Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys

Lot quality assurance sampling (LQAS) surveys are commonly used for monitoring and evaluation in resource-limited settings. Recently several methods have been proposed to combine LQAS with cluster sampling for more timely and cost-effective data collection. For some of these methods, the standard binomial model can be used for constructing decision rules as the clustering can be ignored. For other designs, considered here, clustering is accommodated in the design phase. In this paper, we compare these latter cluster LQAS methodologies and provide recommendations for choosing a cluster LQAS design. We compare technical differences in the three methods and determine situations in which the choice of method results in a substantively different design. We consider two different aspects of the methods: the distributional assumptions and the clustering parameterization. Further, we provide software tools for implementing each method and clarify misconceptions about these designs in the literature. We illustrate the differences in these methods using vaccination and nutrition cluster LQAS surveys as example designs. The cluster methods are not sensitive to the distributional assumptions but can result in substantially different designs (sample sizes) depending on the clustering parameterization. However, none of the clustering parameterizations used in the existing methods appears to be consistent with the observed data, and, consequently, choice between the cluster LQAS methods is not straightforward. Further research should attempt to characterize clustering patterns in specific applications and provide suggestions for best-practice cluster LQAS designs on a setting-specific basis.     

一种基于类均值的肿瘤基因芯片数据的标准化方法

：分析了当前常用的标准化方法在肿瘤基因芯片中引起错误分类的原因,提出了一种基于类均值的标准化方法．该方法对基因表达谱进行双向标准化,并将标准化过程与聚类过程相互缠绕,利用聚类结果来修正参照表达水平．选取了5组肿瘤基因芯片数据,用层次聚类和K-均值聚类算法在不同的方差水平上分别对常用的标准化和基于类均值的标准化处理后的基因表达数据进行聚类分析比较．实验结果表明,基于类均值的标准化方法能有效提高肿瘤基因表达谱聚类结果的质量．     

Imaging of colorectal adenocarcinoma using FT-IR microspectroscopy and cluster analysis

In this paper, three different clustering algorithms were applied to assemble infrared (IR) spectral maps from IR microspectra of tissues. Using spectra from a colorectal adenocarcinoma section, we show how IR images can be assembled by agglomerative hierarchical (AH) clustering (Ward's technique), fuzzy C-means (FCM) clustering, and k-means (KM) clustering. We discuss practical problems of IR imaging on tissues such as the influence of spectral quality and data pretreatment on image quality. Furthermore, the applicability of cluster algorithms to the spatially resolved microspectroscopic data and the degree of correlation between distinct cluster images and histopathology are compared. The use of any of the clustering algorithms dramatically increased the information content of the IR images, as compared to univariate methods of IR imaging (functional group mapping). Among the cluster imaging methods, AH clustering (Ward's algorithm) proved to be the best method in terms of tissue structure differentiation.     

Towards clustering of incomplete microarray data without the use of imputation

MOTIVATION: Clustering technique is used to find groups of genes that show similar expression patterns under multiple experimental conditions. Nonetheless, the results obtained by cluster analysis are influenced by the existence of missing values that commonly arise in microarray experiments. Because a clustering method requires a complete data matrix as an input, previous studies have estimated the missing values using an imputation method in the preprocessing step of clustering. However, a common limitation of these conventional approaches is that once the estimates of missing values are fixed in the preprocessing step, they are not changed during subsequent processes of clustering; badly estimated missing values obtained in data preprocessing are likely to deteriorate the quality and reliability of clustering results. Thus, a new clustering method is required for improving missing values during iterative clustering process. RESULTS: We present a method for Clustering Incomplete data using Alternating Optimization (CIAO) in which a prior imputation method is not required. To reduce the influence of imputation in preprocessing, we take an alternative optimization approach to find better estimates during iterative clustering process. This method improves the estimates of missing values by exploiting the cluster information such as cluster centroids and all available non-missing values in each iteration. To test the performance of the CIAO, we applied the CIAO and conventional imputation-based clustering methods, e.g. k-means based on KNNimpute, for clustering two yeast incomplete data sets, and compared the clustering result of each method using the Saccharomyces Genome Database annotations. The clustering results of the CIAO method are more significantly relevant to the biological gene annotations than those of other methods, indicating its effectiveness and potential for clustering incomplete gene expression data. AVAILABILITY: The software was developed using Java language, and can be executed on the platforms that JVM (Java Virtual Machine) is running. It is available from the authors upon request.     

Pattern classification of phylogeny signals

In this paper we propose the minimum entropy clustering (MEC) method for clustering genes based on their phylogenetic signals. This entropy based method will cluster two genes together when their concatenation can decrease the entropy. An integral feature of MEC is that it chooses the number of clusters automatically, which is a major advantage over the other methods. Our simulation results show that this method is quite successful in clustering genes with a common phylogeny.     

WebGimm: An integrated web-based platform for cluster analysis,functional analysis,and interactive visualization of results

Cluster analysis methods have been extensively researched, but the adoption of new methods is often hindered by technical barriers in their implementation and use. WebGimm is a free cluster analysis web-service, and an open source general purpose clustering web-server infrastructure designed to facilitate easy deployment of integrated cluster analysis servers based on clustering and functional annotation algorithms implemented in R. Integrated functional analyses and interactive browsing of both, clustering structure and functional annotations provides a complete analytical environment for cluster analysis and interpretation of results. The Java Web Start client-based interface is modeled after the familiar cluster/treeview packages making its use intuitive to a wide array of biomedical researchers. For biomedical researchers, WebGimm provides an avenue to access state of the art clustering procedures. For Bioinformatics methods developers, WebGimm offers a convenient avenue to deploy their newly developed clustering methods. WebGimm server, software and manuals can be freely accessed at .     

Detecting clusters of different geometrical shapes in microarray gene expression data

MOTIVATION: Clustering has been used as a popular technique for finding groups of genes that show similar expression patterns under multiple experimental conditions. Many clustering methods have been proposed for clustering gene-expression data, including the hierarchical clustering, k-means clustering and self-organizing map (SOM). However, the conventional methods are limited to identify different shapes of clusters because they use a fixed distance norm when calculating the distance between genes. The fixed distance norm imposes a fixed geometrical shape on the clusters regardless of the actual data distribution. Thus, different distance norms are required for handling the different shapes of clusters. RESULTS: We present the Gustafson-Kessel (GK) clustering method for microarray gene-expression data. To detect clusters of different shapes in a dataset, we use an adaptive distance norm that is calculated by a fuzzy covariance matrix (F) of each cluster in which the eigenstructure of F is used as an indicator of the shape of the cluster. Moreover, the GK method is less prone to falling into local minima than the k-means and SOM because it makes decisions through the use of membership degrees of a gene to clusters. The algorithmic procedure is accomplished by the alternating optimization technique, which iteratively improves a sequence of sets of clusters until no further improvement is possible. To test the performance of the GK method, we applied the GK method and well-known conventional methods to three recently published yeast datasets, and compared the performance of each method using the Saccharomyces Genome Database annotations. The clustering results of the GK method are more significantly relevant to the biological annotations than those of the other methods, demonstrating its effectiveness and potential for clustering gene-expression data. AVAILABILITY: The software was developed using Java language, and can be executed on the platforms that JVM (Java Virtual Machine) is running. It is available from the authors upon request. SUPPLEMENTARY INFORMATION: Supplementary data are available at http://dragon.kaist.ac.kr/gk.     

Evaluation and comparison of gene clustering methods in microarray analysis

MOTIVATION: Microarray technology has been widely applied in biological and clinical studies for simultaneous monitoring of gene expression in thousands of genes. Gene clustering analysis is found useful for discovering groups of correlated genes potentially co-regulated or associated to the disease or conditions under investigation. Many clustering methods including hierarchical clustering, K-means, PAM, SOM, mixture model-based clustering and tight clustering have been widely used in the literature. Yet no comprehensive comparative study has been performed to evaluate the effectiveness of these methods. RESULTS: In this paper, six gene clustering methods are evaluated by simulated data from a hierarchical log-normal model with various degrees of perturbation as well as four real datasets. A weighted Rand index is proposed for measuring similarity of two clustering results with possible scattered genes (i.e. a set of noise genes not being clustered). Performance of the methods in the real data is assessed by a predictive accuracy analysis through verified gene annotations. Our results show that tight clustering and model-based clustering consistently outperform other clustering methods both in simulated and real data while hierarchical clustering and SOM perform among the worst. Our analysis provides deep insight to the complicated gene clustering problem of expression profile and serves as a practical guideline for routine microarray cluster analysis.     

Dynamic model-based clustering for time-course gene expression data

Microarray technology has produced a huge body of time-course gene expression data. Such gene expression data has proved useful in genomic disease diagnosis and genomic drug design. The challenge is how to uncover useful information in such data. Cluster analysis has played an important role in analyzing gene expression data. Many distance/correlation- and static model-based clustering techniques have been applied to time-course expression data. However, these techniques are unable to account for the dynamics of such data. It is the dynamics that characterize the data and that should be considered in cluster analysis so as to obtain high quality clustering. This paper proposes a dynamic model-based clustering method for time-course gene expression data. The proposed method regards a time-course gene expression dataset as a set of time series, generated by a number of stochastic processes. Each stochastic process defines a cluster and is described by an autoregressive model. A relocation-iteration algorithm is proposed to identity the model parameters and posterior probabilities are employed to assign each gene to an appropriate cluster. A bootstrapping method and an average adjusted Rand index (AARI) are employed to measure the quality of clustering. Computational experiments are performed on a synthetic and three real time-course gene expression datasets to investigate the proposed method. The results show that our method allows the better quality clustering than other clustering methods (e.g. k-means) for time-course gene expression data, and thus it is a useful and powerful tool for analyzing time-course gene expression data.     

Genetic algorithm based two-mode clustering of metabolomics data

Metabolomics and other omics tools are generally characterized by large data sets with many variables obtained under different environmental conditions. Clustering methods and more specifically two-mode clustering methods are excellent tools for analyzing this type of data. Two-mode clustering methods allow for analysis of the behavior of subsets of metabolites under different experimental conditions. In addition, the results are easily visualized. In this paper we introduce a two-mode clustering method based on a genetic algorithm that uses a criterion that searches for homogeneous clusters. Furthermore we introduce a cluster stability criterion to validate the clusters and we provide an extended knee plot to select the optimal number of clusters in both experimental and metabolite modes. The genetic algorithm-based two-mode clustering gave biological relevant results when it was applied to two real life metabolomics data sets. It was, for instance, able to identify a catabolic pathway for growth on several of the carbon sources. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. J. A. Hageman and R. A. van den Berg contributed equally to this paper.     

Going beyond Clustering in MD Trajectory Analysis: An Application to Villin Headpiece Folding

Recent advances in computing technology have enabled microsecond long all-atom molecular dynamics (MD) simulations of biological systems. Methods that can distill the salient features of such large trajectories are now urgently needed. Conventional clustering methods used to analyze MD trajectories suffer from various setbacks, namely (i) they are not data driven, (ii) they are unstable to noise and changes in cut-off parameters such as cluster radius and cluster number, and (iii) they do not reduce the dimensionality of the trajectories, and hence are unsuitable for finding collective coordinates. We advocate the application of principal component analysis (PCA) and a non-metric multidimensional scaling (nMDS) method to reduce MD trajectories and overcome the drawbacks of clustering. To illustrate the superiority of nMDS over other methods in reducing data and reproducing salient features, we analyze three complete villin headpiece folding trajectories. Our analysis suggests that the folding process of the villin headpiece is structurally heterogeneous.     

FctClus: A Fast Clustering Algorithm for Heterogeneous Information Networks

It is important to cluster heterogeneous information networks. A fast clustering algorithm based on an approximate commute time embedding for heterogeneous information networks with a star network schema is proposed in this paper by utilizing the sparsity of heterogeneous information networks. First, a heterogeneous information network is transformed into multiple compatible bipartite graphs from the compatible point of view. Second, the approximate commute time embedding of each bipartite graph is computed using random mapping and a linear time solver. All of the indicator subsets in each embedding simultaneously determine the target dataset. Finally, a general model is formulated by these indicator subsets, and a fast algorithm is derived by simultaneously clustering all of the indicator subsets using the sum of the weighted distances for all indicators for an identical target object. The proposed fast algorithm, FctClus, is shown to be efficient and generalizable and exhibits high clustering accuracy and fast computation speed based on a theoretic analysis and experimental verification.     

Optimal search space for clustering gene expression data via consensus.

Ensemble clustering methods have become increasingly important to ease the task of choosing the most appropriate cluster algorithm for a particular data analysis problem. The consensus clustering (CC) algorithm is a recognized ensemble clustering method that uses an artificial intelligence technique to optimize a fitness function. We formally prove the existence of a subspace of the search space for CC, which contains all solutions of maximal fitness and suggests two greedy algorithms to search this subspace. We evaluate the algorithms on two gene expression data sets and one synthetic data set, and compare the result with the results of other ensemble clustering approaches.     

A hybrid genetic algorithm and expectation maximization method for global gene trajectory clustering

Clustering time-course gene expression data (gene trajectories) is an important step towards solving the complex problem of gene regulatory network modeling and discovery as it significantly reduces the dimensionality of the gene space required for analysis. Traditional clustering methods that perform hill-climbing from randomly initialized cluster centers are prone to produce inconsistent and sub-optimal cluster solutions over different runs. This paper introduces a novel method that hybridizes genetic algorithm (GA) and expectation maximization algorithms (EM) for clustering gene trajectories with the mixtures of multiple linear regression models (MLRs), with the objective of improving the global optimality and consistency of the clustering performance. The proposed method is applied to cluster the human fibroblasts and the yeast time-course gene expression data based on their trajectory similarities. It outperforms the standard EM method significantly in terms of both clustering accuracy and consistency. The biological implications of the improved clustering performance are demonstrated.     

Cross-Clustering: A Partial Clustering Algorithm with Automatic Estimation of the Number of Clusters

Four of the most common limitations of the many available clustering methods are: i) the lack of a proper strategy to deal with outliers; ii) the need for a good a priori estimate of the number of clusters to obtain reasonable results; iii) the lack of a method able to detect when partitioning of a specific data set is not appropriate; and iv) the dependence of the result on the initialization. Here we propose Cross-clustering (CC), a partial clustering algorithm that overcomes these four limitations by combining the principles of two well established hierarchical clustering algorithms: Ward’s minimum variance and Complete-linkage. We validated CC by comparing it with a number of existing clustering methods, including Ward’s and Complete-linkage. We show on both simulated and real datasets, that CC performs better than the other methods in terms of: the identification of the correct number of clusters, the identification of outliers, and the determination of real cluster memberships. We used CC to cluster samples in order to identify disease subtypes, and on gene profiles, in order to determine groups of genes with the same behavior. Results obtained on a non-biological dataset show that the method is general enough to be successfully used in such diverse applications. The algorithm has been implemented in the statistical language R and is freely available from the CRAN contributed packages repository.     

Clustering of identical oligomers in coding and noncoding DNA sequences.

We develop a quantitative method for analyzing repetitions of identical short oligomers in coding and noncoding DNA sequences. We analyze sequences presently available in the GenBank separately for primate, mammal, vertebrate, rodent, invertebrate and plant taxonomic partitions. We find that some oligomers "cluster" more than they would if randomly distributed, while other oligomers "repel" each other. To quantify this degree of clustering, we define clustering measures. We find that (i) clustering significantly differs in coding and noncoding DNA; (ii) in most cases, monomers, dimers and tetramers cluster in noncoding DNA but appear to repel each other in coding DNA. (iii) The degree of clustering for different sources (primates, invertebrates, and plants) is more conserved among these sources in the case of coding DNA than in the case of noncoding DNA. (iv) In contrast to other oligomers, we find that trimers always prefer to cluster. (v) Clustering of each particular oligomer is conserved within the same organism.     

Consensus framework for exploring microarray data using multiple clustering methods

The large variety of clustering algorithms and their variants can be daunting to researchers wishing to explore patterns within their microarray datasets. Furthermore, each clustering method has distinct biases in finding patterns within the data, and clusterings may not be reproducible across different algorithms. A consensus approach utilizing multiple algorithms can show where the various methods agree and expose robust patterns within the data. In this paper, we present a software package - Consense, written for R/Bioconductor - that utilizes such an approach to explore microarray datasets. Consense produces clustering results for each of the clustering methods and produces a report of metrics comparing the individual clusterings. A feature of Consense is identification of genes that cluster consistently with an index gene across methods. Utilizing simulated microarray data, sensitivity of the metrics to the biases of the different clustering algorithms is explored. The framework is easily extensible, allowing this tool to be used by other functional genomic data types, as well as other high-throughput OMICS data types generated from metabolomic and proteomic experiments. It also provides a flexible environment to benchmark new clustering algorithms. Consense is currently available as an installable R/Bioconductor package (http://www.ohsucancer.com/isrdev/consense/).     

MSClust: A Multi-Seeds based Clustering algorithm for microbiome profiling using 16S rRNA sequence

Recent developments of next generation sequencing technologies have led to rapid accumulation of 16S rRNA sequences for microbiome profiling. One key step in data processing is to cluster short sequences into operational taxonomic units (OTUs). Although many methods have been proposed for OTU inferences, a major challenge is the balance between inference accuracy and computational efficiency, where inference accuracy is often sacrificed to accommodate the need to analyze large numbers of sequences. Inspired by the hierarchical clustering method and a modified greedy network clustering algorithm, we propose a novel multi-seeds based heuristic clustering method, named MSClust, for OTU inference. MSClust first adaptively selects multi-seeds instead of one seed for each candidate cluster, and the reads are then processed using a greedy clustering strategy. Through many numerical examples, we demonstrate that MSClust enjoys less memory usage, and better biological accuracy compared to existing heuristic clustering methods while preserving efficiency and scalability.     

CLAGen: a tool for clustering and annotating gene sequences using a suffix tree algorithm

Most multiple gene sequence alignment methods rely on conventions regarding the score of a multiple alignment in pairwise fashion. Therefore, as the number of sequences increases, the runtime of sequencing expands exponentially. In order to solve the problem, this paper presents a multiple sequence alignment method using a linear-time suffix tree algorithm to cluster similar sequences at one time without pairwise alignment. After searching for common subsequences, cross-matching common subsequences were generated, and sometimes inexact matching was found. So, a procedure aimed at masking the inexact cross-matching pairs was suggested here. In addition, BLAST was combined with a clustering tool in order to annotate the clusters generated by suffix tree clustering. The proposed method for clustering and annotating genes consists of the following steps: (1) construction of a suffix tree; (2) searching and overlapping common subsequences; (3) grouping subsequence pairs; (4) masking cross-matching pairs; (5) clustering gene sequences; (6) annotating gene clusters by the BLAST search. The performance of the proposed system, CLAGen, was successfully evaluated with 42 gene sequences in a TCA cycle (a citrate cycle) of bacteria. The system generated 11 clusters and found the longest subsequences of each cluster, which are biologically significant.     

Cluster analysis of dynamic parameters of gene expression

Cluster analysis has proven to be a valuable statistical method for analyzing whole genome expression data. Although clustering methods have great utility, they do represent a lower level statistical analysis that is not directly tied to a specific model. To extend such methods and to allow for more sophisticated lines of inference, we use cluster analysis in conjunction with a specific model of gene expression dynamics. This model provides phenomenological dynamic parameters on both linear and non-linear responses of the system. This analysis determines the parameters of two different transition matrices (linear and nonlinear) that describe the influence of one gene expression level on another. Using yeast cell cycle microarray data as test set, we calculated the transition matrices and used these dynamic parameters as a metric for cluster analysis. Hierarchical cluster analysis of this transition matrix reveals how a set of genes influence the expression of other genes activated during different cell cycle phases. Most strikingly, genes in different stages of cell cycle preferentially activate or inactivate genes in other stages of cell cycle, and this relationship can be readily visualized in a two-way clustering image. The observation is prior to any knowledge of the chronological characteristics of the cell cycle process. This method shows the utility of using model parameters as a metric in cluster analysis.