Investigating the relationship between genetic variation and phenotypic traits is a key issue in quantitative genetics. Specifically for Alzheimer's disease, the association between genetic markers and quantitative traits remains vague while, once identified, will provide valuable guidance for the study and development of genetic-based treatment approaches. Currently, to analyze the association of two modalities, sparse canonical correlation analysis (SCCA) is commonly used to compute one sparse linear combination of the variable features for each modality, giving a pair of linear combination vectors in total that maximizes the cross-correlation between the analyzed modalities. One drawback of the plain SCCA model is that the existing findings and knowledge cannot be integrated into the model as priors to help extract interesting correlation as well as identify biologically meaningful genetic and phenotypic markers. To bridge this gap, we introduce preference matrix guided SCCA (PM-SCCA) that not only takes priors encoded as a preference matrix but also maintains computational simplicity. A simulation study and a real-data experiment are conducted to investigate the effectiveness of the model. Both experiments demonstrate that the proposed PM-SCCA model can capture not only genotype-phenotype correlation but also relevant features effectively.

BACKGROUND: In Alzheimer's Diseases (AD) research, multimodal imaging analysis can unveil complementary information from multiple imaging modalities and further our understanding of the disease. One application is to discover disease subtypes using unsupervised clustering. However, existing clustering methods are often applied to input features directly, and could suffer from the curse of dimensionality with high-dimensional multimodal data. The purpose of our study is to identify multimodal imaging-driven subtypes in Mild Cognitive Impairment (MCI) participants using a multiview learning framework based on Deep Generalized Canonical Correlation Analysis (DGCCA), to learn shared latent representation with low dimensions from 3 neuroimaging modalities. RESULTS: DGCCA applies non-linear transformation to input views using neural networks and is able to learn correlated embeddings with low dimensions that capture more variance than its linear counterpart, generalized CCA (GCCA). We designed experiments to compare DGCCA embeddings with single modality features and GCCA embeddings by generating 2 subtypes from each feature set using unsupervised clustering. In our validation studies, we found that amyloid PET imaging has the most discriminative features compared with structural MRI and FDG PET which DGCCA learns from but not GCCA. DGCCA subtypes show differential measures in 5 cognitive assessments, 6 brain volume measures, and conversion to AD patterns. In addition, DGCCA MCI subtypes confirmed AD genetic markers with strong signals that existing late MCI group did not identify. CONCLUSION: Overall, DGCCA is able to learn effective low dimensional embeddings from multimodal data by learning non-linear projections. MCI subtypes generated from DGCCA embeddings are different from existing early and late MCI groups and show most similarity with those identified by amyloid PET features. In our validation studies, DGCCA subtypes show distinct patterns in cognitive measures, brain volumes, and are able to identify AD genetic markers. These findings indicate the promise of the imaging-driven subtypes and their power in revealing disease structures beyond early and late stage MCI.

Brain imaging genetics studies the genetic basis of brain structures and functionalities via integrating genotypic data such as single nucleotide polymorphisms (SNPs) and imaging quantitative traits (QTs). In this area, both multi-task learning (MTL) and sparse canonical correlation analysis (SCCA) methods are widely used since they are superior to those independent and pairwise univariate analysis. MTL methods generally incorporate a few of QTs and could not select features from multiple QTs; while SCCA methods typically employ one modality of QTs to study its association with SNPs. Both MTL and SCCA are computational expensive as the number of SNPs increases. In this paper, we propose a novel multi-task SCCA (MTSCCA) method to identify bi-multivariate associations between SNPs and multi-modal imaging QTs. MTSCCA could make use of the complementary information carried by different imaging modalities. MTSCCA enforces sparsity at the group level via the${\mathrm G}_{2,1}$-norm, and jointly selects features across multiple tasks for SNPs and QTs via the$\ell _{2,1}$-norm. A fast optimization algorithm is proposed using the grouping information of SNPs. Compared with conventional SCCA methods, MTSCCA obtains better correlation coefficients and canonical weights patterns. In addition, MTSCCA runs very fast and easy-to-implement, indicating its potential power in genome-wide brain-wide imaging genetics.

We present an effective deep multiview learning framework to identify population structure using multimodal imaging data. Our approach is based on canonical correlation analysis (CCA). We propose to use deep generalized CCA (DGCCA) to learn a shared latent representation of non-linearly mapped and maximally correlated components from multiple imaging modalities with reduced dimensionality. In our empirical study, this representation is shown to effectively capture more variance in original data than conventional generalized CCA (GCCA) which applies only linear transformation to the multi-view data. Furthermore, subsequent cluster analysis on the new feature set learned from DGCCA is able to identify a promising population structure in an Alzheimer's disease (AD) cohort. Genetic association analyses of the clustering results demonstrate that the shared representation learned from DGCCA yields a population structure with a stronger genetic basis than several competing feature learning methods.

MOTIVATION: Brain imaging genetics studies the complex associations between genotypic data such as single nucleotide polymorphisms (SNPs) and imaging quantitative traits (QTs). The neurodegenerative disorders usually exhibit the diversity and heterogeneity, originating from which different diagnostic groups might carry distinct imaging QTs, SNPs and their interactions. Sparse canonical correlation analysis (SCCA) is widely used to identify bi-multivariate genotype-phenotype associations. However, most existing SCCA methods are unsupervised, leading to an inability to identify diagnosis-specific genotype-phenotype associations. RESULTS: In this article, we propose a new joint multitask learning method, named MT-SCCALR, which absorbs the merits of both SCCA and logistic regression. MT-SCCALR learns genotype-phenotype associations of multiple tasks jointly, with each task focusing on identifying one diagnosis-specific genotype-phenotype pattern. Meanwhile, MT-SCCALR cannot only select relevant SNPs and imaging QTs for each diagnostic group alone, but also allows the selection of those shared by multiple diagnostic groups. We derive an efficient optimization algorithm whose convergence to a local optimum is guaranteed. Compared with two state-of-the-art methods, MT-SCCALR yields better or similar canonical correlation coefficients and classification performances. In addition, it owns much better discriminative canonical weight patterns of great interest than competitors. This demonstrates the power and capability of MTSCCAR in identifying diagnostically heterogeneous genotype-phenotype patterns, which would be helpful to understand the pathophysiology of brain disorders. AVAILABILITY AND IMPLEMENTATION: The software is publicly available at https://github.com/dulei323/MTSCCALR. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Brain imaging genetics becomes more and more important in brain science, which integrates genetic variations and brain structures or functions to study the genetic basis of brain disorders. The multi-modal imaging data collected by different technologies, measuring the same brain distinctly, might carry complementary information. Unfortunately, we do not know the extent to which the phenotypic variance is shared among multiple imaging modalities, which further might trace back to the complex genetic mechanism. In this paper, we propose a novel dirty multi-task sparse canonical correlation analysis (SCCA) to study imaging genetic problems with multi-modal brain imaging quantitative traits (QTs) involved. The proposed method takes advantages of the multi-task learning and parameter decomposition. It can not only identify the shared imaging QTs and genetic loci across multiple modalities, but also identify the modality-specific imaging QTs and genetic loci, exhibiting a flexible capability of identifying complex multi-SNP-multi-QT associations. Using the state-of-the-art multi-view SCCA and multi-task SCCA, the proposed method shows better or comparable canonical correlation coefficients and canonical weights on both synthetic and real neuroimaging genetic data. In addition, the identified modality-consistent biomarkers, as well as the modality-specific biomarkers, provide meaningful and interesting information, demonstrating the dirty multi-task SCCA could be a powerful alternative method in multi-modal brain imaging genetics.

MOTIVATION: Identifying the genetic basis of the brain structure, function and disorder by using the imaging quantitative traits (QTs) as endophenotypes is an important task in brain science. Brain QTs often change over time while the disorder progresses and thus understanding how the genetic factors play roles on the progressive brain QT changes is of great importance and meaning. Most existing imaging genetics methods only analyze the baseline neuroimaging data, and thus those longitudinal imaging data across multiple time points containing important disease progression information are omitted. RESULTS: We propose a novel temporal imaging genetic model which performs the multi-task sparse canonical correlation analysis (T-MTSCCA). Our model uses longitudinal neuroimaging data to uncover that how single nucleotide polymorphisms (SNPs) play roles on affecting brain QTs over the time. Incorporating the relationship of the longitudinal imaging data and that within SNPs, T-MTSCCA could identify a trajectory of progressive imaging genetic patterns over the time. We propose an efficient algorithm to solve the problem and show its convergence. We evaluate T-MTSCCA on 408 subjects from the Alzheimer's Disease Neuroimaging Initiative database with longitudinal magnetic resonance imaging data and genetic data available. The experimental results show that T-MTSCCA performs either better than or equally to the state-of-the-art methods. In particular, T-MTSCCA could identify higher canonical correlation coefficients and capture clearer canonical weight patterns. This suggests that T-MTSCCA identifies time-consistent and time-dependent SNPs and imaging QTs, which further help understand the genetic basis of the brain QT changes over the time during the disease progression. AVAILABILITY AND IMPLEMENTATION: The software and simulation data are publicly available at https://github.com/dulei323/TMTSCCA. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Abstract Background A fundamental problem in RNA-seq data analysis is to identify genes or exons that are differentially expressed with varying experimental conditions based on the read counts. The relativeness of RNA-seq measurements makes the between-sample normalization of read counts an essential step in differential expression (DE) analysis. In most existing methods, the normalization step is performed prior to the DE analysis. Recently, Jiang and Zhan proposed a statistical method which introduces sample-specific normalization parameters into a joint model, which allows for simultaneous normalization and differential expression analysis from log-transformed RNA-seq data. Furthermore, an ℓ0 penalty is used to yield a sparse solution which selects a subset of DE genes. The experimental conditions are restricted to be categorical in their work. Results In this paper, we generalize Jiang and Zhan’s method to handle experimental conditions that are measured in continuous variables. As a result, genes with expression levels associated with a single or multiple covariates can be detected. As the problem being high-dimensional, non-differentiable and non-convex, we develop an efficient algorithm for model fitting. Conclusions Experiments on synthetic data demonstrate that the proposed method outperforms existing methods in terms of detection accuracy when a large fraction of genes are differentially expressed in an asymmetric manner, and the performance gain becomes more substantial for larger sample sizes. We also apply our method to a real prostate cancer RNA-seq dataset to identify genes associated with pre-operative prostate-specific antigen (PSA) levels in patients.

The RNA-sequencing (RNA-seq) is becoming increasingly popular for quantifying gene expression levels. Since the RNA-seq measurements are relative in nature, between-sample normalization is an essential step in differential expression (DE) analysis. The normalization step of existing DE detection algorithms is usually ad hoc and performed only once prior to DE detection, which may be suboptimal since ideally normalization should be based on non-DE genes only and thus coupled with DE detection. We propose a unified statistical model for joint normalization and DE detection of RNA-seq data. Sample-specific normalization factors are modeled as unknown parameters in the gene-wise linear models and jointly estimated with the regression coefficients. By imposing sparsity-inducing L1 penalty (or mixed L1/L2 penalty for multiple treatment conditions) on the regression coefficients, we formulate the problem as a penalized least-squares regression problem and apply the augmented Lagrangian method to solve it. Simulation and real data studies show that the proposed model and algorithms perform better than or comparably to existing methods in terms of detection power and false-positive rate. The performance gain increases with increasingly larger sample size or higher signal to noise ratio, and is more significant when a large proportion of genes are differentially expressed in an asymmetric manner.

MOTIVATION: Brain imaging genetics, which studies the linkage between genetic variations and structural or functional measures of the human brain, has become increasingly important in recent years. Discovering the bi-multivariate relationship between genetic markers such as single-nucleotide polymorphisms (SNPs) and neuroimaging quantitative traits (QTs) is one major task in imaging genetics. Sparse Canonical Correlation Analysis (SCCA) has been a popular technique in this area for its powerful capability in identifying bi-multivariate relationships coupled with feature selection. The existing SCCA methods impose either the ℓ1-norm or its variants to induce sparsity. The ℓ0-norm penalty is a perfect sparsity-inducing tool which, however, is an NP-hard problem. RESULTS: In this paper, we propose the truncated ℓ1-norm penalized SCCA to improve the performance and effectiveness of the ℓ1-norm based SCCA methods. Besides, we propose an efficient optimization algorithms to solve this novel SCCA problem. The proposed method is an adaptive shrinkage method via tuning τ. It can avoid the time intensive parameter tuning if given a reasonable small τ. Furthermore, we extend it to the truncated group-lasso (TGL), and propose TGL-SCCA model to improve the group-lasso-based SCCA methods. The experimental results, compared with four benchmark methods, show that our SCCA methods identify better or similar correlation coefficients, and better canonical loading profiles than the competing methods. This demonstrates the effectiveness and efficiency of our methods in discovering interesting imaging genetic associations. AVAILABILITY AND IMPLEMENTATION: The Matlab code and sample data are freely available at http://www.iu.edu/∼shenlab/tools/tlpscca/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Detecting the sinusoidal order is a prerequisite step for parametric multidimensional sinusoidal frequency estimation methods, whose applications range from radar and wireless communications to nuclear magnetic resonance spectroscopy. Although the Bayesian information criterion (BIC) has been commonly applied for model order selection, its application to sinusoidal order estimation is recent. By means of estimation of Fisher information matrix, we extend the 1-D BIC to multidimensional case for multidimensional sinusoidal order selection. The multidimensional BIC is shown in simulations to outperform the state-of-the-art algorithms in terms of probability of correct detection.

MOTIVATION: Network-based genome-wide association studies (GWAS) aim to identify functional modules from biological networks that are enriched by top GWAS findings. Although gene functions are relevant to tissue context, most existing methods analyze tissue-free networks without reflecting phenotypic specificity. RESULTS: We propose a novel module identification framework for imaging genetic studies using the tissue-specific functional interaction network. Our method includes three steps: (i) re-prioritize imaging GWAS findings by applying machine learning methods to incorporate network topological information and enhance the connectivity among top genes; (ii) detect densely connected modules based on interactions among top re-prioritized genes; and (iii) identify phenotype-relevant modules enriched by top GWAS findings. We demonstrate our method on the GWAS of [18F]FDG-PET measures in the amygdala region using the imaging genetic data from the Alzheimer's Disease Neuroimaging Initiative, and map the GWAS results onto the amygdala-specific functional interaction network. The proposed network-based GWAS method can effectively detect densely connected modules enriched by top GWAS findings. Tissue-specific functional network can provide precise context to help explore the collective effects of genes with biologically meaningful interactions specific to the studied phenotype. AVAILABILITY AND IMPLEMENTATION: The R code and sample data are freely available at http://www.iu.edu/shenlab/tools/gwasmodule/. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Discovering bi-multivariate associations between genetic markers and neuroimaging quantitative traits is a major task in brain imaging genetics. Sparse Canonical Correlation Analysis (SCCA) is a popular technique in this area for its powerful capability in identifying bi-multivariate relationships coupled with feature selection. The existing SCCA methods impose either the ℓ1-norm or its variants. The ℓ0-norm is more desirable, which however remains unexplored since the ℓ0-norm minimization is NP-hard. In this paper, we impose the truncated ℓ1-norm to improve the performance of the ℓ1-norm based SCCA methods. Besides, we propose two efficient optimization algorithms and prove their convergence. The experimental results, compared with two benchmark methods, show that our method identifies better and meaningful canonical loading patterns in both simulated and real imaging genetic analyse.

Recently, the CORe CONsistency DIAgnostic (CORCONDIA) has attractedmore and more attention as an effective tool for determining the number of components in parallel factor analysis (PARAFAC) or Tucker 3 models. In CORCONDIA, a proper user-defined threshold is required to ensure reliable performance. The optimal threshold increases with the signal-to-noise ratio (SNR), which results in significant probability of over-enumeration of the number of components for high SNRs under fixed threshold settings. We propose to first use a threshold interval to obtain lower and upper bounds of the estimates. The estimate takes the upper bound as its initial value and is then refined based on a sequence of hypothesis tests by exploiting the reconstruction error of the PARAFAC decomposition. The proposed scheme provides accurate detection for both low and high SNRs at almost no extra computational cost.

A novel R-dimensional (R ≥ 3) model order selection (MOS) criterion is proposed for estimating the number of sources embedded in noise. By extending the classical r-mode matrix unfolding of a Rth-order measurement tensor to multi-mode matrix unfolding, (2R−1− 1) unfolded matrices are obtained. To maximize the identifiability, the unfolded matrix whose number of rows is closest to that of the columns is chosen. Meanwhile, as the so-obtained unfolded matrix is of large size, a sequence of nested hypothesis tests on its associated eigenvalues is utilized for MOS in the framework of the random matrix theory. The maximum number of sources the proposed enumerator able to identify is on the order of the square root of the product of all dimension sizes, whereas the identifiability of existing criteria is limited to the maximum dimension size minus one. Numerical results are included to illustrate the performance of the proposed enumerator.