Accounting for non-genetic factors by low-rank representation and sparse regression for eQTL mapping

Yang, Can; Wang, Lin; Zhang, Shuqin; Zhao, Hongyu

doi:10.1093/bioinformatics/btt075

Cited by 46 publications

(107 citation statements)

References 32 publications

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“…We add noises to the prior networks by randomly shuffling the elements in them. Furthermore, we use the signal-to-noise ratio defined as

SNR = \sqrt{\frac{W X}{Ξ + E}}

(Yang et al , 2013) to measure the noise ratio in the eQTL datasets. Here, we fix

C = 10, τ = 0.1,

and use different σ ’s to control SNR.…”

Section: Methodsmentioning

confidence: 99%

“…LORS (Yang et al , 2013) uses a low-rank matrix

L \in ℝ^{N \times D}

to account for the variations caused by hidden factors. The objective function of LORS is

\min_{W, μ, L} \frac{1}{2} | | Z - W X - μ 1 - L | {false|}_{F}^{2} + η | | W | {false|}_{1} + λ | | L | {false|}_{*}

where

| | \cdot | {false|}_{*}

is the nuclear norm, η is the empirical parameter for the

ℓ_{1}

penalty to control the sparsity of W and λ is the regularization parameter to control the rank of L .…”

Section: Background: Linear Regression With Graph Regularizermentioning

confidence: 99%

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Graph-regularized dual Lasso for robust eQTL mapping

et al. 2014

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Motivation: As a promising tool for dissecting the genetic basis of complex traits, expression quantitative trait loci (eQTL) mapping has attracted increasing research interest. An important issue in eQTL mapping is how to effectively integrate networks representing interactions among genetic markers and genes. Recently, several Lasso-based methods have been proposed to leverage such network information. Despite their success, existing methods have three common limitations: (i) a preprocessing step is usually needed to cluster the networks; (ii) the incompleteness of the networks and the noise in them are not considered; (iii) other available information, such as location of genetic markers and pathway information are not integrated.Results: To address the limitations of the existing methods, we propose Graph-regularized Dual Lasso (GDL), a robust approach for eQTL mapping. GDL integrates the correlation structures among genetic markers and traits simultaneously. It also takes into account the incompleteness of the networks and is robust to the noise. GDL utilizes graph-based regularizers to model the prior networks and does not require an explicit clustering step. Moreover, it enables further refinement of the partial and noisy networks. We further generalize GDL to incorporate the location of genetic makers and gene-pathway information. We perform extensive experimental evaluations using both simulated and real datasets. Experimental results demonstrate that the proposed methods can effectively integrate various available priori knowledge and significantly outperform the state-of-the-art eQTL mapping methods.Availability: Software for both C++ version and Matlab version is available at http://www.cs.unc.edu/∼weicheng/.Contact: weiwang@cs.ucla.eduSupplementary information: Supplementary data are available at Bioinformatics online.

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“…We add noises to the prior networks by randomly shuffling the elements in them. Furthermore, we use the signal-to-noise ratio defined as

SNR = \sqrt{\frac{W X}{Ξ + E}}

(Yang et al , 2013) to measure the noise ratio in the eQTL datasets. Here, we fix

C = 10, τ = 0.1,

and use different σ ’s to control SNR.…”

Section: Methodsmentioning

confidence: 99%

“…LORS (Yang et al , 2013) uses a low-rank matrix

L \in ℝ^{N \times D}

to account for the variations caused by hidden factors. The objective function of LORS is

\min_{W, μ, L} \frac{1}{2} | | Z - W X - μ 1 - L | {false|}_{F}^{2} + η | | W | {false|}_{1} + λ | | L | {false|}_{*}

where

| | \cdot | {false|}_{*}

is the nuclear norm, η is the empirical parameter for the

ℓ_{1}

penalty to control the sparsity of W and λ is the regularization parameter to control the rank of L .…”

Section: Background: Linear Regression With Graph Regularizermentioning

confidence: 99%

Graph-regularized dual Lasso for robust eQTL mapping

et al. 2014

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show abstract

“…By enlarging the forward searching scope and reduce the backward searching radius, the problem can be solved. An acceleration factor range, as defined in (24), was introduced to reduce the computation time.…”

Section: Algorithm Descriptionmentioning

confidence: 99%

Adaptive semi-supervised affinity propagation clustering algorithm based on structural similarity

Wang

Han

2016

Teh. vjesn.

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Original scientific paper In view of the unsatisfying clustering effect of affinity propagation (AP) clustering algorithm when dealing with data sets of complex structures, an adaptive semi-supervised affinity propagation clustering algorithm based on structural similarity (SAAP-SS) is proposed in this paper. First, a novel structural similarity is proposed by solving a non-linear, low-rank representation problem. Then we perform affinity propagation on the basis of adjusting the similarity matrix by utilizing the known pairwise constraints. Finally, the idea of fireworks explosion is introduced into the process of the algorithm. By adaptively searching the preference space bi-directionally, the algorithm's global and local searching abilities are balanced in order to find the optimal clustering structure. The results of the experiments with both synthetic and real data sets show performance improvements of the proposed algorithm compared with AP, FEO-SAP and K-means methods.Keywords: affinity propagation; fireworks explosion optimization; low rank representation; semi-supervised clustering; structural similarity Prilagodljivi polu-nadzirani algoritam grupiranja za srodno širenje utemeljen na strukturnoj sličnostiIzvorni znanstveni članak Uzimajući u obzir nezadovoljavajuće djelovanje grupiranja srodnog širenja algoritma grupiranja, kada se radi o nizovima podataka složenih struktura, u ovom se radu predlaže prilagodljivi nadzirani algoritam grupiranja srodnog širenja utemeljen na strukturnoj sličnosti (SAAP-SS). Najprije se predlaže nova strukturna sličnost rješavanjem nelinearnog problema zastupljenosti niskoga ranga. Zatim slijedi srodno širenje na temelju podešavanja matrice sličnosti primjenom poznatih udvojenih ograničenja. Na kraju se u postupak algoritma uvodi ideja eksplozija kod vatrometa. Prilagodljivo pretražujući preferencijalni prostor u dva smjera, uravnotežuju se globalne i lokalne pretraživačke sposobnosti algoritma u cilju pronalaženja optimalne strukture grupiranja. Rezultati eksperimenata i sa sintetičkim i s realnim nizovima podataka pokazuju poboljšanja u radu predloženog algoritma u usporedbi s AP, FEO-SAP i K-means metodama.

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“…The most direct approach for SVT is applying full SVD through svd and then soft-threshold the singular values. This approach is in practice used in many matrix learning problems according to the distributed code, e.g., Kalofolias, Bresson, Bronstein, and Vandergheynst (2014); Chi et al (2013); Parikh and Boyd (2013) ;Yang, Wang, Zhang, and Zhao (2013);Zhou, Liu, Wan, and Yu (2014); Zhou and Li (2014); Zhang et al (2017); Otazo, Candès, and Sodickson (2015); Goldstein, Studer, and Baraniuk (2015), to name a few. However, the built-in function svd is for full SVD of a dense matrix, and hence is very time-consuming and computationally expensive for large-scale problems.…”

Section: Introductionmentioning

confidence: 99%

`svt`: Singular Value Thresholding in MATLAB

Cai

Zhou

2017

J. Stat. Soft.

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Many statistical learning methods such as matrix completion, matrix regression, and multiple response regression estimate a matrix of parameters. The nuclear norm regularization is frequently employed to achieve shrinkage and low rank solutions. To minimize a nuclear norm regularized loss function, a vital and most time-consuming step is singular value thresholding, which seeks the singular values of a large matrix exceeding a threshold and their associated singular vectors. Currently MATLAB lacks a function for singular value thresholding. Its built-in svds function computes the top r singular values/vectors by Lanczos iterative method but is only efficient for sparse matrix input, while aforementioned statistical learning algorithms perform singular value thresholding on dense but structured matrices. To address this issue, we provide a MATLAB wrapper function svt that implements singular value thresholding. It encompasses both top singular value decomposition and thresholding, handles both large sparse matrices and structured matrices, and reduces the computation cost in matrix learning algorithms.

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Accounting for non-genetic factors by low-rank representation and sparse regression for eQTL mapping

Abstract: Supplementary data are available at Bioinformatics online.

Cited by 46 publications

References 32 publications

Graph-regularized dual Lasso for robust eQTL mapping

Graph-regularized dual Lasso for robust eQTL mapping

Adaptive semi-supervised affinity propagation clustering algorithm based on structural similarity

`svt`: Singular Value Thresholding in MATLAB

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Accounting for non-genetic factors by low-rank representation and sparse regression for eQTL mapping

Abstract: Supplementary data are available at Bioinformatics online.

Cited by 46 publications

References 32 publications

Graph-regularized dual Lasso for robust eQTL mapping

Graph-regularized dual Lasso for robust eQTL mapping

Adaptive semi-supervised affinity propagation clustering algorithm based on structural similarity

svt: Singular Value Thresholding in MATLAB

Contact Info

Product

Resources

About

`svt`: Singular Value Thresholding in MATLAB