Clustering for Sparsely Sampled Functional Data

James, Gareth; Sugar, Catherine A.

doi:10.1198/016214503000189

Cited by 425 publications

(402 citation statements)

References 19 publications

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“…The polynomial basis was effective in both studies, although a natural cubic spline basis is more flexible and makes fewer assumptions (12)(13)(14)(15)(16). Furthermore, a natural cubic spline parameterization of i (t) resulted in increased power in both studies.…”

Section: Resultsmentioning

confidence: 99%

“…The method that we propose draws on ideas from the extensive statistical literature on time course data analysis (10,11), particularly spline-based methods (12)(13)(14)(15)(16). It is applicable to detecting changes in expression over time within a single biological group and to detecting differences in the behavior of expression over time between two or more groups.…”

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confidence: 99%

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Significance analysis of time course microarray experiments

Storey

Xiao

Leek

et al. 2005

Proc. Natl. Acad. Sci. U.S.A.

544

593

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Characterizing the genome-wide dynamic regulation of gene expression is important and will be of much interest in the future. However, there is currently no established method for identifying differentially expressed genes in a time course study. Here we propose a significance method for analyzing time course microarray studies that can be applied to the typical types of comparisons and sampling schemes. This method is applied to two studies on humans. In one study, genes are identified that show differential expression over time in response to in vivo endotoxin administration. By using our method, 7,409 genes are called significant at a 1% false-discovery rate level, whereas several existing approaches fail to identify any genes. In another study, 417 genes are identified at a 10% false-discovery rate level that show expression changing with age in the kidney cortex. Here it is also shown that as many as 47% of the genes change with age in a manner more complex than simple exponential growth or decay. The methodology proposed here has been implemented in the freely distributed and open-source EDGE software package.T he identification of genes that show changes in expression between varying biological conditions is a frequent goal in microarray experiments (1). Differential expression can be studied from a static or temporal viewpoint. In a static experiment, the arrays are obtained irrespective of time, capturing only a single moment of gene expression. In a temporal experiment the arrays are collected over a time course, allowing one to study the dynamic behavior of gene expression. A large amount of work has been done on the problem of identifying differentially expressed genes in static experiments (2). Because the regulation of gene expression is a dynamic process, it is also important to identify and characterize changes in gene expression over time. Here we present a general statistical method that identifies genes differentially expressed over time.Several clustering methods have been applied to time course microarray data, including hierarchical clustering (3, 4), principal components-based clustering (5), Bayesian model-based clustering (6), and K-means clustering of curves (7,8). None of these clustering methods is directly applicable to identifying genes that show statistically significant changes in expression over time. The K-means clustering method has been modified to compare expression over time between two groups (9), but this method can only be applied to a few hundred genes at a time because of the computational cost of fitting a single model to all genes simultaneously (7,8). This approach also requires that the statistical significance be calculated under the assumption that the clustering model estimated for one of the groups is true, which is nonstandard and potentially problematic.The method that we propose draws on ideas from the extensive statistical literature on time course data analysis (10, 11), particularly spline-based methods (12-16). It is applicable to detecting changes in exp...

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Significance analysis of time course microarray experiments

Storey

Xiao

Leek

et al. 2005

Proc. Natl. Acad. Sci. U.S.A.

544

593

View full text Add to dashboard Cite

show abstract

“…Methods of functional data analysis are becoming increasingly popular, e.g. in the cluster analysis (Jacques and Preda 2013;James and Sugar 2003;Peng and Müller 2008), classification (Chamroukhi et al 2013;Delaigle and Hall 2012;Mosler and Mozharovskyi 2015;Rossi and Villa 2006) and regression (Ferraty et al 2012;Goia and Vieu 2014;Kudraszow and Vieu 2013;Peng et al 2015;Rachdi and Vieu 2006;Wang et al 2015). Unfortunately, multivariate data methods cannot be directly used for functional data, because of the problem of dimensionality and difficulty in putting functional data into order.…”

Section: Introductionmentioning

confidence: 99%

Selected statistical methods of data analysis for multivariate functional data

et al. 2016

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Data in the form of a continuous vector function on a given interval are referred to as multivariate functional data. These data are treated as realizations of multivariate random processes. The paper is devoted to three statistical dimension reduction techniques for multivariate data. For the first one, principal components analysis, the authors present a review of a recent paper (Jacques and Preda in, Comput Stat Data Anal, 71:92-106, 2014). For two others one, canonical variables and discriminant coordinates, the authors extend existing works for univariate functional data to multivariate. These methods for multivariate functional data are presented, illustrated and discussed in the context of analyzing real data sets. Each of these techniques is applied on real data set.

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“…However, most of the existing methods are essentially based on the shapes of the curves; see for example, James and Sugar (2003). In this section, we will cluster the batches based on the relationships between the response curves and the input covariates, not just the shapes of the response curves.…”

Section: Curve Clustering and Model Selectionmentioning

confidence: 99%

Curve prediction and clustering with mixtures of Gaussian process functional regression models

Shi

Wang

2008

Stat Comput

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Shi et al. (2006) proposed a Gaussian process functional regression (GPFR)model to model functional response curves with a set of functional covariates.Two main problems are addressed by this method: modelling nonlinear and nonparametric regression relationship and modelling covariance structure and mean structure simultaneously. The method gives very good results for curve fitting and prediction but side-steps the problem of heterogeneity. In this paper we present a new method for modelling functional data with 'spatially' indexed data, i.e., the heterogeneity is dependent on factors such as region and individual patient's information. For data collected from different sources, we assume that the data corresponding to each curve (or batch) follows a Gaussian process functional regression model as a lower-level model, and introduce an allocation model * Address for correspondence: School of Mathematics and Statistics, University of Newcastle, NE1 7RU, UK. Email: j.q.shi@ncl.ac.uk 1 for the latent indicator variables as a higher-level model. This higher-level model is dependent on the information related to each batch. This method takes advantage of both GPFR and mixture models and therefore improves the accuracy of predictions. The mixture model has also been used for curve clustering, but focusing on the problem of clustering functional relationships between response curve and covariates. The model is examined on simulated data and real data.

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Clustering for Sparsely Sampled Functional Data

Cited by 425 publications

References 19 publications

Significance analysis of time course microarray experiments

Significance analysis of time course microarray experiments

Selected statistical methods of data analysis for multivariate functional data

Curve prediction and clustering with mixtures of Gaussian process functional regression models

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