuzziness of information, the traditional clustering analysis method sometimes cannot meet the requirement in practice. The clustering method based on intuitionistic fuzzy set has attracted more and more scholars attention nowadays. This paper discusses the intuitionistic fuzzy C-means clustering algorithm. There are a number of clustering techniques developed in the past using different distance/similarity measure. In this paper, we proposed a improved edge density minimal spanning tree initilization method using LINEX hellinger distance based weighted LINEX intuitionistic fuzzy c means clustering. IFCM considered an uncertainty parameter called hesitation degree and incorporated a new objective function which is based upon intutionistic fuzzy entropy in the conventional Fuzzy C-means. The clustering algorithm has membership and non membership degrees as intervals. Information regarding membership and typicality degrees of samples to all clusters is given by algorithm. Furthermore, the algorithm is extended for calculating membership and updating prototypes by minimizing the new objective function of weighted LINEX intuitionistic fuzzy c-means. Finally, the developed algorithms are illustrated through conducting experiments on random dataset, partition coefficient and validation function are used to evaluate the validity of clustering also this paper compares the results of proposed method with the results of existing basic intuitionistic fuzzy c-means.

A near-linear transect sampling method for validation of SMAP surface soil moisture in non-complex terrains

ABSTRACT The global validation for SMAP (Soil Moisture Active Passive) Level-4 surface soil moisture using well-established core validation sites does not comprehensively account for all landscapes on earth’s surface due to the diverse nature of their intrinsic characteristics. Due to the inhibitive cost of implementing a standard validation site, this study presents an alternative sampling approach suitable for localized validation of SMAP data in non-complex terrains. It involves clustering a large heterogeneous study area to smaller units of non-complex terrains where landscape-defining characteristics are largely homogeneous, thus permitting the computation of areal soil moisture as a simple arithmetic mean of near-linear point measurements. This allows optimization of limited resources (a hand-held moisture sensor with site-specific calibrations) to balance the need for spatial representativeness of samples in the sampling unit and the need for temporal proximity of sampled measurements to the aggregation time of the satellite product being validated. For ease of movement, transect sampling is implemented along access roads that run across the sampling units to allow sufficient measurement replications within a reasonably short time. Validations with four different landscapes in Kenya show a good agreement between in situ measurements and SMAP with R2 of 0.76, 0.72, 0.80, and 0.82, and biases of −0.0246, +0.0113, 0.0004, and + 0.0035 m3 m−3, respectively for Mawego, Kuresoi, Sotik and Kapsuser sites. These results only marginally differ from those obtained with a spatially distributed sampling method, indicating the potential of the proposed sampling design for time and cost effectiveness in validations at non-complex terrains. An analysis of the temporal variability of SMAP soil moisture in the watershed is also presented, with an assessment of its significance in the selection of sampling sites for validation. Particularly, the concept of temporal stability of soil moisture as a basis for clustering validation sites is evaluated.

Damage identification of plain-woven composites at T > Tg using AE: Damage clustering and initiation detection

In this work, the damage modes and their initiation detections of plain-woven composites under tensile and compressive loads at T > Tg are investigated by conducting a comprehensive analysis of AE signals, including the feature selection, algorithm comparison and clustering validity. According to a newly proposed Pearson correlation coefficient cumulative criterion, the PF and PA are the most representative features of AE signals. A systematic comparison of K-Means, GMM and Hierarchical model, reveals that the Hierarchical model is the most suitable clustering algorithm for plain-woven composites at T > Tg. The cluster validity indexes combined with microscopic observations identify matrix cracking, interface debonding and fiber breakage as the three dominant damage modes, with PF ranges of [0–200 kHz], [200–350 kHz] and [350–600 kHz], respectively, and independent of different loading conditions. Three damage initiation criteria, sentry function, b-value and cumulative AE counts, are compared and the sentry function is determined to be optimal. The damage initiations of matrix cracking, interface debonding and fiber breakage within plain-woven composites at T > Tg can be effectively detected by AE.