Variable selection for generalized canonical correlation analysis

Tenenhaus, Arthur; Philippe, Cathy; Guillemot, Vincent; Cao, Kim‐Anh Lê; Grill, Jacques; Frouin, Vincent

doi:10.1093/biostatistics/kxu001

Cited by 176 publications

(167 citation statements)

References 16 publications

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“…2 Less than 5 % of all simulation runs did not reach convergence after 50 iterations. In case of non-convergence, results from the last iteration run are taken.…”

Section: Resultsmentioning

confidence: 97%

“…After convergence of the algorithm, the values of A 1 and B 1 in subsequent iterations remain stable, and the same observations will be detected as outliers in regressions (2) and (3).…”

Section: The Algorithmmentioning

confidence: 95%

“…, r. In the simulations we conducted, convergence was almost always reached. 2 For data sets with n = 100, p = q = 10, on average 6 iterations per canonical vector pair are needed to converge. For n = 50, p = q = 100, on average 10 iterations are needed to converge.…”

Section: Number Of Canonical Variates To Extractmentioning

confidence: 99%

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Robust Sparse Canonical Correlation Analysis

Wilms

Croux

2015

SSRN Journal

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Background: Canonical correlation analysis (CCA) is a multivariate statistical method which describes the associations between two sets of variables. The objective is to find linear combinations of the variables in each data set having maximal correlation. In genomics, CCA has become increasingly important to estimate the associations between gene expression data and DNA copy number change data. The identification of such associations might help to increase our understanding of the development of diseases such as cancer. However, these data sets are typically high-dimensional, containing a lot of variables relative to the number of objects. Moreover, the data sets might contain atypical observations since it is likely that objects react differently to treatments. We discuss a method for Robust Sparse CCA, thereby providing a solution to both issues. Sparse estimation produces canonical vectors with some of their elements estimated as exactly zero. As such, their interpretability is improved. Robust methods can cope with atypical observations in the data. Results: We illustrate the good performance of the Robust Sparse CCA method by several simulation studies and three biometric examples. Robust Sparse CCA considerably outperforms its main alternatives in (1) correctly detecting the main associations between the data sets, in (2) accurately estimating these associations, and in (3) detecting outliers. Conclusions: Robust Sparse CCA delivers interpretable canonical vectors, while at the same time coping with outlying observations. The proposed method is able to describe the associations between high-dimensional data sets, which are nowadays commonplace in genomics. Furthermore, the Robust Sparse CCA method allows to characterize outliers.

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“…2 Less than 5 % of all simulation runs did not reach convergence after 50 iterations. In case of non-convergence, results from the last iteration run are taken.…”

Section: Resultsmentioning

confidence: 97%

“…After convergence of the algorithm, the values of A 1 and B 1 in subsequent iterations remain stable, and the same observations will be detected as outliers in regressions (2) and (3).…”

Section: The Algorithmmentioning

confidence: 95%

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Robust Sparse Canonical Correlation Analysis

Wilms

Croux

2015

SSRN Journal

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“…Since the development of the sparse estimators derived from 1 penalties such as the Lasso [6] or the Dantzig selector [7], sparse models have been shown to be able to recover the subset of relevant variables in various situations [7]- [10]. That being said, the conditions for support recovery are quite stringent and difficult to assess in practice.…”

Section: Introductionmentioning

confidence: 99%

Significance testing for variable selection in high-dimension

Bécu

Ambroise

Grandvalet

et al. 2015

2015 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB)

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Assessing the uncertainty pertaining to the conclusions derived from experimental data is challenging when there is a high number of possible explanations compared to the number of experiments. We propose a new two-stage "screen and clean" procedure for assessing the uncertainties pertaining to the selection of relevant variables in high-dimensional regression problems. In this two-stage method, screening consists in selecting a subset of candidate variables by a sparsity-inducing penalized regression, while cleaning consists in discarding all variables that do not pass a significance test. This test was originally based on ordinary least squares regression. We propose to improve the procedure by conveying more information from the screening stage to the cleaning stage. Our cleaning stage is based on an adaptively penalized regression whose weights are adjusted in the screening stage. Our procedure is amenable to the computation of p-values, allowing to control the False Discovery Rate. Our experiments show the benefits of our procedure, as we observe a systematic improvement of sensitivity compared to the original procedure.

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“…Witten and Tibshirani (2009) proposed to concatenate all data sets with an appropriate weight applied to each of them. Recently, a promising approach based on regularized generalised Canonical Correlation Analysis (rGCCA) was proposed by (Tenenhaus and Tenenhaus, 2011) as a generalization to the PLS approaches for more than two data sets by maximizing the sum of the correlation in a pairwise fashion between two data sets at a time, followed by a variant that enables variable selection (Tenenhaus, et al, 2014. In this article, we illustrate the usefulness and biological relevance of selected multivariate approaches from Lê Cao et al, (2008; and Tenenhaus et al, (2014) on a clinically relevant biological example, which is an acute renal allograft rejection study from the Biomarkers in Transplantation study. Kidney transplantation is a means to restore kidney function in patients with kidney failure.…”

Section: Introductionmentioning

confidence: 99%

Novel Multivariate Methods for Integration of Genomics and Proteomics Data: Applications in a Kidney Transplant Rejection Study

Günther

Shin

et al. 2014

OMICS: A Journal of Integrative Biology

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Multi-omics research is a key ingredient of data-intensive life sciences research, permitting measurement of biological molecules at different functional levels in the same individual. For a complete picture at the biological systems level, appropriate statistical techniques must however be developed to integrate different 'omics' data sets (e.g., genomics and proteomics). We report here multivariate projection-based analyses approaches to genomics and proteomics data sets, using the case study of and applications to observations in kidney transplant patients who experienced an acute rejection event (n=20) versus non-rejecting controls (n=20). In this data sets, we show how these novel methodologies might serve as promising tools for dimension reduction and selection of relevant features for different analytical frameworks. Unsupervised analyses highlighted the importance of post transplant time-of-rejection, while supervised analyses identified gene and protein signatures that together predicted rejection status with little time effect. The selected genes are part of biological pathways that are representative of immune responses. Gene enrichment profiles revealed increases in innate immune responses and neutrophil activities and a depletion of T lymphocyte related processes in rejection samples as compared to controls. In all, this article offers candidate biomarkers for future detection and monitoring of acute kidney transplant rejection, as well as ways forward for methodological advances to better harness multi-omics data sets.

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Variable selection for generalized canonical correlation analysis

Cited by 176 publications

References 16 publications

Robust Sparse Canonical Correlation Analysis

Robust Sparse Canonical Correlation Analysis

Significance testing for variable selection in high-dimension

Novel Multivariate Methods for Integration of Genomics and Proteomics Data: Applications in a Kidney Transplant Rejection Study

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