Unbalanced Clusters Research Articles

Swarm intelligence based fuzzy routing protocol for clustered wireless sensor networks

Wireless sensor networks are rapidly evolving technological platforms with tremendous applications in several domains. Since sensor nodes are battery powered and may be used in dangerous or inaccessible environments, it is difficult to replace or recharge their power supplies. Clustering is an effective approach to achieve energy efficiency in wireless sensor networks. In clustering-based routing protocols, cluster heads are selected among all sensor nodes within the network, and then clusters are formed by simply assigning each node to the nearest cluster head. The main drawback is that there is no control on the distribution of cluster heads over the network. In addition to the problem of generating unbalanced clusters, almost all routing protocols are designed for a certain application scope, and could not cover all applications. In this paper, we propose a swarm intelligence based fuzzy routing protocol (named SIF), in order to overcome the mentioned drawbacks. In SIF, fuzzy c-means clustering algorithm is utilized to cluster all sensor nodes into balanced clusters, and then appropriate cluster heads are selected via Mamdani fuzzy inference system. This strategy not only guarantees to generate balanced clusters over the network, but also has the ability to determine the precise number of clusters. In fuzzy-based routing protocols in literature, the fuzzy rule base table is defined manually, which is not optimal for all applications. Since tuning the fuzzy rules very affects on the performance of the fuzzy system, we utilize a hybrid swarm intelligence algorithm based on firefly algorithm and simulated annealing to optimize the fuzzy rule base table of SIF. The fitness function can be defined according to the application specifications. Unlike other routing protocols which have been designed for a certain application scope, the main objective of our methodology is to prolong the network lifetime based on the application specifications. In other words, SIF not only prolongs the network lifetime, but also is applicable to any kind of application. Obtained simulation results over 10 heterogeneous networks show that SIF outperforms the existing clustering-based protocols in terms of generating balanced clusters and prolonging the network lifetime.

Unsupervised Profiling of Microglial Arbor Morphologies and Distribution Using a Nonparametric Bayesian Approach

The morphologies of microglial arbors in brain tissue are important indicators of their state of activation, and their spatial distribution indicates patterns of tissue perturbation. This paper presents a non-parametric Bayesian approach to unsupervised quantitative profiling of microglial activation states, and mapping their 3-D spatial distributions across extended brain tissue regions imaged by mosaiced confocal microscopy. Our approach is to perform large-scale automated reconstruction of all the microglia using a learned label-consistent dictionary model for the microglial processes, and extract 136 arbor features per cell. We then fit an infinite Gaussian mixture model with collapsed Gibbs sampling to the arbor features, to discover arbor-morphological classes, their morphological ‘signatures’, and the associated covariance matrices all in an unsupervised manner. This nonparametric approach can handle clusters with arbitrarily shaped covariance matrices, perform automatic model selection, handle unbalanced clusters, and detect overlapping classes, without the need to specify the number of clusters. The results can be used for diverse investigational purposes, including: population-scale modeling, automated discovery of arbor classes and their distinguishing quantitative signatures and features, quantifying the nature and extent of the cellular heterogeneity, and spatial mapping of cellular arbor morphologies, and mapping tissue alterations.

Improving fuzzy c ‐means method for unbalanced dataset

Traditional fuzzy c-means method (FCM) is a famous clustering algorithm, but has a poor clustering performance for unbalanced dataset. To tackle this defect, a new FCM is presented by introducing cluster size into the formula of determining the membership values in every iteration. Experimental results on synthetic and UCI datasets showed that the proposed method has a better clustering performance than traditional FCM in terms of dealing with datasets with unbalanced clusters.

PASCCC: Priority-based application-specific congestion control clustering protocol

Wireless sensor networks comprise resource-starved sensor nodes, which are deployed to sense the environment, gather data, and transmit it to a base station (BS) for further processing. Cluster-based hierarchical-routing protocols are used to efficiently utilize the limited energy of the nodes by organizing them into clusters. Only cluster head (CH) nodes are eligible for gathering data in each cluster and transmitting it to a BS. Unbalanced clusters result in network congestion, thereby causing delay, packet loss, and degradation of Quality of Service (QoS) metrics. In this study, we propose a priority-based application-specific congestion control clustering (PASCCC) protocol, which integrates the mobility and heterogeneity of the nodes to detect congestion in a network. PASCCC decreases the duty cycle of each node by maintaining threshold levels for various applications. The transmitter of a sensor node is triggered when the reading of a specific captured event exceeds a specific threshold level. Time-critical packets are prioritized during congestion in order to maintain their timeliness requirements. In our proposed approach, CHs ensure coverage fidelity by prioritizing the packets of distant nodes over those of nearby nodes. A novel queue scheduling mechanism is proposed for CHs to achieve coverage fidelity, which ensures that the extra resources consumed by distant nodes are utilized effectively. The effectiveness of PASCCC was evaluated based on comparisons with existing clustering protocols. The experimental results demonstrated that PASCCC achieved better performance in terms of the network lifetime, energy consumption, data transmission, and other QoS metrics compared with existing approaches.

A size-insensitive integrity-based fuzzy c-means method for data clustering

Fuzzy c-means (FCM) is one of the most popular techniques for data clustering. Since FCM tends to balance the number of data points in each cluster, centers of smaller clusters are forced to drift to larger adjacent clusters. For datasets with unbalanced clusters, the partition results of FCM are usually unsatisfactory. Cluster size insensitive FCM (csiFCM) dealt with “cluster-size sensitivity” problem by dynamically adjusting the condition value for the membership of each data point based on cluster size after the defuzzification step in each iterative cycle. However, the performance of csiFCM is sensitive to both the initial positions of cluster centers and the “distance” between adjacent clusters. In this paper, we present a cluster size insensitive integrity-based FCM method called siibFCM to improve the deficiency of csiFCM. The siibFCM method can determine the membership contribution of every data point to each individual cluster by considering cluster's integrity, which is a combination of compactness and purity. “Compactness” represents the distribution of data points within a cluster while “purity” represents how far a cluster is away from its adjacent cluster. We tested our siibFCM method and compared with the traditional FCM and csiFCM methods extensively by using artificially generated datasets with different shapes and data distributions, synthetic images, real images, and Escherichia coli dataset. Experimental results showed that the performance of siibFCM is superior to both traditional FCM and csiFCM in terms of the tolerance for “distance” between adjacent clusters and the flexibility of selecting initial cluster centers when dealing with datasets with unbalanced clusters.

Re‐centered kurtosis as a projection pursuit index for multivariate data analysis

High‐dimensional data, which have become common in analytical chemistry, are often rich in information, but useful information may not be discovered without applying advanced data analysis methods. As a powerful tool for exploratory data analysis, projection pursuit (PP) is less widely used in chemistry compared with other methods such as principal component analysis (PCA), although PP often gives better results than PCA. PP does not have a uniquely defined objective function (projection index), and different statistics have been proposed as projection indices. Kurtosis has been widely employed as a projection index, and minimization of kurtosis is helpful in revealing clusters. However, this method often fails when the clusters in a data set are not balanced (i.e., present in unequal proportions). In this work, a newly defined kurtosis, referred to as “re‐centered kurtosis,” is proposed as a projection index. The theory and the optimization algorithms for the re‐centered kurtosis are developed. The utility of the PP method using the proposed re‐centered kurtosis as a projection index to reveal unbalanced clusters is demonstrated by simulated and real experimental data. Copyright © 2013 John Wiley & Sons, Ltd.

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.

Mixed effects regression trees for clustered data

This paper presents an extension of the standard regression tree method to clustered data. Previous works extending tree methods to accommodate correlated data are mainly based on the multivariate repeated-measures approach. We propose a “mixed effects regression tree” method where the correlated observations are viewed as nested within clusters rather than as vectors of multivariate repeated responses. The proposed method can handle unbalanced clusters, allows observations within clusters to be split, and can incorporate random effects and observation-level covariates. We implemented the proposed method using a standard tree algorithm within the framework of the expectation-maximization (EM) algorithm. The simulation results show that the proposed regression tree method provides substantial improvements over standard trees when the random effects are non negligible. A real data example is used to illustrate the method.

A comprehensive validity index for clustering

Cluster validity indices are used for both estimating the quality of a clustering algorithm and for determining the correct number of clusters in data. Even though several indices exist in the literature, most of them are only relevant for data sets that contain at least two clusters. This paper introduces a new bounded index for cluster validity called the score function (SF), a double exponential expression that is based on a ratio of standard cluster parameters. Several artificial and real-life data sets are used to evaluate the performance of the score function. These data sets contain a range of features and patterns such as unbalanced, overlapped and noisy clusters. In addition, cases involving sub-clusters and perfect clusters are tested. The score function is tested against six previously proposed validity indices. In the case of hyper-spheroidal clusters, the index proposed in this paper is found to be always as good or better than these indices. In addition, it is shown to work well on multidimensional and noisy data sets. One of its advantages is the ability to handle single cluster case and sub-cluster hierarchies.

Vortex collisions and energy-dissipation rates in the Ginzburg–Landau heat flow. Part I: Study of the perturbed Ginzburg–Landau equation

We study vortices for solutions of the perturbed Ginzburg-Landau equations \Delta u+ \frac{1}{\varepsilon^2} u(1-|u|^2)=f_\varepsilon where f_\varepsilon is estimated in L^2 . We prove upper bounds for the Ginzburg–Landau energy in terms of \|f_\varepsilon\|_{L^2} , and obtain lower bounds for \|f_\varepsilon\|_{L^2} in term of the vortices when these form “unbalanced clusters” where \sum_i d_i^2\neq (\sum_i d_i)^2 . These results will serve in Part II of this paper to provide estimates on the energy-dissipation rates for solutions of the Ginzburg–Landau heat-flow, which allow to study various phenomena occurring in this flow, among which vortex-collisions; allowing in particular to extend the dynamical law of vortices passed collisions.

Power for T-test comparisons of unbalanced cluster exposure studies.

Studies of individuals sampled in unbalanced clusters have become common in health services and epidemiological research, but available tools for power/sample size estimation and optimal design are currently limited. This paper presents and illustrates power estimation formulas for t-test comparisons of effect of an exposure at the cluster level on continuous outcomes in unbalanced studies with unequal numbers of clusters and/or unequal numbers of subjects per cluster in each exposure arm. Iterative application of these power formulas obtains minimal sample size needed and/or minimal detectable difference. SAS subroutines to implement these algorithms are given in the Appendices. When feasible, power is optimized by having the same number of clusters in each arm k(A) = k(B) and (irrespective of numbers of clusters in each arm) the same total number of subjects in each arm n(A)k(A) = n(B)k(B). Cost beneficial upper limits for numbers of subjects per cluster may be approximately (5/rho) - 5 or less where rho is the intraclass correlation. The methods presented here for simple cluster designs may be extended to some settings involving complex hierarchical weighted cluster samples.

Sample size considerations in observational health care quality studies.

A common objective in health care quality studies involves measuring and comparing the quality of care delivered to cohorts of patients by different health care providers. The data used for inference involve observations on units grouped within clusters, such as patients treated within hospitals. Unlike cluster randomization trials where often clusters are randomized to interventions to learn about individuals, the target of inference in health quality studies is the cluster. Furthermore, randomization is often not performed and the resulting biases may invalidate standard tests. In this paper, we discuss approaches to sample size determination in the design of observational health quality studies when the outcome is binary. Methods for calculating sample size using marginal models are briefly reviewed, but the focus is on hierarchical binomial models. Sample size in unbalanced clusters and stratified designs are characterized. We draw upon the experiences that have arisen from a study funded by the Agency for Healthcare Research and Quality involving assessment of quality of care for patients with cardiovascular disease. If researchers are interested in comparing clusters, hierarchical models are preferred.