Piecewise-constant and low-rank approximation for identification of recurrent copy number variations

A Compact Neural Network for Fused Lasso Signal Approximator

The fused lasso signal approximator (FLSA) is a vital optimization problem with extensive applications in signal processing and biomedical engineering. However, the optimization problem is difficult to solve since it is both nonsmooth and nonseparable. The existing numerical solutions implicate the use of several auxiliary variables in order to deal with the nondifferentiable penalty. Thus, the resulting algorithms are both time- and memory-inefficient. This paper proposes a compact neural network to solve the FLSA. The neural network has a one-layer structure with the number of neurons proportionate to the dimension of the given signal, thanks to the utilization of consecutive projections. The proposed neural network is stable in the Lyapunov sense and is guaranteed to converge globally to the optimal solution of the FLSA. Experiments on several applications from signal processing and biomedical engineering confirm the reasonable performance of the proposed neural network.

A Density Peak-Based Method to Detect Copy Number Variations From Next-Generation Sequencing Data

Copy number variation (CNV) is a common type of structural variations in human genome and confers biological meanings to human complex diseases. Detection of CNVs is an important step for a systematic analysis of CNVs in medical research of complex diseases. The recent development of next-generation sequencing (NGS) platforms provides unprecedented opportunities for the detection of CNVs at a base-level resolution. However, due to the intrinsic characteristics behind NGS data, accurate detection of CNVs is still a challenging task. In this article, we propose a new density peak-based method, called dpCNV, for the detection of CNVs from NGS data. The algorithm of dpCNV is designed based on density peak clustering algorithm. It extracts two features, i.e., local density and minimum distance, from sequencing read depth (RD) profile and generates a two-dimensional data. Based on the generated data, a two-dimensional null distribution is constructed to test the significance of each genome bin and then the significant genome bins are declared as CNVs. We test the performance of the dpCNV method on a number of simulated datasets and make comparison with several existing methods. The experimental results demonstrate that our proposed method outperforms others in terms of sensitivity and F1-score. We further apply it to a set of real sequencing samples and the results demonstrate the validity of dpCNV. Therefore, we expect that dpCNV can be used as a supplementary to existing methods and may become a routine tool in the field of genome mutation analysis.

Robust Recurrent CNV Detection in the Presence of Inter-Subject Variability

The study of recurrent copy number variations (CNVs) plays an important role in understanding the onset and evolution of complex diseases such as cancer. Array-based comparative genomic hybridization (aCGH) is a widely used microarray based technology for identifying CNVs. However, due to high noise levels and inter-sample variability, detecting recurrent CNVs from aCGH data remains a challenging topic. This paper proposes a novel method for identification of the recurrent CNVs. In the proposed method, the noisy aCGH data is modeled as the superposition of three matrices: a full-rank matrix of weighted piece-wise generating signals accounting for the clean aCGH data, a Gaussian noise matrix to model the inherent experimentation errors and other sources of error, and a sparse matrix to capture the sparse inter-sample (sample-specific) variations. We demonstrated the ability of our method to separate accurately recurrent CNVs from sample-specific variations and noise in both simulated (artificial) data and real data. The proposed method produced more accurate results than current state-of-the-art methods used in recurrent CNV detection and exhibited robustness to noise and sample-specific variations.

HetRCNA: A Novel Method to Identify Recurrent Copy Number Alternations from Heterogeneous Tumor Samples Based on Matrix Decomposition Framework

A common strategy to discovering cancer associated copy number aberrations (CNAs) from a cohort of cancer samples is to detect recurrent CNAs (RCNAs). Although the previous methods can successfully identify communal RCNAs shared by nearly all tumor samples, detecting subgroup-specific RCNAs and their related subgroup samples from cancer samples with heterogeneity is still invalid for these existing approaches. In this paper, we introduce a novel integrated method called HetRCNA, which can identify statistically significant subgroup-specific RCNAs and their related subgroup samples. Based on matrix decomposition framework with weight constraint, HetRCNA can successfully measure the subgroup samples by coefficients of left vectors with weight constraint and subgroup-specific RCNAs by coefficients of the right vectors and significance test. When we evaluate HetRCNA on simulated dataset, the results show that HetRCNA gives the best performances among the competing methods and is robust to the noise factors of the simulated data. When HetRCNA is applied on a real breast cancer dataset, our approach successfully identifies a bunch of RCNA regions and the result is highly correlated with the results of the other two investigated approaches. Notably, the genomic regions identified by HetRCNA harbor many breast cancer related genes reported by previous researches.

WaveDec: A Wavelet Approach to Identify Both Shared and Individual Patterns of Copy-Number Variations

Copy-number variations (CNVs) are associated with complex diseases and particular tumor types. Array-based comparative genomic hybridization (aCGH) is a common approach for the detection of CNVs. Traditional CNV detection methods for multiple aCGH samples mainly use batch samples to find common variations, not accounting for the individual characteristics of each sample. Accurately differentiating both the commonly shared and the individual CNV patterns is pivotal to identify cell populations, or to distinguish cell growth (as in cancer) from invasion of new cells. Our preliminary results have now demonstrated that both the shared and individual CNV patterns have distinctive characteristics after wavelet transform.

METHODS

To exploit these characteristics, we propose to formulate a quadratic data-separation problem within the wavelet space to discriminate the shared and individual CNVs from raw data. We have elaborated a numerical solution and shown that the solution can be obtained by solving decoupled subproblems. By this approach, computational costs can be limited, enabling efficient application in the analysis of large sequencing datasets.

RESULTS

The advantages of our proposed method, called WaveDec, have been demonstrated by comparison with popular CNV-detection methods using synthetic and empirical aCGH data. The performance of WaveDec was further validated by experiments with single-cell-sequencing data.

CONCLUSION

WaveDec can successfully differentiate shared and individual patterns, and performs well even in data contaminated with high levels of noise.

SIGNIFICANCE

Both the shared and individual patterns can be uniquely characterized as well as effectively decomposed within the wavelet space.

A Projection Neural Network for Identifying Copy Number Variants

The identification of copy number variations (CNVs) helps the diagnosis of many diseases. One major hurdle in the path of CNVs discovery is that the boundaries of normal and aberrant regions cannot be distinguished from the raw data, since various types of noise contaminate them. To tackle this challenge, the total variation regularization is mostly used in the optimization problems to approximate the noise-free data from corrupted observations. The minimization using such regularization is challenging to deal with since it is non-differentiable. In this paper, we propose a projection neural network to solve the non-smooth problem. The proposed neural network has a simple one-layer structure and is theoretically assured to have the global exponential convergence to the solution of the total variation-regularized problem. The experiments on several real and simulated datasets illustrate the reasonable performance of the proposed neural network and show that its performance is comparable with those of more sophisticated algorithms.

Detection of Significant Copy Number Variations From Multiple Samples in Next-Generation Sequencing Data

Analyzing copy number variations (CNVs) from next-generation sequencing (NGS) data has become a common approach to detect disease susceptibility genes. The main challenge is how to utilize the NGS data with limited coverage depth to detect significant CNVs. Here, we introduce a new statistical method, the derivative of correlation coefficient (DCC), to detect significant CNVs that recurrently occur in multiple samples using read depth signals. We use a sliding window to calculate a correlation coefficient for each genome bin, and compute corresponding derivatives by fitting curves to the correlation coefficient. Then, the detection of significant CNVs was transformed into a problem of detecting significant derivatives reflecting genome breakpoints that can be solved using statistical hypothesis testing. We tested and compared the performance of DCC against several peer methods using a large number of simulation data sets, and validated DCC using several real sequencing data sets derived from the European Genome-Phenome archive, DNA Data Bank of Japan, and the 1000 Genomes Project. Experimental results suggest that DCC is an effective approach for identifying CNVs, outperforming peer methods in the terms of detection power and accuracy. DCC can be used to detect significant or recurrent CNVs in various NGS data sets, thus providing useful information to study genomic mutations and find disease susceptibility genes.

svt: Singular Value Thresholding in MATLAB

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.

Detection Copy Number Variants from NGS with Sparse and Smooth Constraints

It is known that copy number variations (CNVs) are associated with complex diseases and particular tumor types, thus reliable identification of CNVs is of great potential value. Recent advances in next generation sequencing (NGS) data analysis have helped manifest the richness of CNV information. However, the performances of these methods are not consistent. Reliably finding CNVs in NGS data in an efficient way remains a challenging topic, worthy of further investigation. Accordingly, we tackle the problem by formulating CNVs identification into a quadratic optimization problem involving two constraints. By imposing the constraints of sparsity and smoothness, the reconstructed read depth signal from NGS is anticipated to fit the CNVs patterns more accurately. An efficient numerical solution tailored from alternating direction minimization (ADM) framework is elaborated. We demonstrate the advantages of the proposed method, namely ADM-CNV, by comparing it with six popular CNV detection methods using synthetic, simulated, and empirical sequencing data. It is shown that the proposed approach can successfully reconstruct CNV patterns from raw data, and achieve superior or comparable performance in detection of the CNVs compared to the existing counterparts.

A novel network regularized matrix decomposition method to detect mutated cancer genes in tumour samples with inter-patient heterogeneity

Inter-patient heterogeneity is a major challenge for mutated cancer genes detection which is crucial to advance cancer diagnostics and therapeutics. To detect mutated cancer genes in heterogeneous tumour samples, a prominent strategy is to determine whether the genes are recurrently mutated in their interaction network context. However, recent studies show that some cancer genes in different perturbed pathways are mutated in different subsets of samples. Subsequently, these genes may not display significant mutational recurrence and thus remain undiscovered even in consideration of network information. We develop a novel method called mCGfinder to efficiently detect mutated cancer genes in tumour samples with inter-patient heterogeneity. Based on matrix decomposition framework incorporated with gene interaction network information, mCGfinder can successfully measure the significance of mutational recurrence of genes in a subset of samples. When applying mCGfinder on TCGA somatic mutation datasets of five types of cancers, we find that the genes detected by mCGfinder are significantly enriched for known cancer genes, and yield substantially smaller p-values than other existing methods. All the results demonstrate that mCGfinder is an efficient method in detecting mutated cancer genes.

Discovering potential driver genes through an integrated model of somatic mutation profiles and gene functional information

An integrated approach to identify driver genes based on information of somatic mutations, the interaction network and Gene Ontology similarity.

Discovering Recurrent Copy Number Aberrations in Complex Patterns via Non-Negative Sparse Singular Value Decomposition

Recurrent copy number aberrations (RCNAs) in multiple cancer samples are strongly associated with tumorigenesis, and RCNA discovery is helpful to cancer research and treatment. Despite the emergence of numerous RCNA discovering methods, most of them are unable to detect RCNAs in complex patterns that are influenced by complicating factors including aberration in partial samples, co-existing of gains and losses and normal-like tumor samples. Here, we propose a novel computational method, called non-negative sparse singular value decomposition (NN-SSVD), to address the RCNA discovering problem in complex patterns. In NN-SSVD, the measurement of RCNA is based on the aberration frequency in a part of samples rather than all samples, which can circumvent the complexity of different RCNA patterns. We evaluate NN-SSVD on synthetic dataset by comparison on detection scores and Receiver Operating Characteristics curves, and the results show that NN-SSVD outperforms existing methods in RCNA discovery and demonstrate more robustness to RCNA complicating factors. Applying our approach on a breast cancer dataset, we successfully identify a number of genomic regions that are strongly correlated with previous studies, which harbor a bunch of known breast cancer associated genes.

Penalized weighted low-rank approximation for robust recovery of recurrent copy number variations

BACKGROUND

Copy number variation (CNV) analysis has become one of the most important research areas for understanding complex disease. With increasing resolution of array-based comparative genomic hybridization (aCGH) arrays, more and more raw copy number data are collected for multiple arrays. It is natural to realize the co-existence of both recurrent and individual-specific CNVs, together with the possible data contamination during the data generation process. Therefore, there is a great need for an efficient and robust statistical model for simultaneous recovery of both recurrent and individual-specific CNVs.

RESULT

We develop a penalized weighted low-rank approximation method (WPLA) for robust recovery of recurrent CNVs. In particular, we formulate multiple aCGH arrays into a realization of a hidden low-rank matrix with some random noises and let an additional weight matrix account for those individual-specific effects. Thus, we do not restrict the random noise to be normally distributed, or even homogeneous. We show its performance through three real datasets and twelve synthetic datasets from different types of recurrent CNV regions associated with either normal random errors or heavily contaminated errors.

CONCLUSION

Our numerical experiments have demonstrated that the WPLA can successfully recover the recurrent CNV patterns from raw data under different scenarios. Compared with two other recent methods, it performs the best regarding its ability to simultaneously detect both recurrent and individual-specific CNVs under normal random errors. More importantly, the WPLA is the only method which can effectively recover the recurrent CNVs region when the data is heavily contaminated.

Fast dimension reduction and integrative clustering of multi-omics data using low-rank approximation: application to cancer molecular classification

Background

One major goal of large-scale cancer omics study is to identify molecular subtypes for more accurate cancer diagnoses and treatments. To deal with high-dimensional cancer multi-omics data, a promising strategy is to find an effective low-dimensional subspace of the original data and then cluster cancer samples in the reduced subspace. However, due to data-type diversity and big data volume, few methods can integrative and efficiently find the principal low-dimensional manifold of the high-dimensional cancer multi-omics data.

Results

In this study, we proposed a novel low-rank approximation based integrative probabilistic model to fast find the shared principal subspace across multiple data types: the convexity of the low-rank regularized likelihood function of the probabilistic model ensures efficient and stable model fitting. Candidate molecular subtypes can be identified by unsupervised clustering hundreds of cancer samples in the reduced low-dimensional subspace. On testing datasets, our method LRAcluster (low-rank approximation based multi-omics data clustering) runs much faster with better clustering performances than the existing method. Then, we applied LRAcluster on large-scale cancer multi-omics data from TCGA. The pan-cancer analysis results show that the cancers of different tissue origins are generally grouped as independent clusters, except squamous-like carcinomas. While the single cancer type analysis suggests that the omics data have different subtyping abilities for different cancer types.

Conclusions

LRAcluster is a very useful method for fast dimension reduction and unsupervised clustering of large-scale multi-omics data. LRAcluster is implemented in R and freely available via http://bioinfo.au.tsinghua.edu.cn/software/lracluster/.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-2223-8) contains supplementary material, which is available to authorized users.