Cluster Validation Methods Research Articles

Intrinsic functional clustering of the macaque insular cortex.

The functional organization of the primate insula has been studied using a variety of techniques focussing on regional differences in either architecture, connectivity, or function. These complementary methods offered insights into the complex organization of the insula and proposed distinct parcellation schemes at varying levels of detail and complexity. The advent of imaging techniques that allow non-invasive assessment of structural and functional connectivity, has popularized data-driven connectivity-based parcellation methods to investigate the organization of the human insula. Yet, it remains unclear if the subdivisions derived from these data-driven clustering methods reflect meaningful descriptions of the functional specialization of the insula. In this study, we employed hierarchical clustering to examine the cluster parcellations of the macaque insula. As our aim was exploratory, we examined parcellations consisting of two up to ten clusters. Three different cluster validation methods (fingerprinting, silhouette, elbow) converged on a four-cluster solution as the most optimal representation of our data. Examining functional response properties of these clusters, in addition to their brain-wide functional connectivity suggested a functional specialization related to processing gustatory, somato-motor, vestibular and social visual cues. However, a more detailed functional differentiation aligning with previous functional investigations of insula subfields became evident at higher cluster numbers beyond the proposed optimal four clusters. Overall, our findings demonstrate that resting-state-based hierarchical clustering can provide a meaningful description of the insula's functional organization at some level of detail. Nonetheless, cluster parcellations derived from this method are best combined with data obtained through other modalities, to provide a more comprehensive and detailed account of the insula's complex functional organization.

Penerapan Algoritma K-Medoids pada Pengelompokan Wilayah Provinsi di Indonesia Berdasarkan Indikator Pendidikan

Cluster analysis has the goal of grouping data that has the same characteristics into the same cluster and data that has different properties will enter into different clusters. K-Medoids is a grouping method using a representative object as the center point (medoids). The k-medoids method was developed to overcome the weakness of the k-means method which is sensitive to outliers because an object with a large value allows it to deviate from the data distribution in size. After grouping using k-medoids, the results of the grouping were validated. The cluster validation method using the Silhoutte Coefficient (SC) is a method that can be used to see the quality and strength of clusters that combine cohesion and separation methods. This study aims to obtain the optimal cluster from the largest SC value and determine the grouping results of the optimal clusters that are formed. This grouping method is applied to data on education indicators in Indonesia in 2020. Based on the results of the analysis, it is found that the optimal cluster is 2 clusters with a SC value of 0.464, where cluster 1 has 14 provinces and cluster 2 has 20 provinces.
 
 Keywords: K-Medoids, Silhoutte Coefficient, Educational Indicators

Classification of Stroke Using K-Means and Deep Learning Methods

Stroke is a disease caused by blockage or rupture of blood vessels in the brain due to disruption of blood flow, where the blood supply to an area of the brain is suddenly interrupted. This study discusses stroke classification using the K-Means and Deep Learning methods. This study aims to segment patient data to produce patient class labels and classify the results of grouping the data to test the performance of the classification algorithm used. The 4,906 patient data used in this study were grouped using the K-Means method into multiple clusters, including 2 clusters, 3 clusters, 4 clusters, and 5 clusters, and the data grouping findings will be classified. The cluster validation method is the Davies Bouldin Index and the Silhouette Index, while the algorithm used in the classification process is the Deep Learning Algorithm. The classification results produce the most excellent accuracy value in the number of clusters tested, namely 2 clusters of 99.71%.

Mining single-cell time-series datasets with Time Course Inspector

Abstract Summary Thanks to recent advances in live cell imaging of biosensors, microscopy experiments can generate thousands of single-cell time-series. To identify sub-populations with distinct temporal behaviours that correspond to different cell fates, we developed Time Course Inspector (TCI)—a unique tool written in R/Shiny to combine time-series analysis with clustering. With TCI it is convenient to inspect time-series, plot different data views and remove outliers. TCI facilitates interactive exploration of various hierarchical clustering and cluster validation methods. We showcase TCI by analysing a single-cell signalling time-series dataset acquired using a fluorescent biosensor. Availability and implementation https://github.com/pertzlab/shiny-timecourse-inspector. Supplementary information Supplementary data are available at Bioinformatics online.

Hierarchical clustering of mixed variable panel data based on new distance

One of the important aspects of panel data is the poolability of different units in the data set. However, considering that regression parameters (coefficients) are homogeneous across different units, it is normal for the units to be pooled. Clustering may occur in the panel data to solve the problem. In this study, we suggest a new distance for a mixed variable panel data set containing invariant time binary variable, without performing variable conversion to avoid information loss. In this approach, the mixed variable panel data set is divided into pure categorical data and pure numerical data sets. Then, distance measures are calculated using simple matching for the categorical data set and using distance that normalizes all variables in the numerical data set. After distance measures of each data set are combined, the new distance measure is integrated into the agglomerative hierarchical clustering algorithms. The experimental analysis was exemplified by the real data groups using STATA and R software package. The performance of proposed distance is compared with the Gower and K-prototype distances by cluster validation methods. The experimental results demonstrated that the new approach we suggest here provides better clustering results than the Gower and K-prototype approaches.

Developing a municipality typology for modelling decentralised energy systems

One solution to the large-scale integration of renewable energies could be decentralised autonomous municipal energy systems. Several studies have already analysed the technical and economic implications of the mainly decentralised future energy system, but most are restricted in their insights by limited temporal and spatial resolution. This study employs a cluster analysis to develop a municipality typology in order to analyse the techno-economic suitability of municipalities for autonomous energy systems. A total of 34 socio-technical indicators are employed at the municipal level, with a particular focus on the sectors of Private Households and Transport, and the potentials for decentralised renewable energies. Selected quantitative cluster validation methods are employed alongside qualitative criteria to determine the optimal number of clusters. This results in a total of ten clusters, which show a large variation as well as some overlap with respect to specific indicators. An analysis of the municipalities from three German renewable energy projects “Energy Municipalities”, “Bioenergy Villages” and “100% Renewable Energy Regions” shows that in eight of the ten clusters municipalities are aiming for energy autonomy (in varying degrees). It is challenging to differentiate between the clusters regarding readiness for energy autonomy projects, however, especially if the degree of social acceptance and engagement for such projects is to be considered. To answer the more techno-economical part of this question, future work will employ the developed clusters in the context of an energy system optimisation. Insights gained at the municipal level will then be qualitatively transferred to the national context to assess the implications for the whole energy system.

Performance Analysis of Partition and Evolutionary Clustering Methods on Various Cluster Validation Criteria

Large quantity of data has been accumulating tremendously due to digitalization. But the accumulated data are not converted into useful patterns. This gap is conquered by using exploratory data analysis techniques. Clustering is one of the vital technologies in exploratory data analysis. It is a methodology to arrange data objects as per their characteristics. Traditional clustering approaches, namely leader, K-means, ISODATA and evolutionary-based approaches like genetic algorithm, particle swarm optimization, social group optimization methods, are also implemented on benchmark data set. Evolutionary-based clustering methods are derived from the existing hard clustering methods for finding optimal results. Performance analysis of the above clustering techniques should be validated through different cluster validation methods. The performance analysis reveals evolutionary clustering methods convergence rate is better than partition clustering methods. ISODATA performs better in various aspects on large data. In this work analyzed performance of hard and evolutionary clustering methods on execution time, internal cluster validity criteria.

Clustering stability for automated color image segmentation

Abstract Clustering is a well-established technique for segmentation. However, clustering validation is rarely used for this purpose. In this work we adapt a clustering validation method, Clustering Stability (CS), to automatically segment images. CS is not limited by image dimensionality nor by the clustering algorithm. We show clustering and validation acting together as a data-driven process able to find the optimum number of partitions according to our proposed color-texture feature representation. We also describe how to adapt CS to detect the best settings required for feature extraction. The segmentation solutions found by our method are supported by a stability score named STI, which provides an objective quantifiable metric to obtain the final segmentation results. Furthermore, the STI allows to compare multiple alternative solutions and select the most appropriate according to the index meaning. We successfully test our procedure on texture and natural images, and 3D MRI data.

A Systematic Approach to Clustering Whole Trajectories of Mobile Objects in Road Networks

Most of mobile object trajectory clustering analysis to date has been focused on clustering the location points or sub-trajectories extracted from trajectory data. This paper presents TraceMob , a systematic approach to clustering whole trajectories of mobile objects traveling in road networks. TraceMob as a whole trajectory clustering framework has three unique features. First, we design a quality measure for the distance between two whole trajectories. By quality, we mean that the distance measure can capture the complex characteristics of trajectories as a whole including their varying lengths and their constrained movement in the road network space. Second, we develop an algorithm that transforms whole trajectories in a road network space into multidimensional data points in a euclidean space while preserving their relative distances in the transformed metric space. This transformation enables us to effectively shift the clustering task for whole mobile object trajectories in the complex road network space to the traditional clustering task for multidimensional data in a euclidean space. Third, we develop a cluster validation method for evaluating the clustering quality in both the transformed metric space and the road network space. Extensive experimental evaluation with trajectories generated on real road network maps of different cities shows that TraceMob produces higher quality clustering results and outperforms existing approaches by an order of magnitude.

Cluster Validation Method for Determining the Number of Clusters in Categorical Sequences.

Cluster validation, which is the process of evaluating the quality of clustering results, plays an important role for practical machine learning systems. Categorical sequences, such as biological sequences in computational biology, have become common in real-world applications. Different from previous studies, which mainly focused on attribute-value data, in this paper, we work on the cluster validation problem for categorical sequences. The evaluation of sequences clustering is currently difficult due to the lack of an internal validation criterion defined with regard to the structural features hidden in sequences. To solve this problem, in this paper, a novel cluster validity index (CVI) is proposed as a function of clustering, with the intracluster structural compactness and intercluster structural separation linearly combined to measure the quality of sequence clusters. A partition-based algorithm for robust clustering of categorical sequences is also proposed, which provides the new measure with high-quality clustering results by the deterministic initialization and the elimination of noise clusters using an information theoretic method. The new clustering algorithm and the CVI are then assembled within the common model selection procedure to determine the number of clusters in categorical sequence sets. A case study on commonly used protein sequences and the experimental results on some real-world sequence sets from different domains are given to demonstrate the performance of the proposed method.

Selection of global climate models for India using cluster analysis

Global climate models (GCMs) are gaining importance due to their capability to ascertain climate variables that will be useful to develop long, medium and short term water resources planning strategies. The applicability of K-Means cluster analysis is explored for grouping 36 GCMs from Coupled Model Intercomparison Project 5 for maximum temperature (MAXT), minimum temperature (MINT) and a combination of maximum and minimum temperature (COMBT) over India. Cluster validation methods, namely the Davies–Bouldin Index (DBI) and F-statistic, are used to obtain an optimal number of clusters of GCMs for India. The indicator chosen for evaluation of GCMs is the probability density function based skill score. It is noticed that the optimal number of clusters for MAXT, MINT and COMBT scenarios are 3, 2 and 2, respectively. Accordingly, suitable ensembles of GCMs are suggested for India for MAXT, MINT and COMBT individually. The suggested methodology can be extended to any number of GCMs and indicators, with minor modifications.

Comparison of integrated clustering methods for accurate and stable prediction of building energy consumption data

Clustering methods are often used to model energy consumption for two reasons. First, clustering is often used to process data and to improve the predictive accuracy of subsequent energy models. Second, stable clusters that are reproducible with respect to non-essential changes can be used to group, target, and interpret observed subjects. However, it is well known that clustering methods are highly sensitive to the choice of algorithms and variables. This can lead to misleading assessments of predictive accuracy and mis-interpretation of clusters in policymaking.This paper therefore introduces two methods to the modeling of energy consumption in buildings: clusterwise regression, also known as latent class regression, which integrates clustering and regression simultaneously; and cluster validation methods to measure stability. Using a large dataset of multifamily buildings in New York City, clusterwise regression is compared to common two-stage algorithms that use K-means and model-based clustering with linear regression. Predictive accuracy is evaluated using 20-fold cross validation, and the stability of the perturbed clusters is measured using the Jaccard coefficient. These results show that there seems to be an inherent tradeoff between prediction accuracy and cluster stability. This paper concludes by discussing which clustering methods may be appropriate for different analytical purposes.

Cluster validation in problems with increasing dimensionality and unbalanced clusters

Cluster validation methods provide measures to evaluate the quality of a clustering partition on a given data set, and to determine the correct number of clusters. Recently, a new set of validation techniques based on the clusters' negentropy has been introduced. Negentropy-based cluster validation favors data partitions into compact clusters which are not strongly overlapped. Its evaluation is quite simple and it has been shown to perform better than other state of the art techniques. However, like many other cluster validation approaches, it presents problems when validating partitions where some regions contain only a few data points. Different heuristics have been proposed to cope with this problem, which are systematically analyzed in this paper. We study the performance of AIC, BIC, and four negentropy-based validation approaches in synthetic clustering problems of increasing dimensionality, with unbalanced clusters and different degree of overlapping. Our results suggest that negentropy-based validation techniques outperform AIC and BIC when the ratio of the number of points to the dimension is not high, which is a very common situation in most real applications.

Algorithmic paradigms for stability-based cluster validity and model selection statistical methods, with applications to microarray data analysis

The advent of high throughput technologies, in particular microarrays, for biological research has revived interest in clustering, resulting in a plethora of new clustering algorithms. However, model selection, i.e., the identification of the correct number of clusters in a dataset, has received relatively little attention. Indeed, although central for statistics, its difficulty is also well known. Fortunately, a few novel techniques for model selection, representing a sharp departure from previous ones in statistics, have been proposed and gained prominence for microarray data analysis. Among those, the stability-based methods are the most robust and best performing in terms of prediction, but the slowest in terms of time. It is very unfortunate that as fascinating and classic an area of statistics as model selection, with important practical applications, has received very little attention in terms of algorithmic design and engineering. In this paper, in order to partially fill this gap, we make the following contributions: (A) the first general algorithmic paradigm for stability-based methods for model selection; (B) reductions showing that all of the known methods in this class are an instance of the proposed paradigm; (C) a novel algorithmic paradigm for the class of stability-based methods for cluster validity, i.e., methods assessing how statistically significant is a given clustering solution; (D) a general algorithmic paradigm that describes heuristic and very effective speed-ups known in the literature for stability-based model selection methods.Since the performance evaluation of model selection algorithms is mainly experimental, we offer, for completeness and without even attempting to be exhaustive, a representative synopsis of known experimental benchmarking results that highlight the ability of stability-based methods for model selection and the computational resources that they require for the task. As a whole, the contributions of this paper generalize in several respects reference methodologies in statistics and show that algorithmic approaches can yield deep methodological insights into this area, in addition to practical computational procedures.

Pattern recognition approach to identify natural clusters of acoustic emission signals

A new approach is introduced to identify natural clusters of acoustic emission signals. The presented technique is based on an exhaustive screening taking into account all combinations of signal features extracted from the recorded acoustic emission signals. For each possible combination of signal features an investigation of the classification performance of the k-means algorithm is evaluated ranging from two to ten classes. The numerical degree of cluster separation of each partition is calculated utilizing the Davies–Bouldin and Tou indices, Rousseeuw’s silhouette validation method and Hubert’s Gamma statistics. The individual rating of each cluster validation technique is cumulated based on a voting scheme and is evaluated for the number of clusters with best performance. This is defined as the best partitioning for the given signal feature combination. As a second step the numerical ranking of all these partitions is evaluated for the globally optimal partition in a second voting scheme using the cluster validation methods results. This methodology can be used as an automated evaluation of the number of natural clusters and their partitions without previous knowledge about the cluster structure of acoustic emission signals. The suitability of the current approach was evaluated using artificial datasets with defined degree of separation. In addition the application of the approach to clustering of acoustic emission signals is demonstrated for signals obtained from failure during loading of carbon fiber reinforced plastic specimens.

Segmentation of Hyperspectral Images via Subtractive Clustering and Cluster Validation Using One-Class Support Vector Machines

This paper presents an unsupervised hyperspectral image segmentation with a new subtractive-clustering-based similarity segmentation and a novel cluster validation method using one-class support vector (SV) machine (OC-SVM). An estimation of the correct number of clusters is an important task in hyperspectral image segmentation. The proposed cluster validity measure is based on the power of spectral discrimination (PWSD) measure and utilizes the advantage of the inherited cluster contour definition feature of OC-SVM. Hence, this novel cluster validity method is referred to as SV-PWSD. SVs found by OC-SVM are located at the minimum distance to the hyperplane in the feature space and at the arbitrarily shaped cluster contours in the input space. SV-PWSD guides the segmentation/clustering process to find the optimal number of clusters in hyperspectral data. Because of the high computational load of subtractive clustering and OC-SVM, a subset of the image (only ground-truth data) is initially used in the clustering and validation phases. Then, it is proposed to use <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -nearest neighbor classification, with the already clustered subset being used as training data, to project the initial clustering results onto the entire data set.

SC2ATmd: a tool for integration of the figure of merit with cluster analysis for gene expression data

Standard and Consensus Clustering Analysis Tool for Microarray Data (SC²ATmd) is a MATLAB-implemented application specifically designed for the exploration of microarray gene expression data via clustering. Implementation of two versions of the clustering validation method figure of merit allows for performance comparisons between different clustering algorithms, and tailors the cluster analysis process to the varying characteristics of each dataset. Along with standard clustering algorithms this application also offers a consensus clustering method that can generate reproducible clusters across replicate experiments or different clustering algorithms. This application was designed specifically for the analysis of gene expression data, but may be used with any numerical data as long as it is in the right format. SC²ATmd may be freely downloaded from http://www.compbiosci.wfu.edu/tools.htm.

Multi-objective selection for collecting cluster alternatives

Grouping objects into different categories is a basic means of cognition. In the fields of machine learning and statistics, this subject is addressed by cluster analysis. Yet, it is still controversially discussed how to assess the reliability and quality of clusterings. In particular, it is hard to determine the optimal number of clusters inherent in the underlying data. Running different cluster algorithms and cluster validation methods usually yields different optimal clusterings. In fact, several clusterings with different numbers of clusters are plausible in many situations, as different methods are specialized on diverse structural properties. To account for the possibility of multiple plausible clusterings, we employ a multi-objective approach for collecting cluster alternatives (MOCCA) from a combination of cluster algorithms and validation measures. In an application to artificial data as well as microarray data sets, we demonstrate that exploring a Pareto set of optimal partitions rather than a single solution can identify alternative solutions that are overlooked by conventional clustering strategies. Competitive solutions are hereby ranked following an impartial criterion, while the ultimate judgement is left to the investigator.

Adaptive motor unit potential train validation using MUP shape information

A decomposed electromyographic (EMG) signal provides information that can be used clinically or for physiological investigation. However, in all instances the validity of the extracted motor unit potential trains (MUPTs) must first be determined because, as with all pattern recognition applications, errors will occur during decomposition. Moreover, detecting invalid MUPTs during EMG signal decomposition can enhance decompositions results. Eight methods to validate an extracted MUPT using its motor unit potential (MUP) shape information were studied. These MUPT validation methods are based on existing cluster analysis algorithms, four were newly developed adaptive methods and four were classical cluster validation methods. The methods evaluate the shapes of the MUPs of a MUPT to determine whether the MUPT represents the activity of a single motor unit (i.e. it is a valid MUPT) or not. Evaluation results using both simulated and real data show that the newly developed adaptive methods are sufficiently fast and accurate to be used during or after the decomposition of EMG signals. The adaptive gap-based Duda and Hart (AGDH) method had significantly better accuracies in correctly categorizing the MUPTs extracted during decomposition (91.3% and 94.7% for simulated and real data, respectively; assuming 12.7% of the extracted MUPTs are on average invalid). The accuracy with which invalid MUPTs can be detected is dependent on the similarity of the MUP templates of the MUPTs merged to create the invalid train and suggests the need, in some cases, for the combined use of motor unit firing pattern and MUP shape information.

Relational visual cluster validity (RVCV)

The assessment of cluster validity plays a very important role in cluster analysis. Most commonly used cluster validity methods are based on statistical hypothesis testing or finding the best clustering scheme by computing a number of different cluster validity indices. A number of visual methods of cluster validity have been produced to display directly the validity of clusters by mapping data into two- or three-dimensional space. However, these methods may lose too much information to correctly estimate the results of clustering algorithms. Although the visual cluster validity (VCV) method of Hathaway and Bezdek can successfully solve this problem, it can only be applied for object data, i.e. feature measurements. There are very few validity methods that can be used to analyze the validity of data where only a similarity or dissimilarity relation exists – relational data. To tackle this problem, this paper presents a relational visual cluster validity (RVCV) method to assess the validity of clustering relational data. This is done by combining the results of the non-Euclidean relational fuzzy c-means (NERFCM) algorithm with a modification of the VCV method to produce a visual representation of cluster validity. RVCV can cluster complete and incomplete relational data and adds to the visual cluster validity theory. Numeric examples using synthetic and real data are presented.