Introduction to statistical methods to analyze large data sets: principal components analysis.
Ontology highlight
ABSTRACT:
SUBMITTER: Clark NR
PROVIDER: S-EPMC3193798 | biostudies-literature | 2011 Sep
REPOSITORIES: biostudies-literature
Publications
Introduction to statistical methods to analyze large data sets: principal components analysis.
Science signaling 20110906 190
This Teaching Resource provides lecture notes, slides, and a problem set for a series of lectures from a course entitled "Systems Biology: Biomedical Modeling." The materials are a lecture introducing the mathematical concepts behind principal components analysis (PCA). The lecture describes how to handle large data sets with correlation methods and unsupervised clustering with this popular method of analysis, PCA. ...[more]
Similar Datasets
Project description:This Teaching Resource provides lecture notes, slides, and a problem set for a series of lectures introducing the mathematical concepts behind gene-set enrichment analysis (GSEA) and were part of a course entitled "Systems Biology: Biomedical Modeling." GSEA is a statistical functional enrichment analysis commonly applied to identify enrichment of biological functional categories in sets of ranked differentially expressed genes from genome-wide mRNA expression data sets.
| S-EPMC3205944 | biostudies-literature
Project description:BackgroundA key question when analyzing high throughput data is whether the information provided by the measured biological entities (gene, metabolite expression for example) is related to the experimental conditions, or, rather, to some interfering signals, such as experimental bias or artefacts. Visualization tools are therefore useful to better understand the underlying structure of the data in a 'blind' (unsupervised) way. A well-established technique to do so is Principal Component Analysis (PCA). PCA is particularly powerful if the biological question is related to the highest variance. Independent Component Analysis (ICA) has been proposed as an alternative to PCA as it optimizes an independence condition to give more meaningful components. However, neither PCA nor ICA can overcome both the high dimensionality and noisy characteristics of biological data.ResultsWe propose Independent Principal Component Analysis (IPCA) that combines the advantages of both PCA and ICA. It uses ICA as a denoising process of the loading vectors produced by PCA to better highlight the important biological entities and reveal insightful patterns in the data. The result is a better clustering of the biological samples on graphical representations. In addition, a sparse version is proposed that performs an internal variable selection to identify biologically relevant features (sIPCA).ConclusionsOn simulation studies and real data sets, we showed that IPCA offers a better visualization of the data than ICA and with a smaller number of components than PCA. Furthermore, a preliminary investigation of the list of genes selected with sIPCA demonstrate that the approach is well able to highlight relevant genes in the data with respect to the biological experiment.IPCA and sIPCA are both implemented in the R package mixomics dedicated to the analysis and exploration of high dimensional biological data sets, and on mixomics' web-interface.
| S-EPMC3298499 | biostudies-literature
Project description:Principal component analysis (PCA) is a popular dimension reduction method to reduce the complexity and obtain the informative aspects of high-dimensional datasets. When the data distribution is skewed, data transformation is commonly used prior to applying PCA. Such transformation is usually obtained from previous studies, prior knowledge, or trial-and-error. In this work, we develop a model-based method that integrates data transformation in PCA and finds an appropriate data transformation using the maximum profile likelihood. Extensions of the method to handle functional data and missing values are also developed. Several numerical algorithms are provided for efficient computation. The proposed method is illustrated using simulated and real-world data examples.
| S-EPMC4408558 | biostudies-literature
Project description:We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success probabilities of the binary observations. Sparsity is introduced to the principal component (PC) loading vectors for enhanced interpretability and more stable extraction of the principal components. Our sparse PCA is formulated as solving an optimization problem with a criterion function motivated from penalized Bernoulli likelihood. A Majorization-Minimization algorithm is developed to efficiently solve the optimization problem. The effectiveness of the proposed sparse logistic PCA method is illustrated by application to a single nucleotide polymorphism data set and a simulation study.
| S-EPMC2992445 | biostudies-literature
Project description:A statistical modeling approach is proposed for use in searching large microarray data sets for genes that have a transcriptional response to a stimulus. The approach is unrestricted with respect to the timing, magnitude or duration of the response, or the overall abundance of the transcript. The statistical model makes an accommodation for systematic heterogeneity in expression levels. Corresponding data analyses provide gene-specific information, and the approach provides a means for evaluating the statistical significance of such information. To illustrate this strategy we have derived a model to depict the profile expected for a periodically transcribed gene and used it to look for budding yeast transcripts that adhere to this profile. Using objective criteria, this method identifies 81% of the known periodic transcripts and 1,088 genes, which show significant periodicity in at least one of the three data sets analyzed. However, only one-quarter of these genes show significant oscillations in at least two data sets and can be classified as periodic with high confidence. The method provides estimates of the mean activation and deactivation times, induced and basal expression levels, and statistical measures of the precision of these estimates for each periodic transcript.
| S-EPMC33264 | biostudies-literature
Project description:The electroencephalography (EEG) data created in event-related potential (ERP) experiments have a complex high-dimensional structure. Each stimulus presentation, or trial, generates an ERP waveform which is an instance of functional data. The experiments are made up of sequences of multiple trials, resulting in longitudinal functional data and moreover, responses are recorded at multiple electrodes on the scalp, adding an electrode dimension. Traditional EEG analyses involve multiple simplifications of this structure to increase the signal-to-noise ratio, effectively collapsing the functional and longitudinal components by identifying key features of the ERPs and averaging them across trials. Motivated by an implicit learning paradigm used in autism research in which the functional, longitudinal, and electrode components all have critical interpretations, we propose a multidimensional functional principal components analysis (MD-FPCA) technique which does not collapse any of the dimensions of the ERP data. The proposed decomposition is based on separation of the total variation into subject and subunit level variation which are further decomposed in a two-stage functional principal components analysis. The proposed methodology is shown to be useful for modeling longitudinal trends in the ERP functions, leading to novel insights into the learning patterns of children with Autism Spectrum Disorder (ASD) and their typically developing peers as well as comparisons between the two groups. Finite sample properties of MD-FPCA are further studied via extensive simulations.
| S-EPMC5517364 | biostudies-literature
Project description:Electroencephalography (EEG) data possess a complex structure that includes regional, functional, and longitudinal dimensions. Our motivating example is a word segmentation paradigm in which typically developing (TD) children, and children with autism spectrum disorder (ASD) were exposed to a continuous speech stream. For each subject, continuous EEG signals recorded at each electrode were divided into one-second segments and projected into the frequency domain via fast Fourier transform. Following a spectral principal components analysis, the resulting data consist of region-referenced principal power indexed regionally by scalp location, functionally across frequencies, and longitudinally by one-second segments. Standard EEG power analyses often collapse information across the longitudinal and functional dimensions by averaging power across segments and concentrating on specific frequency bands. We propose a hybrid principal components analysis for region-referenced longitudinal functional EEG data, which utilizes both vector and functional principal components analyses and does not collapse information along any of the three dimensions of the data. The proposed decomposition only assumes weak separability of the higher-dimensional covariance process and utilizes a product of one dimensional eigenvectors and eigenfunctions, obtained from the regional, functional, and longitudinal marginal covariances, to represent the observed data, providing a computationally feasible non-parametric approach. A mixed effects framework is proposed to estimate the model components coupled with a bootstrap test for group level inference, both geared towards sparse data applications. Analysis of the data from the word segmentation paradigm leads to valuable insights about group-region differences among the TD and verbal and minimally verbal children with ASD. Finite sample properties of the proposed estimation framework and bootstrap inference procedure are further studied via extensive simulations.
| S-EPMC6920529 | biostudies-literature
Project description:The estimation of multiple sequence alignments of protein sequences is a basic step in many bioinformatics pipelines, including protein structure prediction, protein family identification, and phylogeny estimation. Statistical coestimation of alignments and trees under stochastic models of sequence evolution has long been considered the most rigorous technique for estimating alignments and trees, but little is known about the accuracy of such methods on biological benchmarks. We report the results of an extensive study evaluating the most popular protein alignment methods as well as the statistical coestimation method BAli-Phy on 1192 protein data sets from established benchmarks as well as on 120 simulated data sets. Our study (which used more than 230 CPU years for the BAli-Phy analyses alone) shows that BAli-Phy has better precision and recall (with respect to the true alignments) than the other alignment methods on the simulated data sets but has consistently lower recall on the biological benchmarks (with respect to the reference alignments) than many of the other methods. In other words, we find that BAli-Phy systematically underaligns when operating on biological sequence data but shows no sign of this on simulated data. There are several potential causes for this change in performance, including model misspecification, errors in the reference alignments, and conflicts between structural alignment and evolutionary alignments, and future research is needed to determine the most likely explanation. We conclude with a discussion of the potential ramifications for each of these possibilities. [BAli-Phy; homology; multiple sequence alignment; protein sequences; structural alignment.].
| S-EPMC6472439 | biostudies-literature
Project description:The recent development of high-throughput technology has allowed us to accumulate vast amounts of multi-omics data. Because even single omics data have a large number of variables, integrated analysis of multi-omics data suffers from problems such as computational instability and variable redundancy. Most multi-omics data analyses apply single supervised analysis, repeatedly, for dimensional reduction and variable selection. However, these approaches cannot avoid the problems of redundancy and collinearity of variables. In this study, we propose a novel approach using blockwise component analysis. This would solve the limitations of current methods by applying variable clustering and sparse principal component (sPC) analysis. Our approach consists of two stages. The first stage identifies homogeneous variable blocks, and then extracts sPCs, for each omics dataset. The second stage merges sPCs from each omics dataset, and then constructs a prediction model. We also propose a graphical method showing the results of sparse PCA and model fitting, simultaneously. We applied the proposed methodology to glioblastoma multiforme data from The Cancer Genome Atlas. The comparison with other existing approaches showed that our proposed methodology is more easily interpretable than other approaches, and has comparable predictive power, with a much smaller number of variables.
| S-EPMC7663540 | biostudies-literature
Project description:Principal component analysis (PCA) is routinely used to analyze genome-wide single-nucleotide polymorphism (SNP) data, for detecting population structure and potential outliers. However, the size of SNP datasets has increased immensely in recent years and PCA of large datasets has become a time consuming task. We have developed flashpca, a highly efficient PCA implementation based on randomized algorithms, which delivers identical accuracy in extracting the top principal components compared with existing tools, in substantially less time. We demonstrate the utility of flashpca on both HapMap3 and on a large Immunochip dataset. For the latter, flashpca performed PCA of 15,000 individuals up to 125 times faster than existing tools, with identical results, and PCA of 150,000 individuals using flashpca completed in 4 hours. The increasing size of SNP datasets will make tools such as flashpca essential as traditional approaches will not adequately scale. This approach will also help to scale other applications that leverage PCA or eigen-decomposition to substantially larger datasets.
| S-EPMC3981753 | biostudies-literature