A novel dimension reduction algorithm based on weighted kernel principal analysis for gene expression data.
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ABSTRACT:
SUBMITTER: Liu WB
PROVIDER: S-EPMC8513872 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:Sufficient dimension reduction is popular for reducing data dimensionality without stringent model assumptions. However, most existing methods may work poorly for binary classification. For example, sliced inverse regression (Li, 1991) can estimate at most one direction if the response is binary. In this paper we propose principal weighted support vector machines, a unified framework for linear and nonlinear sufficient dimension reduction in binary classification. Its asymptotic properties are studied, and an efficient computing algorithm is proposed. Numerical examples demonstrate its performance in binary classification.
| S-EPMC5793677 | biostudies-literature
Project description:BackgroundWhen a large number of candidate variables are present, a dimension reduction procedure is usually conducted to reduce the variable space before the subsequent analysis is carried out. The goal of dimension reduction is to find a list of candidate genes with a more operable length ideally including all the relevant genes. Leaving many uninformative genes in the analysis can lead to biased estimates and reduced power. Therefore, dimension reduction is often considered a necessary predecessor of the analysis because it can not only reduce the cost of handling numerous variables, but also has the potential to improve the performance of the downstream analysis algorithms.ResultsWe propose a TMLE-VIM dimension reduction procedure based on the variable importance measurement (VIM) in the frame work of targeted maximum likelihood estimation (TMLE). TMLE is an extension of maximum likelihood estimation targeting the parameter of interest. TMLE-VIM is a two-stage procedure. The first stage resorts to a machine learning algorithm, and the second step improves the first stage estimation with respect to the parameter of interest.ConclusionsWe demonstrate with simulations and data analyses that our approach not only enjoys the prediction power of machine learning algorithms, but also accounts for the correlation structures among variables and therefore produces better variable rankings. When utilized in dimension reduction, TMLE-VIM can help to obtain the shortest possible list with the most truly associated variables.
| S-EPMC3166941 | biostudies-literature
Project description:The construction of the components of Partial Least Squares (PLS) is based on the maximization of the covariance/correlation between linear combinations of the predictors and the response. However, the usual Pearson correlation is influenced by outliers in the response or in the predictors. To cope with outliers, we replace the Pearson correlation with the Spearman rank correlation in the optimization criteria of PLS. The rank-based method of PLS is insensitive to outlying values in both the predictors and response, and incorporates the censoring information by using an approach of Nguyen and Rocke (2004) and two approaches of reweighting and mean imputation of Datta et al. (2007). The performance of the rank-based approaches of PLS, denoted by Rank-based Modified Partial Least Squares (RMPLS), Rank-based Reweighted Partial Least Squares (RRWPLS), and Rank-based Mean-Imputation Partial Least Squares (RMIPLS), is investigated in a simulation study and on four real datasets, under an Accelerated Failure Time (AFT) model, against their un-ranked counterparts, and several other dimension reduction techniques. The results indicate that RMPLS is a better dimension reduction method than other variants of PLS as well as other considered methods in terms of the minimized cross-validation error of fit and the mean squared error of fit in the presence of outliers in the response, and is comparable to other variants of PLS in the absence of outliers. Supplementary Materials are available at http://www.worldscinet.com/jbcb/
| S-EPMC2796584 | 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:BackgroundThe most popular methods for significance analysis on microarray data are well suited to find genes differentially expressed across predefined categories. However, identification of features that correlate with continuous dependent variables is more difficult using these methods, and long lists of significant genes returned are not easily probed for co-regulations and dependencies. Dimension reduction methods are much used in the microarray literature for classification or for obtaining low-dimensional representations of data sets. These methods have an additional interpretation strength that is often not fully exploited when expression data are analysed. In addition, significance analysis may be performed directly on the model parameters to find genes that are important for any number of categorical or continuous responses. We introduce a general scheme for analysis of expression data that combines significance testing with the interpretative advantages of the dimension reduction methods. This approach is applicable both for explorative analysis and for classification and regression problems.ResultsThree public data sets are analysed. One is used for classification, one contains spiked-in transcripts of known concentrations, and one represents a regression problem with several measured responses. Model-based significance analysis is performed using a modified version of Hotelling's T2-test, and a false discovery rate significance level is estimated by resampling. Our results show that underlying biological phenomena and unknown relationships in the data can be detected by a simple visual interpretation of the model parameters. It is also found that measured phenotypic responses may model the expression data more accurately than if the design-parameters are used as input. For the classification data, our method finds much the same genes as the standard methods, in addition to some extra which are shown to be biologically relevant. The list of spiked-in genes is also reproduced with high accuracy.ConclusionThe dimension reduction methods are versatile tools that may also be used for significance testing. Visual inspection of model components is useful for interpretation, and the methodology is the same whether the goal is classification, prediction of responses, feature selection or exploration of a data set. The presented framework is conceptually and algorithmically simple, and a Matlab toolbox (Mathworks Inc, USA) is supplemented.
| S-EPMC2194745 | biostudies-literature
Project description:BackgroundWith the advance of microarray technology, several methods for gene classification and prognosis have been already designed. However, under various denominations, some of these methods have similar approaches. This study evaluates the influence of gene expression variance structure on the performance of methods that describe the relationship between gene expression levels and a given phenotype through projection of data onto discriminant axes.ResultsWe compared Between-Group Analysis and Discriminant Analysis (with prior dimension reduction through Partial Least Squares or Principal Components Analysis). A geometric approach showed that these two methods are strongly related, but differ in the way they handle data structure. Yet, data structure helps understanding the predictive efficiency of these methods. Three main structure situations may be identified. When the clusters of points are clearly split, both methods perform equally well. When the clusters superpose, both methods fail to give interesting predictions. In intermediate situations, the configuration of the clusters of points has to be handled by the projection to improve prediction. For this, we recommend Discriminant Analysis. Besides, an innovative way of simulation generated the three main structures by modelling different partitions of the whole variance into within-group and between-group variances. These simulated datasets were used in complement to some well-known public datasets to investigate the methods behaviour in a large diversity of structure situations. To examine the structure of a dataset before analysis and preselect an a priori appropriate method for its analysis, we proposed a two-graph preliminary visualization tool: plotting patients on the Between-Group Analysis discriminant axis (x-axis) and on the first and the second within-group Principal Components Analysis component (y-axis), respectively.ConclusionDiscriminant Analysis outperformed Between-Group Analysis because it allows for the dataset structure. An a priori knowledge of that structure may guide the choice of the analysis method. Simulated datasets with known properties are valuable to assess and compare the performance of analysis methods, then implementation on real datasets checks and validates the results. Thus, we warn against the use of unchallenging datasets for method comparison, such as the Golub dataset, because their structure is such that any method would be efficient.
| S-EPMC1831790 | biostudies-literature
Project description:BackgroundVisualization of DNA microarray data in two or three dimensional spaces is an important exploratory analysis step in order to detect quality issues or to generate new hypotheses. Principal Component Analysis (PCA) is a widely used linear method to define the mapping between the high-dimensional data and its low-dimensional representation. During the last decade, many new nonlinear methods for dimension reduction have been proposed, but it is still unclear how well these methods capture the underlying structure of microarray gene expression data. In this study, we assessed the performance of the PCA approach and of six nonlinear dimension reduction methods, namely Kernel PCA, Locally Linear Embedding, Isomap, Diffusion Maps, Laplacian Eigenmaps and Maximum Variance Unfolding, in terms of visualization of microarray data.ResultsA systematic benchmark, consisting of Support Vector Machine classification, cluster validation and noise evaluations was applied to ten microarray and several simulated datasets. Significant differences between PCA and most of the nonlinear methods were observed in two and three dimensional target spaces. With an increasing number of dimensions and an increasing number of differentially expressed genes, all methods showed similar performance. PCA and Diffusion Maps responded less sensitive to noise than the other nonlinear methods.ConclusionsLocally Linear Embedding and Isomap showed a superior performance on all datasets. In very low-dimensional representations and with few differentially expressed genes, these two methods preserve more of the underlying structure of the data than PCA, and thus are favorable alternatives for the visualization of microarray data.
| S-EPMC2998530 | biostudies-literature
Project description:BACKGROUND: Health studies and mHealth applications are increasingly resorting to tracking technologies such as Global Positioning Systems (GPS) to study the relation between mobility, exposures, and health. GPS tracking generates large sets of geographic data that need to be transformed to be useful for health research. This paper proposes a method to test the performance of activity place detection algorithms, and compares the performance of a novel kernel-based algorithm with a more traditional time-distance cluster detection method. METHODS: A set of 750 artificial GPS tracks containing three stops each were generated, with various levels of noise.. A total of 9,000 tracks were processed to measure the algorithms' capacity to detect stop locations and estimate stop durations, with varying GPS noise and algorithm parameters. RESULTS: The proposed kernel-based algorithm outperformed the traditional algorithm on most criteria associated to activity place detection, and offered a stronger resilience to GPS noise, managing to detect up to 92.3% of actual stops, and estimating stop duration within 5% error margins at all tested noise levels. CONCLUSIONS: Capacity to detect activity locations is an important feature in a context of increasing use of GPS devices in health and place research. While further testing with real-life tracks is recommended, testing algorithms' performance with artificial track sets for which characteristics are controlled is useful. The proposed novel algorithm outperformed the traditional algorithm under these conditions.
| S-EPMC3637118 | biostudies-literature
Project description:Recent efforts to characterize the human microbiome and its relation to chronic diseases have led to a surge in statistical development for compositional data. We develop likelihood-based sufficient dimension reduction methods (SDR) to find linear combinations that contain all the information in the compositional data on an outcome variable, i.e., are sufficient for modeling and prediction of the outcome. We consider several models for the inverse regression of the compositional vector or transformations of it, as a function of outcome. They include normal, multinomial, and Poisson graphical models that allow for complex dependencies among observed counts. These methods yield efficient estimators of the reduction and can be applied to continuous or categorical outcomes. We incorporate variable selection into the estimation via penalties and address important invariance issues arising from the compositional nature of the data. We illustrate and compare our methods and some established methods for analyzing microbiome data in simulations and using data from the Human Microbiome Project. Displaying the data in the coordinate system of the SDR linear combinations allows visual inspection and facilitates comparisons across studies.
| S-EPMC8677486 | biostudies-literature
Project description:BackgroundThere are many methods for analyzing microarray data that group together genes having similar patterns of expression over all conditions tested. However, in many instances the biologically important goal is to identify relatively small sets of genes that share coherent expression across only some conditions, rather than all or most conditions as required in traditional clustering; e.g. genes that are highly up-regulated and/or down-regulated similarly across only a subset of conditions. Equally important is the need to learn which conditions are the decisive ones in forming such gene sets of interest, and how they relate to diverse conditional covariates, such as disease diagnosis or prognosis.ResultsWe present a method for automatically identifying such candidate sets of biologically relevant genes using a combination of principal components analysis and information theoretic metrics. To enable easy use of our methods, we have developed a data analysis package that facilitates visualization and subsequent data mining of the independent sources of significant variation present in gene microarray expression datasets (or in any other similarly structured high-dimensional dataset). We applied these tools to two public datasets, and highlight sets of genes most affected by specific subsets of conditions (e.g. tissues, treatments, samples, etc.). Statistically significant associations for highlighted gene sets were shown via global analysis for Gene Ontology term enrichment. Together with covariate associations, the tool provides a basis for building testable hypotheses about the biological or experimental causes of observed variation.ConclusionWe provide an unsupervised data mining technique for diverse microarray expression datasets that is distinct from major methods now in routine use. In test uses, this method, based on publicly available gene annotations, appears to identify numerous sets of biologically relevant genes. It has proven especially valuable in instances where there are many diverse conditions (10's to hundreds of different tissues or cell types), a situation in which many clustering and ordering algorithms become problematic. This approach also shows promise in other topic domains such as multi-spectral imaging datasets.
| S-EPMC1501050 | biostudies-literature