On sparse Fisher discriminant method for microarray data analysis.
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ABSTRACT:
SUBMITTER: Fung ES
PROVIDER: S-EPMC2241932 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:Recent years have seen active developments of various penalized regression methods, such as LASSO and elastic net, to analyze high dimensional data. In these approaches, the direction and length of the regression coefficients are determined simultaneously. Due to the introduction of penalties, the length of the estimates can be far from being optimal for accurate predictions. We introduce a new framework, regression by projection, and its sparse version to analyze high dimensional data. The unique nature of this framework is that the directions of the regression coefficients are inferred first, and the lengths and the tuning parameters are determined by a cross validation procedure to achieve the largest prediction accuracy. We provide a theoretical result for simultaneous model selection consistency and parameter estimation consistency of our method in high dimension. This new framework is then generalized such that it can be applied to principal components analysis, partial least squares and canonical correlation analysis. We also adapt this framework for discriminant analysis. Compared to the existing methods, where there is relatively little control of the dependency among the sparse components, our method can control the relationships among the components. We present efficient algorithms and related theory for solving the sparse regression by projection problem. Based on extensive simulations and real data analysis, we demonstrate that our method achieves good predictive performance and variable selection in the regression setting, and the ability to control relationships between the sparse components leads to more accurate classification. In supplemental materials available online, the details of the algorithms and theoretical proofs, and R codes for all simulation studies are provided.
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Project description:BackgroundWith the development of next generation sequencing (NGS) technology and genotype imputation methods, statistical methods have been proposed to test a set of genomic variants together to detect if any of them is associated with the phenotype or disease. In practice, within the set, there is an unknown proportion of variants truly causal or associated with the disease. There is a demand for statistical methods with high power in both dense and sparse scenarios, where the proportion of causal or associated variants is large or small respectively.ResultsWe propose a new association test - weighted Adaptive Fisher (wAF) that can adapt to both dense and sparse scenarios by adding weights to the Adaptive Fisher (AF) method we developed before. Using simulation, we show that wAF enjoys comparable or better power to popular methods such as sequence kernel association tests (SKAT and SKAT-O) and adaptive SPU (aSPU) test. We apply wAF to a publicly available schizophrenia dataset, and successfully detect thirteen genes. Among them, three genes are supported by existing literature; six are plausible as they either relate to other neurological diseases or have relevant biological functions.ConclusionsThe proposed wAF method is a powerful disease-variants association test in both dense and sparse scenarios. Both simulation studies and real data analysis indicate the potential of wAF for new biological findings.
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Project description:Recently, low-rank and sparse model-based dimensionality reduction (DR) methods have aroused lots of interest. In this paper, we propose an effective supervised DR technique named block-diagonal constrained low-rank and sparse-based embedding (BLSE). BLSE has two steps, i.e., block-diagonal constrained low-rank and sparse representation (BLSR) and block-diagonal constrained low-rank and sparse graph embedding (BLSGE). Firstly, the BLSR model is developed to reveal the intrinsic intra-class and inter-class adjacent relationships as well as the local neighborhood relations and global structure of data. Particularly, there are mainly three items considered in BLSR. First, a sparse constraint is required to discover the local data structure. Second, a low-rank criterion is incorporated to capture the global structure in data. Third, a block-diagonal regularization is imposed on the representation to promote discrimination between different classes. Based on BLSR, informative and discriminative intra-class and inter-class graphs are constructed. With the graphs, BLSGE seeks a low-dimensional embedding subspace by simultaneously minimizing the intra-class scatter and maximizing the inter-class scatter. Experiments on public benchmark face and object image datasets demonstrate the effectiveness of the proposed approach.
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Project description:There are two key challenges when using a linear discriminant analysis in the high-dimensional setting, including singularity of the covariance matrix and difficulty of interpreting the resulting classifier. Although several methods have been proposed to address these problems, they focused only on identifying a parsimonious set of variables maximizing classification accuracy. However, most methods did not consider dependency between variables and efficacy of selected variables appropriately. To address these limitations, here we propose a new approach that directly estimates the sparse discriminant vector without a need of estimating the whole inverse covariance matrix, by formulating a quadratic optimization problem. Furthermore, this approach also allows to integrate external information to guide the structure of covariance matrix. We evaluated the proposed model with simulation studies. We then applied it to the transcriptomic study that aims to identify genomic markers predictive of the response to cancer immunotherapy, where the covariance matrix was constructed based on the prior knowledge available in the pathway database.
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Project description:BackgroundVariable selection on high throughput biological data, such as gene expression or single nucleotide polymorphisms (SNPs), becomes inevitable to select relevant information and, therefore, to better characterize diseases or assess genetic structure. There are different ways to perform variable selection in large data sets. Statistical tests are commonly used to identify differentially expressed features for explanatory purposes, whereas Machine Learning wrapper approaches can be used for predictive purposes. In the case of multiple highly correlated variables, another option is to use multivariate exploratory approaches to give more insight into cell biology, biological pathways or complex traits.ResultsA simple extension of a sparse PLS exploratory approach is proposed to perform variable selection in a multiclass classification framework.ConclusionssPLS-DA has a classification performance similar to other wrapper or sparse discriminant analysis approaches on public microarray and SNP data sets. More importantly, sPLS-DA is clearly competitive in terms of computational efficiency and superior in terms of interpretability of the results via valuable graphical outputs. sPLS-DA is available in the R package mixOmics, which is dedicated to the analysis of large biological data sets.
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Project description:Genomic instability in cancer leads to abnormal genome copy number alterations (CNA) that are associated with the development and behavior of tumors. Advances in microarray technology have allowed for greater resolution in detection of DNA copy number changes (amplifications or deletions) across the genome. However, the increase in number of measured signals and accompanying noise from the array probes present a challenge in accurate and fast identification of breakpoints that define CNA. This article proposes a novel detection technique that exploits the use of piece wise constant (PWC) vectors to represent genome copy number and sparse Bayesian learning (SBL) to detect CNA breakpoints.First, a compact linear algebra representation for the genome copy number is developed from normalized probe intensities. Second, SBL is applied and optimized to infer locations where copy number changes occur. Third, a backward elimination (BE) procedure is used to rank the inferred breakpoints; and a cut-off point can be efficiently adjusted in this procedure to control for the false discovery rate (FDR).The performance of our algorithm is evaluated using simulated and real genome datasets and compared to other existing techniques. Our approach achieves the highest accuracy and lowest FDR while improving computational speed by several orders of magnitude. The proposed algorithm has been developed into a free standing software application (GADA, Genome Alteration Detection Algorithm).http://biron.usc.edu/~piquereg/GADA
| S-EPMC2704547 | biostudies-literature
Project description:Microarray technology provides a powerful tool for the expression profile of thousands of genes simultaneously, which makes it possible to explore the molecular and metabolic etiology of the development of a complex disease under study. However, classical statistical methods and technologies fail to be applicable to microarray data. Therefore, it is necessary and motivating to develop powerful methods for large-scale statistical analyses. In this paper, we described a novel method, called Ranking Analysis of Microarray Data (RAM). RAM, which is a large-scale two-sample t-test method, is based on comparisons between a set of ranked T statistics and a set of ranked Z values (a set of ranked estimated null scores) yielded by a "randomly splitting" approach instead of a "permutation" approach and a two-simulation strategy for estimating the proportion of genes identified by chance, i.e., the false discovery rate (FDR). The results obtained from the simulated and observed microarray data show that RAM is more efficient in identification of genes differentially expressed and estimation of FDR under undesirable conditions such as a large fudge factor, small sample size, or mixture distribution of noises than Significance Analysis of Microarrays.
| S-EPMC2584353 | biostudies-literature
Project description:BackgroundData clustering analysis has been extensively applied to extract information from gene expression profiles obtained with DNA microarrays. To this aim, existing clustering approaches, mainly developed in computer science, have been adapted to microarray data analysis. However, previous studies revealed that microarray datasets have very diverse structures, some of which may not be correctly captured by current clustering methods. We therefore approached the problem from a new starting point, and developed a clustering algorithm designed to capture dataset-specific structures at the beginning of the process.ResultsThe clustering algorithm is named Fuzzy clustering by Local Approximation of MEmbership (FLAME). Distinctive elements of FLAME are: (i) definition of the neighborhood of each object (gene or sample) and identification of objects with "archetypal" features named Cluster Supporting Objects, around which to construct the clusters; (ii) assignment to each object of a fuzzy membership vector approximated from the memberships of its neighboring objects, by an iterative converging process in which membership spreads from the Cluster Supporting Objects through their neighbors. Comparative analysis with K-means, hierarchical, fuzzy C-means and fuzzy self-organizing maps (SOM) showed that data partitions generated by FLAME are not superimposable to those of other methods and, although different types of datasets are better partitioned by different algorithms, FLAME displays the best overall performance. FLAME is implemented, together with all the above-mentioned algorithms, in a C++ software with graphical interface for Linux and Windows, capable of handling very large datasets, named Gene Expression Data Analysis Studio (GEDAS), freely available under GNU General Public License.ConclusionThe FLAME algorithm has intrinsic advantages, such as the ability to capture non-linear relationships and non-globular clusters, the automated definition of the number of clusters, and the identification of cluster outliers, i.e. genes that are not assigned to any cluster. As a result, clusters are more internally homogeneous and more diverse from each other, and provide better partitioning of biological functions. The clustering algorithm can be easily extended to applications different from gene expression analysis.
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Project description:MOTIVATION: DNA microarray analysis is characterized by obtaining a large number of gene variables from a small number of observations. Cluster analysis is widely used to analyze DNA microarray data to make classification and diagnosis of disease. Because there are so many irrelevant and insignificant genes in a dataset, a feature selection approach must be employed in data analysis. The performance of cluster analysis of this high-throughput data depends on whether the feature selection approach chooses the most relevant genes associated with disease classes. RESULTS: Here we proposed a new method using multiple Orthogonal Partial Least Squares-Discriminant Analysis (mOPLS-DA) models and S-plots to select the most relevant genes to conduct three-class disease classification and prediction. We tested our method using Golub's leukemia microarray data. For three classes with subtypes, we proposed hierarchical orthogonal partial least squares-discriminant analysis (OPLS-DA) models and S-plots to select features for two main classes and their subtypes. For three classes in parallel, we employed three OPLS-DA models and S-plots to choose marker genes for each class. The power of feature selection to classify and predict three-class disease was evaluated using cluster analysis. Further, the general performance of our method was tested using four public datasets and compared with those of four other feature selection methods. The results revealed that our method effectively selected the most relevant features for disease classification and prediction, and its performance was better than that of the other methods.
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Project description:Sparse representation classification (SRC) is one of the most promising classification methods for supervised learning. This method can effectively exploit discriminating information by introducing a [Symbol: see text]1 regularization terms to the data. With the desirable property of sparisty, SRC is robust to both noise and outliers. In this study, we propose a weighted meta-sample based non-parametric sparse representation classification method for the accurate identification of tumor subtype. The proposed method includes three steps. First, we extract the weighted meta-samples for each sub class from raw data, and the rationality of the weighting strategy is proven mathematically. Second, sparse representation coefficients can be obtained by [Symnbol: see text]1 regularization of underdetermined linear equations. Thus, data dependent sparsity can be adaptively tuned. A simple characteristic function is eventually utilized to achieve classification. Asymptotic time complexity analysis is applied to our method. Compared with some state-of-the-art classifiers, the proposed method has lower time complexity and more flexibility. Experiments on eight samples of publicly available gene expression profile data show the effectiveness of the proposed method.
| S-EPMC4130588 | biostudies-literature