Right Number Of Clusters Research Articles

Influence of Backpack Carriage and Walking Speed on Muscle Synergies in Healthy Children.

Four to five muscle synergies account for children's locomotion and appear to be consistent across alterations in speed and slopes. Backpack carriage induces alterations in gait kinematics in healthy children, raising questions regarding the clinical consequences related to orthopedic and neurological diseases and ergonomics. However, to support clinical decisions and characterize backpack carriage, muscle synergies can help with understanding the alterations induced in this condition at the motor control level. In this study, we investigated how children adjust the recruitment of motor patterns during locomotion, when greater muscular demands are required (backpack carriage). Twenty healthy male children underwent an instrumental gait analysis and muscle synergies extraction during three walking conditions: self-selected, fast and load conditions. In the fast condition, a reduction in the number of synergies (three to four) was needed for reconstructing the EMG signal with the same accuracy as in the other conditions (three to five). Synergies were grouped in only four clusters in the fast condition, while five clusters were needed for the self-selected condition. The right number of clusters was not clearly identified in the load condition. Speed and backpack carriage altered nearly every spatial-temporal parameter of gait, whereas kinematic alterations reflected mainly hip and pelvis adaptations. Although the synergistic patterns were consistent across conditions, indicating a similar motor pattern in different conditions, the fast condition required fewer synergies for reconstructing the EMG signal with the same level of accuracy.

An Improved K-Means Clustering Process Solicitation for Mine Blood Donors Information

The exponential rise in accidents and the introduction of new, supposedly trendy ways of living have contributed to the dire need for the needy to have an organ or blood transfusion. Circumstances refer to a circumstance where proper care should be taken when collecting the necessary blood or original parts for transfusion, typically in dire circumstances. To determine the distance at which the interested and qualified donors are located, a thorough investigation must be conducted. People are often first categorized according to their blood type, eligibility, and region. Following that, people group together according to locality. A healthy person can safely donate blood twice within 56 days, as this is the minimal time between successful donations that has been established as a norm. The decision to donate an organ is often made after careful consideration of the severity of the situation, the donor's health, and the health of the recipient. Knowledge data finding tasks can be made easier with the help of KEEL, an open-source programme. The graphs that are produced show clearly how the proposed algorithm varies from the standard K-means method. Therefore, it will be quite useful in the present day and could end up saving lots of lives. The necessity to decide ahead of time on the total number of groups is just one of the issues with the K-means clustering method. In practise, it is difficult to anticipate the precise number of clusters. When the number of clusters is small, incongruous clustering is more common, but when the number of clusters is large, like clustering is more common. Thanks to a method called Active Cluster with Modified k-means clustering, which finds the right number of clusters on the fly, the issue is now resolved

K-Means Hybridization with Enhanced Firefly Algorithm for High-Dimension Automatic Clustering

K-means clustering is not able to select the right number of clusters of data items having high-dimension. So, for determining the ideal number of clusters, we have combined PCA with the Silhouette and Elbow approaches. Additionally, we have a large number of meta-heuristic swarm intelligence algorithms which is influenced by nature and were previously used to solve the automatic data clustering problem. Firefly offers reliable and effective automatic data clustering. The Firefly algorithm automatically divides the entire population into subpopulations, which slows down the convergence and reduces the of capturing local minima in high-dimensional optimization problems. Thus, for automatic clustering, we demonstrated an improved firefly, i.e., we offered a hybridized K-means with an ODFA model. The experimental section displays the results and graphs for the Silhouette, Elbow, and Firefly algorithms.

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

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

Two-step clustering-based pipeline for big dynamic functional network connectivity data.

BackgroundDynamic functional network connectivity (dFNC) estimated from resting-state functional magnetic imaging (rs-fMRI) studies the temporally varying functional integration between brain networks. In a conventional dFNC pipeline, a clustering stage to summarize the connectivity patterns that are transiently but reliably realized over the course of a scanning session. However, identifying the right number of clusters (or states) through a conventional clustering criterion computed by running the algorithm repeatedly over a large range of cluster numbers is time-consuming and requires substantial computational power even for typical dFNC datasets, and the computational demands become prohibitive as datasets become larger and scans longer. Here we developed a new dFNC pipeline based on a two-step clustering approach to analyze large dFNC data without having access to huge computational power.MethodsIn the proposed dFNC pipeline, we implement two-step clustering. In the first step, we randomly use a sub-sample dFNC data and identify several sets of states at different model orders. In the second step, we aggregate all dFNC states estimated from all iterations in the first step and use this to identify the optimum number of clusters using the elbow criteria. Additionally, we use this new reduced dataset and estimate a final set of states by performing a second kmeans clustering on the aggregated dFNC states from the first k-means clustering. To validate the reproducibility of results in the new pipeline, we analyzed four dFNC datasets from the human connectome project (HCP).ResultsWe found that both conventional and proposed dFNC pipelines generate similar brain dFNC states across all four sessions with more than 99% similarity. We found that the conventional dFNC pipeline evaluates the clustering order and finds the final dFNC state in 275 min, while this process takes only 11 min for the proposed dFNC pipeline. In other words, the new pipeline is 25 times faster than the traditional method in finding the optimum number of clusters and finding the final dFNC states. We also found that the new method results in better clustering quality than the conventional approach (p < 0.001). We show that the results are replicated across four different datasets from HCP.ConclusionWe developed a new analytic pipeline that facilitates the analysis of large dFNC datasets without having access to a huge computational power source. We validated the reproducibility of the result across multiple datasets.

Comparison of clustering in tuberculosis using fuzzy c-means and k-means methods

Tuberculosis (TB) is a health problem that has yet to be resolved in Indonesia. Based on WHO data, in 2021 Indonesia will still be in the third rank of the highest TB cases in the world. This study aims to determine how many groups of TB patients are based on age, gender, HIV status, history of diabetes mellitus, chest X-ray, and the results of the Molecular Rapid Test (TCM). The data used in this study were 985 from 2017 to 2020. The method used in this research is K-Nearest Neighbor (KNN) in carrying out the imputation process, as well as comparing the k-means and Fuzzy C-Means (FCM) methods in classifying TB data. Before doing the grouping, the data cleaning process is carried out by an imputation process which is useful for filling in the missing data in this case, using the KNN method. To produce maximum results of data grouping or clustering, it is necessary to determine the right number of clusters. For this reason, this study tries to compare the elbow, silhouette coefficient, and Davies Bouldin Index (DBI) methods. The application of the KNN method in the data imputation process in this study is to use k=5. The application of the K-Means algorithm is to form groups of TB patients based on six features. Determination of the optimal number of clusters using the K-means and FCM methods shows the optimal number of clusters, namely K = 2 but with different values. The results of the clustering test using the elbow method with the K-means and FCM methods are 93288.49. The DBI value for the K-means and FCM methods is 0.4937. Meanwhile, the clustering trial with the silhouette coefficient on K-means yields a value of 0.6318 which is better than the FCM which produces a value of 0.6321. This shows that the results of clustering k-means with silhouette coefficients produce better cluster quality because they have a lower silhouette coefficient value than FCM.

A Novel Hybrid Clustering Approach Based on Black Hole Algorithm for Document Clustering

In information retrieval and text mining, document clustering is a big challenge because the amount of document collection has been increasing, day by day. The problem of clustering is NP-hard, use of meta-heuristic algorithms to solve these problems could be an effective method. When the solution space is large, traditional methods are unable to find a solution in a reasonable amount of time. K-means is a heuristic clustering algorithm, two main issues with heuristic algorithms are the early convergence and trapping in local optima. Moreover, finding the right number of clusters is one of the main drawbacks of the k-means algorithm. The correct value of k is always confusing, different researchers used different methods to solve this problem. To overcome these mentioned problems, this study presents a novel Hybrid approach for document clustering. One of the challenges in existing BH algorithm is the input data type. Recently, the algorithm was only accepting textual data. Another flaw in the existing model is that it doesn&#x2019;t choose how many clusters k to form automatically, and the centroids are chosen at random in it. In this paper, we have constructed a Hybrid cluster identification approach which consists of the Elbow method and Silhouette score for cluster k identification. This paper mainly offers three novel combination of model to represent text documents, namely i) K-mean++ - BH + TF-IDF with fix k ii) K-mean++ - BH + W2V with fix k iii) Hybrid Black Hole with automated k. The proposed improvements have validated on the document clustering problem. Cluster analysis based on two evaluation measures, external (Purity) and internal measures (Silhouette score) are used to report the findings. Experiments have been carried out on the four al-phanumeric datasets (Doc50, Reuters, WebKB and News20) as well as on two numeric datasets (Iris and Wine) respectively. The complete result analysis is reported in detail with respect to each research contribution to compare the performance of the proposed algorithm with existing clustering methods. Result shows that the proposed Hybrid BH algorithm outperforms better than the existing clustering methods for all datasets. The clustering of data with and without stop words is examined; additionally, the two alternative word embedding used for data exploration in conjunction with proposed model are also evaluated. In the present study, proposed Hybrid BH algorithm handles the optimal value of k efficiently. This is one of the major contributions of the paper, concluded that Hybrid Black Hole is an effective algorithm for cluster analysis.

New internal clustering validation measure for contiguous arbitrary‐shape clusters

In this study a new internal clustering validation index is proposed. It is based on a measure of the uniformity of the data in clusters. It uses the local density of each cluster, in particular, the normalized variability of the density within the clusters to find the ideal partition. The new validity measure allows it to capture the spatial pattern of the data and obtain the right number of clusters in an automatic way. This new approach, unlike the traditional one that usually identifies well-separated compact clouds, works with arbitrary-shape clusters that may be contiguous or even overlapped. The proposed clustering measure has been evaluated on nine artificial data sets, with different cluster distributions and an increasing number of classes, on three highly nonlinear data sets, and on 17 real data sets. It has been compared with nine well-known clustering validation indices with very satisfactory results. This proves that including density in the definition of clustering validation indices may be useful to identify the right partition of arbitrary-shape and different-size clusters.

Cluster Validity Index to Determine the Optimal Number Clusters of Fuzzy Clustering for Classify Customer Buying Behavior

One of the strategies in order to compete in Batik MSMEs is to look at the characteristics of the customer. To make it easier to see the characteristics of customer buying behavior, it is necessary to classify customers based on similarity of characteristics using fuzzy clustering. One of the parameters that must be determined at the beginning of the fuzzy clustering method is the number of clusters. Increasing the number of clusters does not guarantee the best performance, but the right number of clusters greatly affects the performance of fuzzy clustering. So to get optimal number cluster, we can measured the result of clustering in each number cluster using the cluster validity index. From several types of cluster validity index, NPC give the best value. Optimal number cluster that obtained by the validity index is 2 and this number cluster give classify result with small variance value

Dynamic Time Warping Clustering to Discover Socioeconomic Characteristics in Smart Water Meter Data

Socio-economic characteristics are influencing the temporal and spatial variability of water demand - the biggest source of uncertainties within water distribution system modeling. Improving our knowledge on these influences can be utilized to decrease demand uncertainties. This paper aims to link smart water meter data to socio-economic user characteristics by applying a novel clustering algorithm that uses dynamic time warping on daily demand patterns. The approach is tested on simulated and measured single family home datasets. We show that the novel algorithm performs better compared to commonly used clustering methods, both, in finding the right number of clusters as well as assigning patterns correctly. Additionally, the methodology can be used to identify outliers within clusters of demand patterns. Furthermore, this study investigates which socio-economic characteristics (e.g. employment status, number of residents) are prevalent within single clusters and, consequently, can be linked to the shape of the cluster's barycenters. In future, the proposed methods in combination with stochastic demand models can be used to fill data-gaps in hydraulic models.

Clustering of modal-valued symbolic data

Symbolic Data Analysis is based on special descriptions of data - symbolic objects (SO). Such descriptions preserve more detailed information about units and their clusters than the usual representations with mean values. A special kind of symbolic object is a representation with frequency or probability distributions (modal values). This representation enables us to consider in the clustering process the variables of all measurement types at the same time. In the paper a clustering criterion function for SOs is proposed such that the representative of each cluster is again composed of distributions of variables' values over the cluster. The corresponding leaders clustering method is based on this result. It is also shown that for the corresponding agglomerative hierarchical method a generalized Ward's formula holds. Both methods are compatible - they are solving the same clustering optimization problem. The leaders method efficiently solves clustering problems with large number of units; while the agglomerative method can be applied alone on the smaller data set, or it could be applied on leaders, obtained with compatible nonhierarchical clustering method. Such a combination of two compatible methods enables us to decide upon the right number of clusters on the basis of the corresponding dendrogram. The proposed methods were applied on different data sets. In the paper, some results of clustering of ESS data are presented.

Defeat and entrapment: more than meets the eye? Applying network analysis to estimate dimensions of highly correlated constructs

BackgroundDefeat and entrapment have been shown to be of central relevance to the development of different disorders. However, it remains unclear whether they represent two distinct constructs or one overall latent variable. One reason for the unclarity is that traditional factor analytic techniques have trouble estimating the right number of clusters in highly correlated data. In this study, we applied a novel approach based on network analysis that can deal with correlated data to establish whether defeat and entrapment are best thought of as one or multiple constructs.MethodsExplanatory graph analysis was used to estimate the number of dimensions within the 32 items that make up the defeat and entrapment scales in two samples: an online community sample of 480 participants, and a clinical sample of 147 inpatients admitted to a psychiatric hospital after a suicidal attempt or severe suicidal crisis. Confirmatory Factor analysis (CFA) was used to test whether the proposed structure fits the data.ResultsIn both samples, bootstrapped exploratory graph analysis suggested that the defeat and entrapment items belonged to different dimensions. Within the entrapment items, two separate dimensions were detected, labelled internal and external entrapment. Defeat appeared to be multifaceted only in the online sample. When comparing the CFA outcomes of the one, two, three and four factor models, the one factor model was preferred.ConclusionsDefeat and entrapment can be viewed as distinct, yet, highly associated constructs. Thus, although replication is needed, results are in line with theories differentiating between these two constructs.

A Primer on Cluster Analysis by James C. Bezdek [By the Book

This book focuses on four widely used basic clustering methods suitable for most unlabeled data. The algorithms are k-means, fuzzy c-means (FCM), expectation maximization (EM), and a couple for relational clustering (sequential, agglomerative, hierarchical, and nonoverlapping). There is also a discussion of how to choose the right number of clusters for each approach. This includes internal and external validity measures for the clusters obtained by applying an algorithm. The book includes more than the four basic methods when variants and competitors are noted during discussions of the methods, and it dives into clustering approaches for big data. At the end of the chapters are historical notes, exercises, and additional examples of other algorithms. To whom is this book useful? If you have read this far, it is likely you. It is especially valuable for someone just starting to use clustering who wants background information on major underlying approaches. There are many nicely illustrated examples of clustering and validation of clusters. It is also of interest to people who know about clustering and use/develop algorithms. The book has a deep, rigorous mathematical treatment of the subject and covers work in an area with which only few are completely familiar. The historical notes are likely to be informational to most. Finally, if you teach a course on clustering, this would serve as a great textbook. It includes a deep discussion of algorithms and their variations with exercises, then moves to the modern problem of clustering big-data sets. It also shows how to evaluate the resulting partition (set of clusters). To whom is this book useful? If you have read this far, it is likely you. It is especially valuable for someone just starting to use clustering who wants background information on major underlying approaches. There are many nicely illustrated examples of clustering and validation of clusters. It is also of interest to people who know about clustering and use/develop algorithms. The book has a deep, rigorous mathematical treatment of the subject and covers work in an area with which only few are completely familiar. The historical notes are likely to be informational to most. Finally, if you teach a course on clustering, this would serve as a great textbook. It includes a deep discussion of algorithms and their variations with exercises, then moves to the modern problem of clustering big-data sets. It also shows how to evaluate the resulting partition (set of clusters).

Methods for geographic profiling of biological invasions with multiple origin sites

Geographic profiling is a method that proved to be useful also in order to investigate the point of origin of a biological invasion. K-means clustering and Voronoi diagrams can partition a data set of geographic positions of populations invading a defined area and are, therefore, useful in cases in which an invasion had more introduction events as points of origin. One critical point of the method is to identify the right number of clusters in which to divide the starting data set formed by groups of points on a map. The Silhouette method proved to be capable of identifying the best number of subsets (clusters) of the general set of observations by providing different values for different subdivisions of the set of observations in clusters. For each cluster, the corresponding Voronoi tessellation was built on the starting map. To test the method, we did a simulation of clusters of data (points) on a map and we verified whether the proposed methods worked efficiently with the simulated data set with hundred repeats and using a varying number of clusters on the same map. The used techniques revealed to be efficient in finding the highest probability area of the map that would include the starting points for each cluster. A case study consisted in a known data set, that is, the spreading pattern of Caulerpa racemosa var. cylindracea (sea grapes), that was compatible (highest probability) with an original point of introduction in southern Italy and long distance (thousands of kilometers) secondary spreads via anthropic dispersal. The proposed techniques may also be applied to other kinds of data sets of biological data distributed on a map or in general on a geometrical surface.

Assessing variation in life‐history tactics within a population using mixture regression models: a practical guide for evolutionary ecologists

Mixed models are now well-established methods in ecology and evolution because they allow accounting for and quantifying within- and between-individual variation. However, the required normal distribution of the random effects can often be violated by the presence of clusters among subjects, which leads to multi-modal distributions. In such cases, using what is known as mixture regression models might offer a more appropriate approach. These models are widely used in psychology, sociology, and medicine to describe the diversity of trajectories occurring within a population over time (e.g. psychological development, growth). In ecology and evolution, however, these models are seldom used even though understanding changes in individual trajectories is an active area of research in life-history studies. Our aim is to demonstrate the value of using mixture models to describe variation in individual life-history tactics within a population, and hence to promote the use of these models by ecologists and evolutionary ecologists. We first ran a set of simulations to determine whether and when a mixture model allows teasing apart latent clustering, and to contrast the precision and accuracy of estimates obtained from mixture models versus mixed models under a wide range of ecological contexts. We then used empirical data from long-term studies of large mammals to illustrate the potential of using mixture models for assessing within-population variation in life-history tactics. Mixture models performed well in most cases, except for variables following a Bernoulli distribution and when sample size was small. The four selection criteria we evaluated [Akaike information criterion (AIC), Bayesian information criterion (BIC), and two bootstrap methods] performed similarly well, selecting the right number of clusters in most ecological situations. We then showed that the normality of random effects implicitly assumed by evolutionary ecologists when using mixed models was often violated in life-history data. Mixed models were quite robust to this violation in the sense that fixed effects were unbiased at the population level. However, fixed effects at the cluster level and random effects were better estimated using mixture models. Our empirical analyses demonstrated that using mixture models facilitates the identification of the diversity of growth and reproductive tactics occurring within a population. Therefore, using this modelling framework allows testing for the presence of clusters and, when clusters occur, provides reliable estimates of fixed and random effects for each cluster of the population. In the presence or expectation of clusters, using mixture models offers a suitable extension of mixed models, particularly when evolutionary ecologists aim at identifying how ecological and evolutionary processes change within a population. Mixture regression models therefore provide a valuable addition to the statistical toolbox of evolutionary ecologists. As these models are complex and have their own limitations, we provide recommendations to guide future users.

Clustering with a Novel Global Harmony Search Algorithm for Image Segmentation

A state-feedback based harmony search (SFHS) algorithm to clustering data is presented to solve the problems that the traditional evolutionary-based clustering algorithms easily trap into the local optimum. Firstly, the state-feedback mechanism is introduced into HS algorithm, and the harmony memory difference metric is defined to adaptively adjust harmony memory considering rate and pitch adjusting bandwidth, which makes the convergence and efficiency of the harmony search (HS) algorithm improved obviously. Secondly, in the SFHS-based clustering algorithm, the decision variables in the harmony vector represent cluster centers, and the harmony vector represents a partition of data, the best partition of data can be obtained by updating the harmony memory. Finally, a novel validity metric is presented to determine the right number of clusters. Simulation experiments have been carried out on remote sensing images and animal images, and the relevant results are compared with the ANT-based clustering algorithm and the traditional HS-based clustering algorithms, it shows that the SFHS-based clustering algorithm has better convergence.

Afan Oromo Sense Clustering in Hierarchical and Partitional Techniques

This paper presents the sense clustering of multi-sense words in Afan Oromo. The main idea of this work is to cluster contexts which is providing a useful way to discover semantically related senses. The similar contexts of a given senses of target word are clustered using three hierarchical and two partitional clustering. All contexts of related senses are included in the clustering and thus performed over all the contexts in the corpus. The underlying hypothesis is that clustering captures the reflected unity among the contexts and each cluster reveal possible relationships existing among the contexts. As the experiment shows, from the total five clusters, the EM and K-Means clusters which yield significantly higher accuracy than hierarchical (single clustering, complete clustering and average clustering) result. For Afan Oromo, EM and K-means enhance the accuracy of sense clustering than hierarchical clustering algorithms. Each cluster representing a unique sense. Some words have two senses to the five senses. As the result shows an average accuracy of test set was 85.5% which is encouraging with the unsupervised machine learning work. By using this approach, finding the right number of clusters is equivalent to finding the number of senses. The achieved result was encouraging, despite it is less resource requirement.

A novel iterative partitioning approach for building prime clusters

Cluster analysis is an iterative process of knowledge discovery by segregating the data objects into significant and logical groups. An efficient clustering algorithm will produce groups of similar objects which are tightly bonded within the groups and independent between groups. In this paper, we propose a new iterative, non-parametric, partitioning clustering algorithm called prime equivalence clustering algorithm PECA based on computation of distance to subsets of attributes where object values are closer. The right number of clusters and the final partition of the datasets are automatically determined without any prior knowledge. The performance of this algorithm has been studied on benchmark datasets and it is proven better than the well-known clustering algorithms.

A hybrid clustering technique combining a novel genetic algorithm with K-Means

Many existing clustering techniques including K-Means require a user input on the number of clusters. It is often extremely difficult for a user to accurately estimate the number of clusters in a data set. The genetic algorithms (GAs) generally determine the number of clusters automatically. However, they typically choose the genes and the number of genes randomly. If we can identify the right genes in the initial population then GAs have better possibility to produce a high quality clustering result than the case when we randomly choose the genes. We propose a novel GA based clustering technique that is capable of automatically finding the right number of clusters and identifying the right genes through a novel initial population selection approach. With the help of our novel fitness function, and gene rearrangement operation it produces high quality cluster centers. The centers are then fed into K-Means as initial seeds in order to produce an even higher quality clustering solution by allowing the initial seeds to readjust as needed. Our experimental results indicate a statistically significant superiority (according to the sign test analysis) of our technique over five recent techniques on twenty natural data sets used in this study based on six evaluation criteria.

Clustering of electrical transmission systems based on network topology and stability

A proper understanding and modelling of the behaviour of heavily loaded large-scale electrical transmission systems is essential for a secure and uninterrupted operation. In this paper, we present methods to cluster electrical power networks based on different criteria into regions. These regions are useful for the efficient modelling of large transcontinental electricity networks, switching operation decisions or placement of redundant parts of the monitoring and control system. In alternating current electricity networks, power oscillations are normal, but they can become dangerous if they build up. The first approach uses the correlation between results of a stability assessment for these oscillations at every node for the cluster criterion. The second method concentrates on the network topology and uses spectral clustering on the network graph to create clusters where all nodes are interconnected. In this work, we also discuss the problem how to choose the right number of clusters and how the discussed clustering methods can be used for an efficient modelling of large electricity networks or in protection and control systems.