Comparison of Penalty Functions for Sparse Canonical Correlation Analysis

Sparse multiway canonical correlation analysis for multimodal stroke recovery data

Conventional canonical correlation analysis (CCA) measures the association between two datasets and identifies relevant contributors. However, it encounters issues with execution and interpretation when the sample size is smaller than the number of variables or there are more than two datasets. Our motivating example is a stroke-related clinical study on pigs. The data are multimodal and consist of measurements taken at multiple time points and have many more variables than observations. This study aims to uncover important biomarkers and stroke recovery patterns based on physiological changes. To address the issues in the data, we develop two sparse CCA methods for multiple datasets. Various simulated examples are used to illustrate and contrast the performance of the proposed methods with that of the existing methods. In analyzing the pig stroke data, we apply the proposed sparse CCA methods along with dimension reduction techniques, interpret the recovery patterns, and identify influential variables in recovery.

Quantitative multi-species toxicity modeling: Does a multi-species, machine learning model provide better performance than a single-species model for the evaluation of acute aquatic toxicity by organic pollutants?

The toxicological profile of any chemical is defined by multiple endpoints and testing procedures, including representative test species from different trophic levels. While computer-aided methods play an increasingly important role in supporting ecotoxicology research and chemical hazard assessment, most of the recently developed machine learning models are directed towards a single, specific endpoint. To overcome this limitation and accelerate the process of identifying potentially hazardous environmental pollutants, we are introducing an effective approach for quantitative, multi-species modeling. The proposed approach is based on canonical correlation analysis that finds a pair(s) of uncorrelated, linear combinations of the original variables that best defines the overall variability within and between multiple biological responses and predictor variables. Its effectiveness was confirmed by the machine learning model for estimating acute toxicity of diverse organic pollutants in aquatic species from three trophic levels: algae (Pseudokirchneriella subcapitata), daphnia (Daphnia magna), and fish (Oryzias latipes). The multi-species model achieved a favorable predictive performance that were in line with predictive models derived for the aquatic organisms individually. The chemical bioavailability and reactivity parameters (n-octanol/water partition coefficient, chemical potential, and molecular size and volume) were important to accurately predict acute ecotoxicity to the three aquatic organisms. To facilitate the use of this approach, an open-source, Python-based script, named qMTM (quantitative Multi-species Toxicity Modeling) has been provided.

Strategies for multivariate analyses of imaging genetics study in Alzheimer's disease

Alzheimer's disease (AD) is an incurable neurodegenerative disease primarily affecting the elderly population. Early diagnosis of AD is critical for the management of this disease. Imaging genetics examines the influence of genetic variants (i.e., single nucleotide polymorphisms (SNPs)) on brain structure and function and many novel approaches of imaging genetics are proposed for studying AD. We review and synthesize the Alzheimer's Disease Neuroimaging Initiative (ADNI) genetic associations with quantitative disease endophenotypes including structural and functional neuroimaging, diffusion tensor imaging (DTI), positron emission tomography (PET), and fluid biomarker assays. In this review, we survey recent publications using neuroimaging and genetic data of AD, with a focus on methods capturing multivariate effects accommodating the large number variables from both imaging data and genetic data. We review methods focused on bridging the imaging and genetic data by establishing genotype-phenotype association, including sparse canonical correlation analysis, parallel independent component analysis, sparse reduced rank regression, sparse partial least squares, genome-wide association study, and so on. The broad availability and wide scope of ADNI genetic and phenotypic data has advanced our understanding of the genetic basis of AD and has nominated novel targets for future pharmaceutical therapy and biomarker development.

Integrating multi-OMICS data through sparse canonical correlation analysis for the prediction of complex traits: a comparison study

Motivation

Recent developments in technology have enabled researchers to collect multiple OMICS datasets for the same individuals. The conventional approach for understanding the relationships between the collected datasets and the complex trait of interest would be through the analysis of each OMIC dataset separately from the rest, or to test for associations between the OMICS datasets. In this work we show that integrating multiple OMICS datasets together, instead of analysing them separately, improves our understanding of their in-between relationships as well as the predictive accuracy for the tested trait. Several approaches have been proposed for the integration of heterogeneous and high-dimensional (p≫n) data, such as OMICS. The sparse variant of canonical correlation analysis (CCA) approach is a promising one that seeks to penalize the canonical variables for producing sparse latent variables while achieving maximal correlation between the datasets. Over the last years, a number of approaches for implementing sparse CCA (sCCA) have been proposed, where they differ on their objective functions, iterative algorithm for obtaining the sparse latent variables and make different assumptions about the original datasets.

Results

Through a comparative study we have explored the performance of the conventional CCA proposed by Parkhomenko et al., penalized matrix decomposition CCA proposed by Witten and Tibshirani and its extension proposed by Suo et al. The aforementioned methods were modified to allow for different penalty functions. Although sCCA is an unsupervised learning approach for understanding of the in-between relationships, we have twisted the problem as a supervised learning one and investigated how the computed latent variables can be used for predicting complex traits. The approaches were extended to allow for multiple (more than two) datasets where the trait was included as one of the input datasets. Both ways have shown improvement over conventional predictive models that include one or multiple datasets.

Availability and implementation

https://github.com/theorod93/sCCA.

Supplementary information

Supplementary data are available at Bioinformatics online.

Integrative analysis of transcriptomic and metabolomic data via sparse canonical correlation analysis with incorporation of biological information

Integrative analysis of high dimensional omics data is becoming increasingly popular. At the same time, incorporating known functional relationships among variables in analysis of omics data has been shown to help elucidate underlying mechanisms for complex diseases. In this article, our goal is to assess association between transcriptomic and metabolomic data from a Predictive Health Institute (PHI) study that includes healthy adults at a high risk of developing cardiovascular diseases. Adopting a strategy that is both data-driven and knowledge-based, we develop statistical methods for sparse canonical correlation analysis (CCA) with incorporation of known biological information. Our proposed methods use prior network structural information among genes and among metabolites to guide selection of relevant genes and metabolites in sparse CCA, providing insight on the molecular underpinning of cardiovascular disease. Our simulations demonstrate that the structured sparse CCA methods outperform several existing sparse CCA methods in selecting relevant genes and metabolites when structural information is informative and are robust to mis-specified structural information. Our analysis of the PHI study reveals that a number of gene and metabolic pathways including some known to be associated with cardiovascular diseases are enriched in the set of genes and metabolites selected by our proposed approach.

Multivariate association between single-nucleotide polymorphisms in Alzgene linkage regions and structural changes in the brain: discovery, refinement and validation

Using publicly-available data from the Alzheimer’s Disease Neuroimaging Initiative, we investigate the joint association between single-nucleotide polymorphisms (SNPs) in previously established linkage regions for Alzheimer’s disease (AD) and rates of decline in brain structure. In an initial, discovery stage of analysis, we applied a weighted

Robust sparse canonical correlation analysis

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.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0317-9) contains supplementary material, which is available to authorized users.

ATHENA: the analysis tool for heritable and environmental network associations

MOTIVATION

Advancements in high-throughput technology have allowed researchers to examine the genetic etiology of complex human traits in a robust fashion. Although genome-wide association studies have identified many novel variants associated with hundreds of traits, a large proportion of the estimated trait heritability remains unexplained. One hypothesis is that the commonly used statistical techniques and study designs are not robust to the complex etiology that may underlie these human traits. This etiology could include non-linear gene × gene or gene × environment interactions. Additionally, other levels of biological regulation may play a large role in trait variability.

RESULTS

To address the need for computational tools that can explore enormous datasets to detect complex susceptibility models, we have developed a software package called the Analysis Tool for Heritable and Environmental Network Associations (ATHENA). ATHENA combines various variable filtering methods with machine learning techniques to analyze high-throughput categorical (i.e. single nucleotide polymorphisms) and quantitative (i.e. gene expression levels) predictor variables to generate multivariable models that predict either a categorical (i.e. disease status) or quantitative (i.e. cholesterol levels) outcomes. The goal of this article is to demonstrate the utility of ATHENA using simulated and biological datasets that consist of both single nucleotide polymorphisms and gene expression variables to identify complex prediction models. Importantly, this method is flexible and can be expanded to include other types of high-throughput data (i.e. RNA-seq data and biomarker measurements).

AVAILABILITY

ATHENA is freely available for download. The software, user manual and tutorial can be downloaded from http://ritchielab.psu.edu/ritchielab/software.

Group sparse canonical correlation analysis for genomic data integration

BACKGROUND

The emergence of high-throughput genomic datasets from different sources and platforms (e.g., gene expression, single nucleotide polymorphisms (SNP), and copy number variation (CNV)) has greatly enhanced our understandings of the interplay of these genomic factors as well as their influences on the complex diseases. It is challenging to explore the relationship between these different types of genomic data sets. In this paper, we focus on a multivariate statistical method, canonical correlation analysis (CCA) method for this problem. Conventional CCA method does not work effectively if the number of data samples is significantly less than that of biomarkers, which is a typical case for genomic data (e.g., SNPs). Sparse CCA (sCCA) methods were introduced to overcome such difficulty, mostly using penalizations with l-1 norm (CCA-l1) or the combination of l-1and l-2 norm (CCA-elastic net). However, they overlook the structural or group effect within genomic data in the analysis, which often exist and are important (e.g., SNPs spanning a gene interact and work together as a group).

RESULTS

We propose a new group sparse CCA method (CCA-sparse group) along with an effective numerical algorithm to study the mutual relationship between two different types of genomic data (i.e., SNP and gene expression). We then extend the model to a more general formulation that can include the existing sCCA models. We apply the model to feature/variable selection from two data sets and compare our group sparse CCA method with existing sCCA methods on both simulation and two real datasets (human gliomas data and NCI60 data). We use a graphical representation of the samples with a pair of canonical variates to demonstrate the discriminating characteristic of the selected features. Pathway analysis is further performed for biological interpretation of those features.

CONCLUSIONS

The CCA-sparse group method incorporates group effects of features into the correlation analysis while performs individual feature selection simultaneously. It outperforms the two sCCA methods (CCA-l1 and CCA-group) by identifying the correlated features with more true positives while controlling total discordance at a lower level on the simulated data, even if the group effect does not exist or there are irrelevant features grouped with true correlated features. Compared with our proposed CCA-group sparse models, CCA-l1 tends to select less true correlated features while CCA-group inclines to select more redundant features.

Population level inference for multivariate MEG analysis

Multivariate analysis is a very general and powerful technique for analysing Magnetoencephalography (MEG) data. An outstanding problem however is how to make inferences that are consistent over a group of subjects as to whether there are condition-specific differences in data features, and what are those features that maximise these differences. Here we propose a solution based on Canonical Variates Analysis (CVA) model scoring at the subject level and random effects Bayesian model selection at the group level. We apply this approach to beamformer reconstructed MEG data in source space. CVA estimates those multivariate patterns of activation that correlate most highly with the experimental design; the order of a CVA model is then determined by the number of significant canonical vectors. Random effects Bayesian model comparison then provides machinery for inferring the optimal order over the group of subjects. Absence of a multivariate dependence is indicated by the null model being the most likely. This approach can also be applied to CVA models with a fixed number of canonical vectors but supplied with different feature sets. We illustrate the method by identifying feature sets based on variable-dimension MEG power spectra in the primary visual cortex and fusiform gyrus that are maximally discriminative of data epochs before versus after visual stimulation.