Multiple Canonical Correlation Analysis Research Articles

NetMUG: a novel network-guided multi-view clustering workflow for dissecting genetic and facial heterogeneity.

Introduction: Multi-view data offer advantages over single-view data for characterizing individuals, which is crucial in precision medicine toward personalized prevention, diagnosis, or treatment follow-up. Methods: Here, we develop a network-guided multi-view clustering framework named netMUG to identify actionable subgroups of individuals. This pipeline first adopts sparse multiple canonical correlation analysis to select multi-view features possibly informed by extraneous data, which are then used to construct individual-specific networks (ISNs). Finally, the individual subtypes are automatically derived by hierarchical clustering on these network representations. Results: We applied netMUG to a dataset containing genomic data and facial images to obtain BMI-informed multi-view strata and showed how it could be used for a refined obesity characterization. Benchmark analysis of netMUG on synthetic data with known strata of individuals indicated its superior performance compared with both baseline and benchmark methods for multi-view clustering. The clustering derived from netMUG achieved an adjusted Rand index of 1 with respect to the synthesized true labels. In addition, the real-data analysis revealed subgroups strongly linked to BMI and genetic and facial determinants of these subgroups. Discussion: netMUG provides a powerful strategy, exploiting individual-specific networks to identify meaningful and actionable strata. Moreover, the implementation is easy to generalize to accommodate heterogeneous data sources or highlight data structures.

Covariation of preadult environmental exposures, adult brain imaging phenotypes, and adult personality traits.

Exposure to preadult environmental exposures may have long-lasting effects on mental health by affecting the maturation of the brain and personality, two traits that interact throughout the developmental process. However, environment-brain-personality covariation patterns and their mediation relationships remain unclear. In 4297 healthy participants (aged 18-30 years), we combined sparse multiple canonical correlation analysis with independent component analysis to identify the three-way covariation patterns of 59 preadult environmental exposures, 760 adult brain imaging phenotypes, and five personality traits, and found two robust environment-brain-personality covariation models with sex specificity. One model linked greater stress and less support to weaker functional connectivity and activity in the default mode network, stronger activity in subcortical nuclei, greater thickness and volume in the occipital, parietal and temporal cortices, and lower agreeableness, consciousness and extraversion as well as higher neuroticism. The other model linked higher urbanicity and better socioeconomic status to stronger functional connectivity and activity in the sensorimotor network, smaller volume and surface area and weaker functional connectivity and activity in the medial prefrontal cortex, lower white matter integrity, and higher openness to experience. We also conducted mediation analyses to explore the potential bidirectional mediation relationships between adult brain imaging phenotypes and personality traits with the influence of preadult environmental exposures and found both environment-brain-personality and environment-personality-brain pathways. We finally performed moderated mediation analyses to test the potential interactions between macro- and microenvironmental exposures and found that one category of exposure moderated the mediation pathways of another category of exposure. These results improve our understanding of the effects of preadult environmental exposures on the adult brain and personality traits and may facilitate the design of targeted interventions to improve mental health by reducing the impact of adverse environmental exposures.

Canonical correlation analysis for multi-omics: Application to cross-cohort analysis.

Integrative approaches that simultaneously model multi-omics data have gained increasing popularity because they provide holistic system biology views of multiple or all components in a biological system of interest. Canonical correlation analysis (CCA) is a correlation-based integrative method designed to extract latent features shared between multiple assays by finding the linear combinations of features-referred to as canonical variables (CVs)-within each assay that achieve maximal across-assay correlation. Although widely acknowledged as a powerful approach for multi-omics data, CCA has not been systematically applied to multi-omics data in large cohort studies, which has only recently become available. Here, we adapted sparse multiple CCA (SMCCA), a widely-used derivative of CCA, to proteomics and methylomics data from the Multi-Ethnic Study of Atherosclerosis (MESA) and Jackson Heart Study (JHS). To tackle challenges encountered when applying SMCCA to MESA and JHS, our adaptations include the incorporation of the Gram-Schmidt (GS) algorithm with SMCCA to improve orthogonality among CVs, and the development of Sparse Supervised Multiple CCA (SSMCCA) to allow supervised integration analysis for more than two assays. Effective application of SMCCA to the two real datasets reveals important findings. Applying our SMCCA-GS to MESA and JHS, we identified strong associations between blood cell counts and protein abundance, suggesting that adjustment of blood cell composition should be considered in protein-based association studies. Importantly, CVs obtained from two independent cohorts also demonstrate transferability across the cohorts. For example, proteomic CVs learned from JHS, when transferred to MESA, explain similar amounts of blood cell count phenotypic variance in MESA, explaining 39.0% ~ 50.0% variation in JHS and 38.9% ~ 49.1% in MESA. Similar transferability was observed for other omics-CV-trait pairs. This suggests that biologically meaningful and cohort-agnostic variation is captured by CVs. We anticipate that applying our SMCCA-GS and SSMCCA on various cohorts would help identify cohort-agnostic biologically meaningful relationships between multi-omics data and phenotypic traits.

Multi-omic analysis reveals enriched pathways associated with COVID-19 and COVID-19 severity.

COVID-19 is a disease characterized by its seemingly unpredictable clinical outcomes. In order to better understand the molecular signature of the disease, a recent multi-omics study was done which looked at correlations between biomolecules and used a tree- based machine learning approach to predict clinical outcomes. This study specifically looked at patients admitted to the hospital experiencing COVID-19 or COVID-19 like symptoms. In this paper we examine the same multi-omics data, however we take a different approach, and we identify stable molecules of interest for further pathway analysis. We used stability selection, regularized regression models, enrichment analysis, and principal components analysis on proteomics, metabolomics, lipidomics, and RNA sequencing data, and we determined key molecules and biological pathways in disease severity, and disease status. In addition to the individual omics analyses, we perform the integrative method Sparse Multiple Canonical Correlation Analysis to analyse relationships of the different view of data. Our findings suggest that COVID-19 status is associated with the cell cycle and death, as well as the inflammatory response. This relationship is reflected in all four sets of molecules analyzed. We further observe that the metabolic processes, particularly processes to do with vitamin absorption and cholesterol are implicated in COVID-19 status and severity.

Double information preserving canonical correlation analysis

The methods based on canonical correlation analysis (CCA-based methods) are typical and effective methods for unsupervised dimensionality reduction of multi-view data. However, the traditional CCA-based methods ignore the dissimilarity information while considering the similarity information of samples, which will make the heterogeneous samples in the subspace cannot be well separated. In this paper, we propose a novel unsupervised multi-view dimensionality reduction method: Double Information Preserving Canonical Correlation Analysis (DIPCCA). DIPCCA aims at finding two projection matrices by integrating two cross double weight graphs with CCA to explore the similarity and dissimilarity information of data in cross views. Furthermore, on the basis of consistency and complementarity, DIPCCA uses the similarity information to maintain the local structure, and the dissimilarity information to disperse embedded samples of distinct clusters, so as to extract more discriminative features. Moreover, CCA and a new locality-preserving CCA are two special cases of DIPCCA when parameters take special values. In order to better extract the features of nonlinear data and more than two views, DIPCCA is extended to Double Information Preserving Kernel Canonical Correlation Analysis and Double Information Preserving Multiple Canonical Correlation Analysis, respectively. Experiments on an artificial dataset and three real multi-view datasets show our proposed methods have better performance than the traditional CCA-based methods.

Single-cell RNA sequencing reveals the induction of novel myeloid and myeloid-associated cell populations in visceral fat with long-term obesity.

Macrophages and other immune cells are important contributors to obesity-associated inflammation; however, the cellular identities of these specific populations remain unknown. In this study, we identified individual populations of myeloid cells found in mouse epididymal/visceral adipose tissue by single-cell RNA sequencing, immunofluorescence, and flow cytometry. Multiple canonical correlation analysis identified 11 unique myeloid and myeloid-associate cell populations. In obese mice, we detected an increased percentage of monocyte-derived pro-inflammatory cells expressing Cd9 and Trem2, as well as significantly decreased percentages of multiple cell populations, including tissue-resident cells expressing Lyve1, Mafb, and Mrc1. We have identified and validated a novel myeloid/macrophage population defined by Ly6a expression, exhibiting both myeloid and mesenchymal characteristics, which increased with obesity and showed high pro-fibrotic characteristics in vitro. Our mouse adipose tissue myeloid cell atlas provides an important resource to investigate obesity-associated inflammation and fibrosis.

Identifying Protein–metabolite Networks Associated with COPD Phenotypes

Chronic obstructive pulmonary disease (COPD) is a disease in which airflow obstruction in the lung makes it difficult for patients to breathe. Although COPD occurs predominantly in smokers, there are still deficits in our understanding of the additional risk factors in smokers. To gain a deeper understanding of the COPD molecular signatures, we used Sparse Multiple Canonical Correlation Network (SmCCNet), a recently developed tool that uses sparse multiple canonical correlation analysis, to integrate proteomic and metabolomic data from the blood of 1008 participants of the COPDGene study to identify novel protein–metabolite networks associated with lung function and emphysema. Our aim was to integrate -omic data through SmCCNet to build interpretable networks that could assist in the discovery of novel biomarkers that may have been overlooked in alternative biomarker discovery methods. We found a protein–metabolite network consisting of 13 proteins and 7 metabolites which had a −0.34 correlation (p-value = 2.5 × 10−28) to lung function. We also found a network of 13 proteins and 10 metabolites that had a −0.27 correlation (p-value = 2.6 × 10−17) to percent emphysema. Protein–metabolite networks can provide additional information on the progression of COPD that complements single biomarker or single -omic analyses.

Discriminative Robust Head-Pose and Gaze Estimation Using Kernel-DMCCA Features Fusion

There remain outstanding challenges for improving accuracy of multi-feature information for head-pose and gaze estimation. The proposed framework employs discriminative analysis for head-pose and gaze estimation using kernel discriminative multiple canonical correlation analysis (K-DMCCA). The feature extraction component of the framework includes spatial indexing, statistical and geometrical elements. Head-pose and gaze estimation is constructed by feature aggregation and transforming features into a higher dimensional space using K-DMCCA for accurate estimation. The two main contributions are: Enhancing fusion performance through the use of kernel-based DMCCA, and by introducing an improved iris region descriptor based on quadtree. The overall approach is also inclusive of statistical and geometrical indexing that are calibration free (does not require any subsequent adjustment). We validate the robustness of the proposed framework across a wide variety of datasets, which consist of different modalities (RGB and Depth), constraints (wide range of head-poses, not only frontal), quality (accurately labelled for validation), occlusion (due to glasses, hair bang, facial hair) and illumination. Our method achieved an accurate head-pose and gaze estimation of 4.8∘ using Cave, 4.6∘ using MPII, 5.1∘ using ACS, 5.9∘ using EYEDIAP, 4.3∘ using OSLO and 4.6∘ using UULM datasets.

Consistency and overfitting of multi-omics methods on experimental data.

Knowledge on the relationship between different biological modalities (RNA, chromatin, etc.) can help further our understanding of the processes through which biological components interact. The ready availability of multi-omics datasets has led to the development of numerous methods for identifying sources of common variation across biological modalities. However, evaluation of the performance of these methods, in terms of consistency, has been difficult because most methods are unsupervised. We present a comparison of sparse multiple canonical correlation analysis (Sparse mCCA), angle-based joint and individual variation explained (AJIVE) and multi-omics factor analysis (MOFA) using a cross-validation approach to assess overfitting and consistency. Both large and small-sample datasets were used to evaluate performance, and a permuted null dataset was used to identify overfitting through the application of our framework and approach. In the large-sample setting, we found that all methods demonstrated consistency and lack of overfitting; however, in the small-sample size setting, AJIVE provided the most stable results. We provide an R package so that our framework and approach can be applied to evaluate other methods and datasets.

The Labeled Multiple Canonical Correlation Analysis for Information Fusion

The objective of multimodal information fusion is to mathematically analyze information carried in different sources and create a new representation which will be more effectively utilized in pattern recognition and other multimedia information processing tasks. In this paper, we introduce a new method for multimodal information fusion and representation based on the Labeled Multiple Canonical Correlation Analysis (LMCCA). By incorporating class label information of the training samples,the proposed LMCCA ensures that the fused features carry discriminative characteristics of the multimodal information representations, and are capable of providing superior recognition performance. We implement a prototype of LMCCA to demonstrate its effectiveness on handwritten digit recognition,face recognition and object recognition utilizing multiple features,bimodal human emotion recognition involving information from both audio and visual domains. The generic nature of LMCCA allows it to take as input features extracted by any means,including those by deep learning (DL) methods. Experimental results show that the proposed method enhanced the performance of both statistical machine learning (SML) methods, and methods based on DL.

Fault Detection for Non-Gaussian Processes Using Multiple Canonical Correlation Analysis Models and Box-Cox Transformation

Although the canonical correlation analysis (CCA)-based method has been successfully applied to Gaussian processes, the methods cannot obtain good results for the non-Gaussian processes. Meanwhile, due to the different operating conditions of the systems in actual operation, the data generated under different operating conditions is greatly different, which makes the fault detection more difficult. To deal with these problems, a fault detection method based on multiple canonical correlation analysis models and Box-Cox transformation is proposed. The method divides all conditions into some categories of conditions and builds the switching rules. Then the current condition is determined and switched in real time through real-time status data and switching rules. Since the systems are the non-Gaussian processes, the quadratic statistic established by the CCA for each condition is non-negative and non-Gaussian distributed variable. So, Box-Cox transformation is used to convert quadratic statistic into Gaussian distributed variables, such that the properties of Gaussian distribution can be employed to determine the ranges of the quadratic statistic corresponding to different health conditions. Finally, the fault detecting thresholds of the models are established based on a 99.7% confidence interval of the Gaussian distribution. The proposed method is applied to the process of monitoring of the suspension system. The application results indicate that the proposed approach can give higher fault detection rate and lower false positive rate and improves the detection ability.

Discriminative Multiple Canonical Correlation Analysis for Information Fusion.

In this paper, we propose the discriminative multiple canonical correlation analysis (DMCCA) for multimodal information analysis and fusion. DMCCA is capable of extracting more discriminative characteristics from multimodal information representations. Specifically, it finds the projected directions, which simultaneously maximize the within-class correlation and minimize the between-class correlation, leading to better utilization of the multimodal information. In the process, we analytically demonstrate that the optimally projected dimension by DMCCA can be quite accurately predicted, leading to both superior performance and substantial reduction in computational cost. We further verify that canonical correlation analysis (CCA), multiple canonical correlation analysis (MCCA) and discriminative canonical correlation analysis (DCCA) are special cases of DMCCA, thus establishing a unified framework for canonical correlation analysis. We implement a prototype of DMCCA to demonstrate its performance in handwritten digit recognition and human emotion recognition. Extensive experiments show that DMCCA outperforms the traditional methods of serial fusion, CCA, MCCA, and DCCA.

Adaptive Sparse Multiple Canonical Correlation Analysis With Application to Imaging (Epi)Genomics Study of Schizophrenia.

Finding correlations across multiple data sets in imaging and (epi)genomics is a common challenge. Sparse multiple canonical correlation analysis (SMCCA) is a multivariate model widely used to extract contributing features from each data while maximizing the cross-modality correlation. The model is achieved by using the combination of pairwise covariances between any two data sets. However, the scales of different pairwise covariances could be quite different and the direct combination of pairwise covariances in SMCCA is unfair. The problem of "unfair combination of pairwise covariances" restricts the power of SMCCA for feature selection. In this paper, we propose a novel formulation of SMCCA, called adaptive SMCCA, to overcome the problem by introducing adaptive weights when combining pairwise covariances. Both simulation and real-data analysis show the outperformance of adaptive SMCCA in terms of feature selection over conventional SMCCA and SMCCA with fixed weights. Large-scale numerical experiments show that adaptive SMCCA converges as fast as conventional SMCCA. When applying it to imaging (epi)genetics study of schizophrenia subjects, we can detect significant (epi)genetic variants and brain regions, which are consistent with other existing reports. In addition, several significant brain-development related pathways, e.g., neural tube development, are detected by our model, demonstrating imaging epigenetic association may be overlooked by conventional SMCCA. All these results demonstrate that adaptive SMCCA are well suited for detecting three-way or multiway correlations and thus can find widespread applications in multiple omics and imaging data integration.

Canonical variate regression.

In many fields, multi-view datasets, measuring multiple distinct but interrelated sets of characteristics on the same set of subjects, together with data on certain outcomes or phenotypes, are routinely collected. The objective in such a problem is often two-fold: both to explore the association structures of multiple sets of measurements and to develop a parsimonious model for predicting the future outcomes. We study a unified canonical variate regression framework to tackle the two problems simultaneously. The proposed criterion integrates multiple canonical correlation analysis with predictive modeling, balancing between the association strength of the canonical variates and their joint predictive power on the outcomes. Moreover, the proposed criterion seeks multiple sets of canonical variates simultaneously to enable the examination of their joint effects on the outcomes, and is able to handle multivariate and non-Gaussian outcomes. An efficient algorithm based on variable splitting and Lagrangian multipliers is proposed. Simulation studies show the superior performance of the proposed approach. We demonstrate the effectiveness of the proposed approach in an [Formula: see text] intercross mice study and an alcohol dependence study.

The relationship of benthic community metrics to pyrethroids, metals, and sediment characteristics in Cache Slough, California

ABSTRACTA bioassessment multiple stressor study was conducted at 12 sites in Cache Slough, California during the Spring and Fall of 2012, 2013 and 2014. Specific study goals were to: (1) collect and identify benthic macroinvertebrates and develop a suite of benthic metrics; (2) measure total organic carbon (TOC), grain size, bulk metals, simultaneously extracted metals (SEM) and acid volatile sulfides (AVS), and 8 pyrethroids in sediment; (3) measure basic water quality parameters; and, (4) use univariate and stepwise multiple regressions and canonical correlation analysis to determine the relationship between various benthic metrics (i.e., taxa richness, abundance) and TOC, grain size, metals (bulk metals and SEM/AVS) and pyrethroids using the 3-year database. Five benthic metrics showed statistically significant relationships with environmental variables. Taxonomic Richness, a metric that decreases with stress, tended to be greater in less organic-rich, coarser sediments and the apparent relationships with toxicants such as pyrethroids or metals were diminished when these conditions are taken into account. The % Amphipod metric, which has a variable response to environmental stressors, showed a direct relationship with arsenic, an inverse relationship with chromium and an inverse relationship with % silt. The % Corbicula metric, which has a variable response to environmental stressors, was directly correlated with cypermethrin and nickel. Therefore, it appears that Corbicula tends to be associated with more contaminated sediments in Cache Slough. The metric % Collectors/Filterers & Collectors/Gatherers, a metric that increases in stressed environments, was reported to increase in sediments with higher arsenic concentrations. This relationship makes ecological sense because this metric should increase with an increase in arsenic concentrations. The benthic metric Abundance, a metric that decreases with stress, was reported to be inversely correlated with % TOC and % silt. The abundance of benthic communities increases in coarser, less organic rich sediments. In general, relatively few statistically significant relationships were observed between the various combinations of benthic metrics and environmental variables. Benthic communities in Cache Slough appear to be more closely associated with sediment characteristics and with metals concentrations than with the pyrethroid concentrations.

Collaborative regression.

We consider the scenario where one observes an outcome variable and sets of features from multiple assays, all measured on the same set of samples. One approach that has been proposed for dealing with these type of data is "sparse multiple canonical correlation analysis" (sparse mCCA). All of the current sparse mCCA techniques are biconvex and thus have no guarantees about reaching a global optimum. We propose a method for performing sparse supervised canonical correlation analysis (sparse sCCA), a specific case of sparse mCCA when one of the datasets is a vector. Our proposal for sparse sCCA is convex and thus does not face the same difficulties as the other methods. We derive efficient algorithms for this problem that can be implemented with off the shelf solvers, and illustrate their use on simulated and real data.

Sparse Canonical Correlation Analysis: New Formulation and Algorithm

In this paper, we study canonical correlation analysis (CCA), which is a powerful tool in multivariate data analysis for finding the correlation between two sets of multidimensional variables. The main contributions of the paper are: 1) to reveal the equivalent relationship between a recursive formula and a trace formula for the multiple CCA problem, 2) to obtain the explicit characterization for all solutions of the multiple CCA problem even when the corresponding covariance matrices are singular, 3) to develop a new sparse CCA algorithm, and 4) to establish the equivalent relationship between the uncorrelated linear discriminant analysis and the CCA problem. We test several simulated and real-world datasets in gene classification and cross-language document retrieval to demonstrate the effectiveness of the proposed algorithm. The performance of the proposed method is competitive with the state-of-the-art sparse CCA algorithms.

A Three Year Assessment of the Influence of Physical Habitat, Pyrethroids and Metals on Benthic Communities in Two Urban Calfornia Streams

This three year study was designed to characterize benthic communities (macroinvertebrates) and physical habitat annually in two urban stream areas (Arcade Creek and Salinas streams) in California. Concurrent water quality evaluations, physical sediment parameters, pyrethroids, and bulk metals [including simultaneously extracted metals (SEM) and acid volatile sulfides (AVS) ratios] were also measured in both study areas. The relationship of various benthic metrics to physical habitat metrics, pyrethroids, and metals was evaluated for the the three year data set (2009 -2011) using univariate analysis, stepwise multiple regression analysis and canonical correlation analysis. Habitat conditions were determined to be poor in Arcade Creek and extremely poor in the Salinas streams. Tolerant benthic taxa were dominant in both study areas but degraded communities more apparent in Salinas streams. Canonical correlation analysis of the three year data set for Arcade Creek indicated that, while benthic community diversity was inversely related to toxicants (metals and pyrethroids) in the sediments, community composition appeared to be more closely related to physical habitat quality. The statistical analyses conducted on the three year data set from Salinas streams detected fewer and weaker relationships between benthic metrics and environmental variables than did the analyses of data from Arcade Creek, likely due to the greater degree of overall environmental degradation of the Salinas streams. However, habitat (particularly sediment deposition) appeared to be the most significant stressor. In summary the tthree year data sets for both streams showed more significant relationships with benthic metrics and habitat metrics than with pyrethroid or metals.

Time-series alignment by non-negative multiple generalized canonical correlation analysis

BackgroundQuantitative analysis of differential protein expressions requires to align temporal elution measurements from liquid chromatography coupled to mass spectrometry (LC/MS). We propose multiple Canonical Correlation Analysis (mCCA) as a method to align the non-linearly distorted time scales of repeated LC/MS experiments in a robust way.ResultsMultiple canonical correlation analysis is able to map several time series to a consensus time scale. The alignment function is learned in a supervised fashion. We compare our approach with previously published methods for aligning mass spectrometry data on a large proteomics dataset. The proposed method significantly increases the number of proteins that are identified as being differentially expressed in different biological samples.ConclusionJointly aligning multiple liquid chromatography/mass spectrometry samples by mCCA substantially increases the detection rate of potential bio-markers which significantly improves the interpretability of LC/MS data.

Exploring two methods for statistical downscaling of Central European phenological time series.

In this study we set out to investigate the possibility of linking phenological phases throughout the vegetation cycle, as a local-scale biological phenomenon, directly with large-scale atmospheric variables via two different empirical downscaling techniques. In recent years a number of methods have been developed to transfer atmospheric information at coarse General Circulation Model's grid resolutions to local scales and individual points. Here multiple linear regression (MLR) and canonical correlation analysis (CCA) have been selected as downscaling methods. Different validation experiments (e.g. temporal cross-validation, split-sample tests) are used to test the performance of both approaches and compare them for time series of 17 phenological phases and air temperatures from Central Europe as microscale variables. A number of atmospheric variables over the North Atlantic and Europe are utilized as macroscale predictors. The period considered is 1951-1998. Temporal cross-validation reveals that the CCA model generally performs better than MLR, which explains 20%-50% of the phenological variances, whereas the CCA model shows a range from 40% to over 60% throughout most of the vegetation cycle. To show the validity of employing phenological observations for downscaling purposes both methods (MLR and CCA) are also applied to gridded local air temperature time series over Central Europe. In this case there is no obvious superiority of the CCA model over the MLR model. Both models show explained variances from 40% to over 70% in the temporal cross-validation experiment. The results of this study indicate that time series of phenological occurrence dates are very compatible with the needs of empirical downscaling originally developed of local-scale atmospheric variables.