Performing Dimensionality Reduction Research Articles

Abstract 865: Using machine learning to detect heterogeneity in single cell multi-omics datasets

Abstract Background: While scRNA-seq helps in obtaining high-resolution views of single-cell heterogeneity through characterization of the functional state of cells, our understanding of the cellular properties and population architectures of heterogeneous tissues will be greatly advanced by the multi-omics investigation of single cells. Recently, several computational methods have been developed to integrate data from multiple different single cell experiments measuring individual analytes. But unambiguous inference that a cellular phenotype is caused by a genotype can only be achieved by their measurement from the same single cell. To address this gap, we have developed the Tapestri multi-omics workflow to analyze the RNA and DNA information from the same cell. Methods: After pre-processing of the reads, cell calling is done by identifying the good barcodes using both DNA and RNA reads. DNA reads are processed to identify genetic variants in each cell. The variant cell matrix is then filtered for data completeness to ensure only high-quality data is used in downstream processing. Ploidy is estimated using by normalizing DNA reads, genetic variants and ploidy information together is used to identify subclones. The RNA reads are log normalized and scaled within each cell. Next we set the mean expression of each transcript to 0 and scale the variance to 1. This avoids downstream analysis being skewed by high expressors. We then trained a random forest classifier to identify significantly differentially expressed transcripts across subclones which were identified using genetic variants and ploidy information. Results: Using the top differentially expressed transcripts we performed dimensionality reduction followed by clustering of cell types. The resulting visualization showed how well the genotypic and transcriptomic datasets integrated with one another. We tested this method on a model system with Raji and KG1 cell lines titrated at 50:50 ratio and were clearly able to associate the transcriptional variation with the genotypic variation of the 2 different cell lines. The method was also validated on a PBMC sample to ensure robustness of methods. We were able to identify the different cell types present the sample and were able to overlay that information with genetic variants to identify sub-clones in the identified cell types. Citation Format: Saurabh Gulati, Shu Wang, Saurabh Parikh, Ben Liu, Kaustubh Gokhale, Manimozhi Manivannan, Sombeet Sahu, Dong Kim, Anup Parikh. Using machine learning to detect heterogeneity in single cell multi-omics datasets [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 865.

A Review of H2, CH4, and Hydrocarbon Formation in Experimental Serpentinization Using Network Analysis

The origin of methane and light hydrocarbons (HC) in natural fluids from serpentinization has commonly been attributed to the abiotic reduction of oxidized carbon by H2 through Fischer-Tropsch Type (FTT) reactions. Multiple experimental serpentinization studies attempted to identify the parameters that control the abiotic production of H2, CH4, and light HC. H2 is systematically and significantly formed in experiments, indicating that its production during serpentinization is well established. However, the large variance in concentration (eight orders of magnitude) is difficult to address because of the large number of parameters that vary from one experiment to another. CH4 and light HC production is much lower and also highly variable, leading to a vivid debate on potential role of metal catalysts and organic contamination. We have built a dataset that includes experimental setups, conditions, reactants, and products from 30 peer-reviewed articles reporting on experimental serpentinization and performed dimensionality reduction and network analysis to achieve an unbiased reading of the literature and fuel the debate. Our analysis distinguishes four experimental communities that highlights usual experimental protocols and the conditions tested so far. As expected, H2 production is mainly controlled by T and P though a strong variability remains within a given P-T range. Accessory metal-bearing phases seem to favor H2 production, while their role as catalyst or reactant is hampered by the lack of mineralogical characterization. CH4 and light HC concentrations are highly variable, uncorrelated to each other, and much lower than concentrations of potential reactants (H2, initial carbon). Accessory phases proposed as FTT catalysts do not enhance CH4 production, confirming the inefficiency of this reaction. CH4 only displays a positive correlation with temperature suggesting a kinetic/thermal control on its forming reaction. The carbon budget of some experiments indicates contamination in agreement with available labeled 13C studies. Salts in initial solutions are possible sources of organic contaminants. Natural systems certainly exploit longer reaction time or other reactional paths to form the observed CH4 and HC. The reducing potential of serpentinization can also produce intermediate metastable carbon phases in liquid or solid as observed in natural samples that should be targeted in future experiments.

Likelihood Ratio Test in Multivariate Linear Regression: from Low to High Dimension

Multivariate linear regressions are widely used statistical tools in many applications to model the associations between multiple related responses and a set of predictors. To infer such associations, it is often of interest to test the structure of the regression coefficients matrix, and the likelihood ratio test (LRT) is one of the most popular approaches in practice. Despite its popularity, it is known that the classical $\chi^2$ approximations for LRTs often fail in high-dimensional settings, where the dimensions of responses and predictors $(m,p)$ are allowed to grow with the sample size $n$. Though various corrected LRTs and other test statistics have been proposed in the literature, the fundamental question of when the classic LRT starts to fail is less studied, an answer to which would provide insights for practitioners, especially when analyzing data with $m/n$ and $p/n$ small but not negligible. Moreover, the power performance of the LRT in high-dimensional data analysis remains underexplored. To address these issues, the first part of this work gives the asymptotic boundary where the classical LRT fails and develops the corrected limiting distribution of the LRT for a general asymptotic regime. The second part of this work further studies the test power of the LRT in the high-dimensional setting. The result not only advances the current understanding of asymptotic behavior of the LRT under alternative hypothesis, but also motivates the development of a power-enhanced LRT. The third part of this work considers the setting with $p>n$, where the LRT is not well-defined. We propose a two-step testing procedure by first performing dimension reduction and then applying the proposed LRT. Theoretical properties are developed to ensure the validity of the proposed method. Numerical studies are also presented to demonstrate its good performance.

Accelerating a Geometrical Approximated PCA Algorithm Using AVX2 and CUDA

Remote sensing data has known an explosive growth in the past decade. This has led to the need for efficient dimensionality reduction techniques, mathematical procedures that transform the high-dimensional data into a meaningful, reduced representation. Projection Pursuit (PP) based algorithms were shown to be efficient solutions for performing dimensionality reduction on large datasets by searching low-dimensional projections of the data where meaningful structures are exposed. However, PP faces computational difficulties in dealing with very large datasets—which are common in hyperspectral imaging, thus raising the challenge for implementing such algorithms using the latest High Performance Computing approaches. In this paper, a PP-based geometrical approximated Principal Component Analysis algorithm (gaPCA) for hyperspectral image analysis is implemented and assessed on multi-core Central Processing Units (CPUs), Graphics Processing Units (GPUs) and multi-core CPUs using Single Instruction, Multiple Data (SIMD) AVX2 (Advanced Vector eXtensions) intrinsics, which provide significant improvements in performance and energy usage over the single-core implementation. Thus, this paper presents a cross-platform and cross-language perspective, having several implementations of the gaPCA algorithm in Matlab, Python, C++ and GPU implementations based on NVIDIA Compute Unified Device Architecture (CUDA). The evaluation of the proposed solutions is performed with respect to the execution time and energy consumption. The experimental evaluation has shown not only the advantage of using CUDA programming in implementing the gaPCA algorithm on a GPU in terms of performance and energy consumption, but also significant benefits in implementing it on the multi-core CPU using AVX2 intrinsics.

Dimensionality Reduction Techniques: Comparative Analysis

It has been spotted an exponential growth in terms of dimension in real world data. Some example of higher dimensional data may includes speech signal, sensor data, medical data, criminal data and data related to recommendation process for different field like news, movies (Netflix) and e-commerce. To empowering learning accuracy in the area of machine learning and enhancing mining performance one need to remove redundant feature and feature not relevant for mining and learning task from this high dimension dataset. There exist many supervised and unsupervised methodologies in literature to perform dimension reduction. The objective of paper is to present most prominent methodologies related to the field of dimension reduction and highlight advantages along with disadvantages of these algorithms which can act as starting point for beginners of this field.

Joint learning dimension reduction and clustering of single-cell RNA-sequencing data.

Single-cell RNA-sequencing (scRNA-seq) profiles transcriptome of individual cells, which enables the discovery of cell types or subtypes by using unsupervised clustering. Current algorithms perform dimension reduction before cell clustering because of noises, high-dimensionality and linear inseparability of scRNA-seq data. However, independence of dimension reduction and clustering fails to fully characterize patterns in data, resulting in an undesirable performance. In this study, we propose a flexible and accurate algorithm for scRNA-seq data by jointly learning dimension reduction and cell clustering (aka DRjCC), where dimension reduction is performed by projected matrix decomposition and cell type clustering by non-negative matrix factorization. We first formulate joint learning of dimension reduction and cell clustering into a constrained optimization problem and then derive the optimization rules. The advantage of DRjCC is that feature selection in dimension reduction is guided by cell clustering, significantly improving the performance of cell type discovery. Eleven scRNA-seq datasets are adopted to validate the performance of algorithms, where the number of single cells varies from 49 to 68579 with the number of cell types ranging from 3 to 14. The experimental results demonstrate that DRjCC significantly outperforms 13 state-of-the-art methods in terms of various measurements on cell type clustering (on average 17.44% by improvement). Furthermore, DRjCC is efficient and robust across different scRNA-seq datasets from various tissues. The proposed model and methods provide an effective strategy to analyze scRNA-seq data. The software is coded using matlab, and is free available for academic https://github.com/xkmaxidian/DRjCC. Supplementary data are available at Bioinformatics online.

Envelope-based sparse partial least squares

Sparse partial least squares (SPLS) is widely used in applied sciences as a method that performs dimension reduction and variable selection simultaneously in linear regression. Several implementations of SPLS have been derived, among which the SPLS proposed in Chun and Keleş (J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 3–25) is very popular and highly cited. However, for all of these implementations, the theoretical properties of SPLS are largely unknown. In this paper, we propose a new version of SPLS, called the envelope-based SPLS, using a connection between envelope models and partial least squares (PLS). We establish the consistency, oracle property and asymptotic normality of the envelope-based SPLS estimator. The large-sample scenario and high-dimensional scenario are both considered. We also develop the envelope-based SPLS estimators under the context of generalized linear models, and discuss its theoretical properties including consistency, oracle property and asymptotic distribution. Numerical experiments and examples show that the envelope-based SPLS estimator has better variable selection and prediction performance over the SPLS estimator (J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 3–25).

On change-point estimation under Sobolev sparsity

In this paper, we consider the estimation of a change-point for possibly high-dimensional data in a Gaussian model, using a maximum likelihood method. We are interested in how dimension reduction can affect the performance of the method. We provide an estimator of the change-point that has a minimax rate of convergence, up to a logarithmic factor. The minimax rate is in fact composed of a fast rate —dimension-invariant— and a slow rate —increasing with the dimension. Moreover, it is proved that considering the case of sparse data, with a Sobolev regularity, there is a bound on the separation of the regimes above which there exists an optimal choice of dimension reduction, leading to the fast rate of estimation. We propose an adaptive dimension reduction procedure based on Lepski’s method and show that the resulting estimator attains the fast rate of convergence. Our results are then illustrated by a simulation study. In particular, practical strategies are suggested to perform dimension reduction.

L2,p-Norm Based Discriminant Subspace Clustering Algorithm

Discriminative subspace clustering (DSC) combines Linear Discriminant Analysis (LDA) with clustering algorithm, such as K-means (KM), to form a single framework to perform dimension reduction and clustering simultaneously. It has been verified to be effective for high-dimensional data. However, most existing DSC algorithms rigidly use the Frobenius norm (F-norm) to define model that may not always suitable for the given data. In this paper, DSC is extended in the sense of $l_{2, p}$ -norm, which is a general form of the F-norm, to obtain a family of DSC algorithms which provide more alternative models for practical applications. In order to achieve this goal. Firstly, an efficient algorithm for the $l_{p}$ -norm based KM (KM $_{\mathrm {p}}$ ) clustering is proposed. Then, based on the equivalence of LDA and linear regression, a $l_{\mathrm {2,}p}$ -norm based LDA ( $l_{\mathrm {2,}p}$ -LDA) is proposed, and an efficient Iteratively Reweighted Least Squares algorithm for $l_{\mathrm {2,}p}$ -LDA is presented. Finally, KMp and $l_{2, p}$ -LDA are combined into a single framework to form an efficient generalized DSC algorithm: $l_{2,{p}}$ -norm based DSC clustering ( $l_{2,{p}}$ -DSC). In addition, the effects of the parameters on the proposed algorithm are analyzed, and based on the theory of robust statistics, a special case of $l_{2,{p}}$ -DSC, which can show better robustness on the data sets with noise and outlier, is studied. Extensive experiments are performed to verify the effectiveness of our proposed algorithm.

Joint dimensionality reduction and metric learning for image set classification

Compared with the traditional classification task based on a single image, an image set contains more complementary information, which is of great benefit to correctly classify a query subject. Thus, image set classification has attracted much attention from researchers. However, the main challenge is how to effectively represent an image set to fully exploit the latent discriminative feature. Unlike in previous works where an image set was represented by a single or a hybrid mode, in this paper, we propose a novel multi-model fusion method across the Euclidean space to the Riemannian manifold to jointly accomplish dimensionality reduction and metric learning. To achieve the goal of our framework, we first introduce three distance metric learning models, namely, Euclidean-Euclidean, Riemannian-Riemannian and Euclidean-Riemannian to better exploit the complementary information of an image set. Then, we aim to simultaneously learn two mappings performing dimensionality reduction and a metric matrix by integrating the two heterogeneous spaces (i.e., the Euclidean space and the Riemannian manifold space) into the common induced Mahalanobis space in which the within-class data sets are close and the between-class data sets are separated. This strategy can effectively handle the severe drawback of not considering the distance metric learning when performing dimensionality reduction in the existing set based methods. Furthermore, to learn a complete Mahalanobis metric, we adopt the L2,1 regularized metric matrix for optimal feature selection and classification. The results of extensive experiments on face recognition, object classification, gesture recognition and handwritten classification demonstrated well the effectiveness of the proposed method compared with other image set based algorithms.

ScReClassify: post hoc cell type classification of single-cell rNA-seq data

BackgroundSingle-cell RNA-sequencing (scRNA-seq) is a fast emerging technology allowing global transcriptome profiling on the single cell level. Cell type identification from scRNA-seq data is a critical task in a variety of research such as developmental biology, cell reprogramming, and cancers. Typically, cell type identification relies on human inspection using a combination of prior biological knowledge (e.g. marker genes and morphology) and computational techniques (e.g. PCA and clustering). Due to the incompleteness of our current knowledge and the subjectivity involved in this process, a small amount of cells may be subject to mislabelling.ResultsHere, we propose a semi-supervised learning framework, named scReClassify, for ‘post hoc’ cell type identification from scRNA-seq datasets. Starting from an initial cell type annotation with potentially mislabelled cells, scReClassify first performs dimension reduction using PCA and next applies a semi-supervised learning method to learn and subsequently reclassify cells that are likely mislabelled initially to the most probable cell types. By using both simulated and real-world experimental datasets that profiled various tissues and biological systems, we demonstrate that scReClassify is able to accurately identify and reclassify misclassified cells to their correct cell types.ConclusionsscReClassify can be used for scRNA-seq data as a post hoc cell type classification tool to fine-tune cell type annotations generated by any cell type classification procedure. It is implemented as an R package and is freely available from https://github.com/SydneyBioX/scReClassify

Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks

Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions, etc. Because of these functional uncertainties, the stochastic parameter space is often high-dimensional, requiring hundreds, or even thousands, of parameters to describe it. This poses an insurmountable challenge to response surface modeling since the number of forward model evaluations needed to construct an accurate surrogate grows exponentially with the dimension of the uncertain parameter space; a phenomenon referred to as the curse of dimensionality. State-of-the-art methods for high-dimensional uncertainty propagation seek to alleviate the curse of dimensionality by performing dimensionality reduction in the uncertain parameter space. However, one still needs to perform forward model evaluations that potentially carry a very high computational burden. We propose a novel methodology for high-dimensional uncertainty propagation of elliptic SPDEs which lifts the requirement for a deterministic forward solver. Our approach is as follows. We parameterize the solution of the elliptic SPDE using a deep residual network (ResNet). In a departure from traditional squared residual (SR) based loss function for training the ResNet, we introduce a physics-informed loss function derived from variational principles. Specifically, our loss function is the expectation of the energy functional of the PDE over the stochastic variables. We demonstrate our solver-free approach through various examples where the elliptic SPDE is subjected to different types of high-dimensional input uncertainties. Also, we solve high-dimensional uncertainty propagation and inverse problems.

Two-Step Feature Selection for Identifying Developmental Differences in Resting fMRI Intrinsic Connectivity Networks

Functional connectivity derived from functional magnetic resonance imaging (fMRI) is used as an effective way to assess brain architecture. There has been a growing interest in its application to the study of intrinsic connectivity networks (ICNs) during different brain development stages. fMRI data are of high dimension but small sample size, and it is crucial to perform dimension reduction before pattern analysis of ICNs. Feature selection is thus used to reduce redundancy, lower the complexity of learning, and enhance the interpretability. To study the varying patterns of ICNs in different brain development stages, we propose a two-step feature selection method. First, an improved support vector machine based recursive feature elimination method is utilized to study the differences of connectivity during development. To further reduce the highly correlated features, a combination of F-score and correlation score is applied. This method was then applied to analysis of the Philadelphia Neurodevelopmental Cohort (PNC) data. The two-step feature selection was randomly performed 20 times, and those features that showed up consistently in the experiments were chosen as the essential ICN differences between different brain ages. Our results indicate that ICN differences exist in brain development, and they are related to task control, cognition, information processing, attention, and other brain functions. In particular, compared with children, young adults exhibit increasing functional connectivity in the sensory/somatomotor network, cingulo-opercular task control network, visual network, and some other subnetworks. In addition, the connectivity in young adults decreases between the default mode network and other subnetworks such as the fronto-parietal task control network. The results are coincident with the fact that the connectivity within the brain alters from segregation to integration as an individual grows.

To reduce or not to reduce: a study on spatio-temporal surveillance

The majority of control charts based on scan statistics for spatio-temporal surveillance use full observation vectors. In high-dimensional applications, dimension-reduction techniques are usually applied. Typically, the dimension reduction is conducted as a post-processing step rather than in the data acquisition stage and thus, a full sample covariance matrix is required. When the dimensionality of data is high, (i) the sample covariance matrix tends to be ill-conditioned due to a limited number of samples; (ii) the inversion of such a sample covariance matrix causes numerical issues; and (iii) aggregating information from all variables may lead to high communication costs in sensor networks. In this paper, we propose a set of reduced-dimension (RD) control charts that perform dimension reduction during the data acquisition process by spatial scanning. The proposed methods avoid computational difficulties and possibly high communication costs. We derive a theoretical measure that characterizes the performance difference between the RD approach and the full observation approach. The numerical results show that the RD approach has little performance loss under several commonly used spatial models while enjoying all the benefits of implementation. A case study on water quality monitoring demonstrates the effectiveness of the proposed methods in real applications.

A group bridge approach for component selection in nonparametric accelerated failure time additive regression model

We study a nonparametric accelerated failure time (AFT) additive regression model whose covariates have nonparametric effects on the censored survival time. The proposed model is more flexible than the linear AFT model and can be used to perform dimension reduction and model building. Specifically, it can be used to discover the functional forms of all the covariates, whether a function is a zero or nonzero component; if it is a nonzero component, whether it is linear or nonlinear. First, we treat all the components as unknown nonlinear functions. B-splines are used to model these nonparametric components. A group bridge penalized variable selection approach based on the inverse probability-of-censoring weighted least squares is developed to select important nonparametric components and discover their functional forms simultaneously. Meanwhile, we compare the group bridge and group LASSO methods. The simulation results demonstrate that the group bridge method provides more accurate estimation and better selection performance than the group LASSO method, and the proposed method has satisfactory performance even with relatively high censoring rates. Two real data analyses are used to illustrate the application of the proposed method to censored survival data.

MFPCA: Multiscale Functional Principal Component Analysis.

We consider the problem of performing dimension reduction on heteroscedastic functional data where the variance is in different scales over entire domain. The aim of this paper is to propose a novel multiscale functional principal component analysis (MFPCA) approach to address such heteroscedastic issue. The key ideas of MFPCA are to partition the whole domain into several subdomains according to the scale of variance, and then to conduct the usual functional principal component analysis (FPCA) on each individual subdomain. Both theoretically and numerically, we show that MFPCA can capture features on areas of low variance without estimating high-order principal components, leading to overall improvement of performance on dimension reduction for heteroscedastic functional data. In contrast, traditional FPCA prioritizes optimizing performance on the subdomain of larger data variance and requires a practically prohibitive number of components to characterize data in the region bearing relatively small variance.

Robust singer identification of Indian playback singers

Singing voice analysis has been a topic of research to assist several applications in the domain of music information retrieval system. One such major area is singer identification (SID). There has been enormous increase in production of movies and songs in Bollywood industry over the last 50 decades. Surveying this extensive dataset of singers, the paper presents singer identification system for Indian playback singers. Four acoustic features namely—formants, harmonic spectral envelope, vibrato, and timbre—that uniquely describe the singer are extracted from the singing voice segments. Using the combination of these multiple acoustic features, we address the major challenges in SID like the variations in singer’s voice, testing of multilingual songs, and the album effect. Systematic evaluation shows the SID is robust against the variations in singer’s singing style and structure of songs and is effective in identifying the cover songs and singers. The results are investigated on in-house cappella database consisting of 26 singers and 550 songs. By performing dimension reduction of the feature vector and using Support Vector Machine classifier, we achieved an accuracy of 86% using fourfold cross validation process. In addition, performance comparison of the proposed work with other existing approaches reveals the superiority in terms of volume of dataset and song duration.

Defining gait patterns using Parallel Factor 2 (PARAFAC2): A new analysis of previously published data

Three-dimensional gait analysis (3D–GA) is commonly used to answer clinical questions of the form “which joints and what variables are most affected during when”. When studying high-dimensional datasets, traditional dimension reduction methods (e.g. principal components analysis) require “data flattening”, which may make the ensuing solutions difficult to interpret. The aim of the present study is to present a case study of how a multi-dimensional dimension reduction technique, Parallel Factor 2 (PARAFAC2), provides a clinically interpretable set of solutions to typical biomechanical datasets where different variables are collected during walking and running. Three-dimensional kinematic and kinetic data used for the present analyses came from two publicly available datasets on walking (n = 33) and running (n = 28). For each dataset, a four-dimensional array was constructed as follows: Mode A was time normalized cycle points; mode B was the number of participants multiplied by the number of speed conditions tested; mode C was the number of joint degrees of freedom, and mode D was variable (angle, velocity, moment, power). Five factors for walking and four factors for running were extracted which explained 79.23% and 84.64% of their dataset’s variance. The factor which explains the greatest variance was swing-phase sagittal plane knee kinematics (walking), and kinematics and kinetics (running). Qualitatively, all extracted factors increased in magnitude with greater speed in both walking and running. This study is a proof of concept that PARAFAC2 is useful for performing dimension reduction and producing clinically interpretable solutions to guide clinical decision making.

Identifying clinically important COPD sub-types using data-driven approaches in primary care population based electronic health records

BackgroundCOPD is a highly heterogeneous disease composed of different phenotypes with different aetiological and prognostic profiles and current classification systems do not fully capture this heterogeneity. In this study we sought to discover, describe and validate COPD subtypes using cluster analysis on data derived from electronic health records.MethodsWe applied two unsupervised learning algorithms (k-means and hierarchical clustering) in 30,961 current and former smokers diagnosed with COPD, using linked national structured electronic health records in England available through the CALIBER resource. We used 15 clinical features, including risk factors and comorbidities and performed dimensionality reduction using multiple correspondence analysis. We compared the association between cluster membership and COPD exacerbations and respiratory and cardiovascular death with 10,736 deaths recorded over 146,466 person-years of follow-up. We also implemented and tested a process to assign unseen patients into clusters using a decision tree classifier.ResultsWe identified and characterized five COPD patient clusters with distinct patient characteristics with respect to demographics, comorbidities, risk of death and exacerbations. The four subgroups were associated with 1) anxiety/depression; 2) severe airflow obstruction and frailty; 3) cardiovascular disease and diabetes and 4) obesity/atopy. A fifth cluster was associated with low prevalence of most comorbid conditions.ConclusionsCOPD patients can be sub-classified into groups with differing risk factors, comorbidities, and prognosis, based on data included in their primary care records. The identified clusters confirm findings of previous clustering studies and draw attention to anxiety and depression as important drivers of the disease in young, female patients.

A powerful and efficient multivariate approach for voxel-level connectome-wide association studies

We describe an approach to multivariate analysis, termed structured kernel principal component regression (sKPCR), to identify associations in voxel-level connectomes using resting-state functional magnetic resonance imaging (rsfMRI) data. This powerful and computationally efficient multivariate method can identify voxel-phenotype associations based on the whole-brain connectivity pattern of voxels, and it can detect linear and non-linear signals in both volume-based and surface-based rsfMRI data. For each voxel, sKPCR first extracts low-dimensional signals from the spatially smoothed connectivities by structured kernel principal component analysis, and then tests the voxel-phenotype associations by an adaptive regression model. The method's power is derived from appropriately modelling the spatial structure of the data when performing dimension reduction, and then adaptively choosing an optimal dimension for association testing using the adaptive regression strategy. Simulations based on real connectome data have shown that sKPCR can accurately control the false-positive rate and that it is more powerful than many state-of-the-art approaches, such as the connectivity-wise generalized linear model (GLM) approach, multivariate distance matrix regression (MDMR), adaptive sum of powered score (aSPU) test, and least-square kernel machine (LSKM). Moreover, since sKPCR can reduce the computational cost of non-parametric permutation tests, its computation speed is much faster. To demonstrate the utility of sKPCR for real data analysis, we have also compared sKPCR with the above methods based on the identification of voxel-wise differences between schizophrenic patients and healthy controls in four independent rsfMRI datasets. The results showed that sKPCR had better between-sites reproducibility and a larger proportion of overlap with existing schizophrenia meta-analysis findings. Code for our approach can be downloaded from https://github.com/weikanggong/sKPCR.