Clustering method for fMRI activation detection using optimal number of clusters

Active and Passive Methods of Detecting Parkinson's Disease.

Clustering is a group of unsupervised statistical techniques commonly used in many disciplines. Considering their applications to fish abundance data, many technical details need to be considered to ensure reasonable interpretation. However, the reliability and stability of the clustering methods have rarely been studied in the contexts of fisheries. This study presents an intensive evaluation of three common clustering methods, including hierarchical clustering (HC), K-means (KM), and expectation-maximization (EM) methods, based on fish community surveys in the coastal waters of Shandong, China. We evaluated the performances of these three methods considering different numbers of clusters, data size, and data transformation approaches, focusing on the consistency validation using the index of average proportion of non-overlap (APN). The results indicate that the three methods tend to be inconsistent in the optimal number of clusters. EM showed relatively better performances to avoid unbalanced classification, whereas HC and KM provided more stable clustering results. Data transformation including scaling, square-root, and log-transformation had substantial influences on the clustering results, especially for KM. Moreover, transformation also influenced clustering stability, wherein scaling tended to provide a stable solution at the same number of clusters. The APN values indicated improved stability with increasing data size, and the effect leveled off over 70 samples in general and most quickly in EM. We conclude that the best clustering method can be chosen depending on the aim of the study and the number of clusters. In general, KM is relatively robust in our tests. We also provide recommendations for future application of clustering analyses. This study is helpful to ensure the credibility of the application and interpretation of clustering methods.

BackgroundCluster analysis is the most common unsupervised method for finding hidden groups in data. Clustering presents two main challenges: (1) finding the optimal number of clusters, and (2) removing “outliers” among the objects being clustered. Few clustering algorithms currently deal directly with the outlier problem. Furthermore, existing methods for identifying the number of clusters still have some drawbacks. Thus, there is a need for a better algorithm to tackle both challenges.ResultsWe present a new approach, implemented in an R package called Thresher, to cluster objects in general datasets. Thresher combines ideas from principal component analysis, outlier filtering, and von Mises-Fisher mixture models in order to select the optimal number of clusters. We performed a large Monte Carlo simulation study to compare Thresher with other methods for detecting outliers and determining the number of clusters. We found that Thresher had good sensitivity and specificity for detecting and removing outliers. We also found that Thresher is the best method for estimating the optimal number of clusters when the number of objects being clustered is smaller than the number of variables used for clustering. Finally, we applied Thresher and eleven other methods to 25 sets of breast cancer data downloaded from the Gene Expression Omnibus; only Thresher consistently estimated the number of clusters to lie in the range of 4–7 that is consistent with the literature.ConclusionsThresher is effective at automatically detecting and removing outliers. By thus cleaning the data, it produces better estimates of the optimal number of clusters when there are more variables than objects. When we applied Thresher to a variety of breast cancer datasets, it produced estimates that were both self-consistent and consistent with the literature. We expect Thresher to be useful for studying a wide variety of biological datasets.

A fundamental problem in data clustering is how to determine the correct number of clusters. The k-adaptive medoid set ant colony optimization (ACO) clustering (METACOC-K) algorithm is superior in solving clustering problems. However, METACOC-K does not guarantee in finding the best number of clusters. It assumed the number of clusters based on an adaptive parameter strategy that lacks feedback learning. This has restrained the algorithm in producing compact clusters and the optimal number of clusters. In this paper, a self-adaptive ACO clustering (S-ACOC) algorithm is proposed to produce the optimal number of clusters by incorporating a self-adaptive parameter strategy. The S-ACOC algorithm is a centroid-based algorithm that automatically adjusts the number of clusters during the algorithm run. The selection of the number of clusters is based on a construction graph that reflects the influence of a pheromone in algorithm learning. Experiments were conducted on real-world datasets to evaluate the performance of the proposed algorithm. The external evaluation metrics (purity, F-measure, and entropy) were used to compare the results of the proposed algorithm with other swarm clustering algorithms, including a genetic algorithm (GA), particle swarm optimization (PSO), and METACOC-K. Results showed that S-ACOC provides higher purity (50%) and lower entropy (40%) than GA, PSO, and METACOC-K. Experiments were also performed on several predefined clusters, and results demonstrate that the S-ACOC algorithm is superior to GA, PSO, and METACOC-K. Based on the superior performance, S-ACOC can be used to solve clustering problems in various application domains.

With the development of shale gas reservoirs, various fracture propagation models have been developed to predict hydraulic fracture geometry by considering the stress shadow effects. Also, many researchers have been working on development of various production-simulation approaches to simulate production from the complex fracture geometries. The objective of this study is to combine the fracture propagation modeling and reservoir simulation to optimize production in shale gas reservoirs. First, we have developed a semi-analytical model to simulate shale gas production from the complex non-planar fracture geometry with varying fracture width and fracture permeability along fracture length. The important gas transport mechanisms including gas slippage, gas diffusion, and gas desorption are considered. Second, we integrate the semi-analytical model with a three-dimensional fracture propagation model, which fully couples elastic deformation of the rock and fluid flow to simulate complex hydraulic fracture propagation, to optimize fracture treatment design in Marcellus shale gas reservoirs. Specifically, the fracture propagation model is utilized to predict the more-realistic non-planar fracture geometry with varying fracture width and fracture permeability along fracture length. In this study, the effect of varying number of perforation clusters within a given stage ranging from 2 to 5 on the fracture propagation was investigated. Three values of stage spacing were considered including 100 ft, 200 ft, and 300 ft. After predicting the non-planar fracture geometry, the semi-analytical model is employed to simulate production from such fracture geometries. According to the well productivity, the optimal number of clusters per stage for varying stage spacing is discussed and determined. In addition, we compared the well performance with the optimal number of perforation clusters for the stage spacing of 100 ft, 200 ft, and 300 ft under a given horizontal well length of 2,500 ft. Furthermore, we used the integrated approach to analyze a well performance from Marcellus shale gas reservoirs. Through the field case study, the more-realistic non-planar fracture geometry was quantified. Also, the difference between the non-planar fracture geometry and ideal planar fracture geometry with equal fracture width and fracture half-length was compared. Finally, the optimal fracture treatment design for the field well development was recommended. This work can provide new insights into optimization of number of perforation clusters per stage within a given fracture stage and a better understanding of the non-planar fracture geometry in shale gas reservoirs.

Averaging amplitudes over consecutive time samples (i.e., time window) is widely used to calculate the peak amplitude of event-related potentials (ERPs). Cluster analysis of the spatio-temporal ERP data is a promising tool to determine the time window of an ERP of interest. However, determining an appropriate number of clusters to optimally represent ERPs is still challenging. Here, we develop a new method to estimate the optimal number of clusters utilizing consensus clustering. Various polarity dependent clustering methods, namely, k-means, hierarchical clustering, fuzzy c-means, self-organizing map, spectral clustering, and Gaussian mixture model, are used to configure consensus clustering after assessing them individually. When a range of clusters is applied many times, the optimal number of clusters should correspond to the expectation, which is the average of the obtained mean inner-similarities of estimated time windows across all conditions and groups converge in the satisfactory thresholds. In order to assess our method, the proposed method has been applied to simulated data and prospective memory experiment ERP data aimed to qualify N2 and P3, and N300 and prospective positivity components, respectively. The results of determining the optimal number of clusters meet at six cluster maps for both ERP data. In addition, our results revealed that the proposed method could be reliably applied to ERP data to determine the appropriate time window for the ERP of interest when the measurement interval is not accurately defined.

The MR brain image analysis is used to extract clinical information that improve diagnosis and treatment of disease. Brain tumors are one of the most common brain diseases. Clustering is a process for segmenting and classifying objects. There are many clustering strategies such as the hard clustering scheme and the fuzzy clustering scheme, each of them has its own special characteristics. In this work Fuzzy C-Mean clustering was implemented to segment three abnormal brain MR images, and the performance of it was analyised. This algorithms was applied to cluster the images into different clusters number: 5-9 with different values of membership grade: 0.50-0.90 with steps of 0,05 for each cluster number. The percentage of the unclassified pixels that were produced from implementing FCM algorithm with different configuration was calculated. The minimum values of the objective function of the FCM algorithm for different number of clusters and for different membership grade values were also calculated. The results showed that an optimal number of clusters that corresponds to optimal segmentation error is depending on the slice condition. In this experiment, the optimal cluster number was found to be 6. The fluctuation around this number is affected also by the anatomical structure of the slice. In addition, it can be concluded that the objective function may not be the superior criterion for the judgments of goodness, where it may be a few number of pixels with high uncertainty is the source of high error.

Fuzzy clustering is a popular unsupervised learning method that is used in cluster analysis. Fuzzy clustering allows a data point to belong to two or more clusters. Fuzzy c-means is the most well-known method that is applied to cluster analysis, however, the shortcoming is that the number of clusters need to be predefined. This paper proposes a clustering approach based on Particle Swarm Optimization (PSO). This PSO approach determines the optimal number of clusters automatically with the help of a threshold vector. The algorithm first randomly partitions the data set within a preset number of clusters, and then uses a reconstruction criterion to evaluate the performance of the clustering results. The experiments conducted demonstrate that the proposed algorithm automatically finds the optimal number of clusters. Furthermore, to visualize the results principal component analysis projection, conventional Sammon mapping, and fuzzy Sammon mapping were used

To find an optimal cluster size and number of clusters for a reasonable estimate of the prevalence of cataract blindness in people aged > or = 50 years in 19 rural districts of a state in India. Cluster sampling methodology was used in 19 rural districts of Karnataka State, India. In each district, 15 clusters were randomly selected and 90 people aged > or = 50 years were examined in each cluster. As a result the visual acuity and lens status of a total of 22,218 people were assessed. For each district, the design effect for cluster size ranging from 20 to 90 was calculated and the optimal cluster size and the required number of clusters to achieve an accuracy of 1% errors and 80% confidence was assessed. The age and gender adjusted prevalence of cataract blindness varied from 1.58% to 7.24%, which justifies district level surveys. The design effect is nearly 1.5 for clusters of sizes 30 and 40. With an average prevalence of 4.93% with 1% error and 80% confidence level, the optimal number of clusters is 37 and 28 for a cluster size of 30 and 40 respectively and the average sample size for a district around 1100. Rapid assessments for cataract blindness in those aged > or = 50 years can be conducted at district level in India with existing resources and at affordable costs. These provide reliable data, essential for effective monitoring and planning. Other parameters, for instance, surgical coverage can also be assessed. The availability of standardized software for data entry and analysis and strict adherence to survey procedures is essential.

Conventional clustering methods such as k-means or subtractive clustering need some information include the optimal number of clusters, otherwise, they lead to the poor results. However in many practical situations it is often so difficult to determine the best number of clusters. On the other hand, there are other clustering algorithms such as Rival Penalized Competitive Learning (RPCL) or ISODATA which find the number of clusters automatically. But these clustering methods have a problem in locating the cluster centers appropriately. In this paper, a novel hybrid structure is proposed which uses these two types of clustering algorithms as complementary to improve clustering performance. Moreover, a new weighted version of RPCL algorithm which is called here WRPCL is suggested. This structure not only outperforms the choice of the optimal number of clusters but also improves the performance of the overall clustering result.

Transmissions in the mmWave spectrum benefit from a-priori knowledge of radio channel propagation models. This paper is concerned with one important task that helps provide a more accurate channel model, namely, the clustering of all multipath components arriving at the receiver. Our work focuses on directive transmissions in urban outdoor scenarios and shows the importance of the correct estimation of the number of clusters for mmWave radio channels simulated with a software ray-tracer tool. We investigate the effectiveness of k-means and k-power-means clustering algorithms in predicting the number of clusters through the use of cluster validity indices (CVIs) and score fusion techniques. Our investigation shows that clustering is a difficult task because the optimal number of clusters is not always given by one or by a combination of more CVIs. However, using score fusion methods, we find the optimal partitioning for the k-means algorithm based on the power and time of arrival of the multipath rays or based on their angle of arrival. When the k-power-means algorithm is used, the power of each arriving ray is the most important clustering factor, making the dominant received paths pull the other ones around them, to form a cluster. Thus, the number of clusters is smaller and the decision based on CVIs or score fusion factors easier to be taken.

Typically clustering algorithms provide clustering solutions with prespecified number of clusters. The lack of a priori knowledge on the true number of underlying clusters in the dataset makes it important to have a metric to compare the clustering solutions with different number of clusters. This article quantifies a notion of persistence of clustering solutions that enables comparing solutions with different number of clusters. The persistence relates to the range of dataresolution scales over which a clustering solution persists; it is quantified in terms of the maximum over two-norms of all the associated cluster-covariance matrices. Thus we associate a persistence value for each element in a set of clustering solutions with different number of clusters. We show that the datasets where natural clusters are a priori known, the clustering solutions that identify the natural clusters are most persistent - in this way, this notion can be used to identify solutions with true number of clusters. Detailed experiments on a variety of standard and synthetic datasets demonstrate that the proposed persistence-based indicator outperforms the existing approaches, such as, gap-statistic method, X-means, Gmeans, PG-means, dip-means algorithms and informationtheoretic method, in accurately identifying the clustering solutions with true number of clusters. Interestingly, our method can be explained in terms of the phase-transition phenomenon in the deterministic annealing algorithm, where the number of distinct cluster centers changes (bifurcates) with respect to an annealing parameter.

Traditional supervised clustering methods require the user to provide the number of clusters before we start any data exploration. The data engineer also has to select the initial cluster seeds. In c-means clustering method, the performance efficiency of the algorithm depends mainly on the initial selection of number of clusters and cluster seeds. With the real world data, the initial selection of cluster count and centroids becomes a tedious task. In this paper we propose a modified clustering algorithm which works on the principles of fuzzy clustering. The method we propose is using a modified form of popular fuzzy c-means algorithm for membership calculation. The algorithm begins on the assumption that all the data points are initial centroids. . The clusters are continuously merged based on a threshold value until we get the optimum number of clusters. The algorithm is also capable of detecting the outliers The algorithm is tested with the data for Gross National Happiness (GNH) program of Bhutan and found to be highly efficient in segmenting natural data sets.

Identification of coherent generators (CGs) is necessary for the area-based monitoring and protection system of a wide area power system. Synchrophasor has enabled smarter monitoring and control measures to be devised; hence, measurement-based methodologies can be implemented in online applications to identify the CGs. This paper presents a new framework for coherency identification that is based on the dynamic coupling of generators. A distance matrix that contains the dissimilarity indices between any pair of generators is constructed from the pairwise dynamic coupling of generators after the post-disturbance data are obtained by phasor measurement units (PMUs). The dataset is embedded in Euclidean space to produce a new dataset with a metric distance between the points, and then the support vector clustering (SVC) technique is applied to the embedded dataset to identify the final clusters of generators. Unlike other clustering methods that need a priori knowledge about the number of clusters or the parameters of clustering, this information is set in an automatic search procedure that results in the optimal number of clusters. The algorithm is verified by time-domain simulations of defined scenarios in 39 bus and 118 bus test systems. Finally, the clustering result of 39 bus systems is validated by cluster validity measures, and a comparative study investigates the efficacy of the proposed algorithm to cluster the generators with an optimal number of clusters and also its computational efficiency compared with other clustering methods.

Because of the complexity of data sets from the real world, it is difficult to classify the data sets clearly and effectively, thus we prefer to adopt fuzzy clustering approaches to analyze the data sets. However, due to the variety of fuzzy clustering algorithms, the different number of clusters will lead to different clustering results. The number of clusters is closely related to the clustering division, so how to determine the number of fuzzy clustering (k ) has become a problem. Until now, many researchers have proposed utilizing fuzzy clustering validity indexes to deal with this kind of problem. However, the effectiveness index of fuzzy clustering can only be evaluated on the basis of the fuzzy clustering algorithm FCM to divide the clusters. When the range of k value is too large, FCM’s clustering for different k values is quite time-consuming. From this perspective, this paper proposes a fuzzy clustering optimal k selection method based on multi-objective optimization (FMOEA-K). Different from the traditional methods, this method combines the fuzzy clustering effectiveness index with multi-objective optimization algorithm (MOEA), and uses multi-objective optimization algorithm to search the appropriate cluster center concurrently. Because of the concurrency of the multi-objective optimization algorithm, the calculation time is shortened. The experimental results show that compared with the traditional method, the FMOEA-K can shorten the calculation time and improve the accuracy of calculating the optimal k value.