Two-stage linked component analysis for joint decomposition of multiple biologically related data sets.

Integrative analysis of multiple data sets has the potential of fully leveraging the vast amount of high throughput biological data being generated. In particular such analysis will be powerful in making inference from publicly available collections of genetic, transcriptomic and epigenetic data sets which are designed to study shared biological processes, but which vary in their target measurements, biological variation, unwanted noise, and batch variation. Thus, methods that enable the joint analysis of multiple data sets are needed to gain insights into shared biological processes that would otherwise be hidden by unwanted intra-data set variation. Here, we propose a method called two-stage linked component analysis (2s-LCA) to jointly decompose multiple biologically related experimental data sets with biological and technological relationships that can be structured into the decomposition. The consistency of the proposed method is established and its empirical performance is evaluated via simulation studies. We apply 2s-LCA to jointly analyze four data sets focused on human brain development and identify meaningful patterns of gene expression in human neurogenesis that have shared structure across these data sets.

Performance Comparison of Compressed Sensing Algorithms for Accelerating T1ρ Mapping of Human Brain.

BACKGROUND: 3D-T1ρ mapping is useful to quantify various neurologic disorders, but data are currently time-consuming to acquire. PURPOSE: To compare the performance of five compressed sensing (CS) algorithms-spatiotemporal finite differences (STFD), exponential dictionary (EXP), 3D-wavelet transform (WAV), low-rank (LOW) and low-rank plus sparse model with spatial finite differences (L + S SFD)-for 3D-T1ρ mapping of the human brain with acceleration factors (AFs) of 2, 5, and 10. STUDY TYPE: Retrospective. SUBJECTS: Eight healthy volunteers underwent T1ρ imaging of the whole brain. FIELD STRENGTH/SEQUENCE: The sequence was fully sampled 3D Cartesian ultrafast gradient echo sequence with a customized T1ρ preparation module on a clinical 3T scanner. ASSESSMENT: The fully sampled data was undersampled by factors of 2, 5, and 10 and reconstructed with the five CS algorithms. Image reconstruction quality was evaluated and compared to the SENSE reconstruction of the fully sampled data (reference) and T1ρ estimation errors were assessed as a function of AF. STATISTICAL TESTS: Normalized root mean squared errors (nRMSE) and median normalized absolute deviation (MNAD) errors were calculated to compare image reconstruction errors and T1ρ estimation errors, respectively. Linear regression plots, Bland-Altman plots, and Pearson correlation coefficients (CC) are shown. RESULTS: For image reconstruction quality, at AF = 2, EXP transforms had the lowest mRMSE (1.56%). At higher AF values, STFD performed better, with the smallest errors (3.16% at AF = 5, 4.32% at AF = 10). For whole-brain quantitative T1ρ mapping, at AF = 2, EXP performed best (MNAD error = 1.62%). At higher AF values (AF = 5, 10), the STFD technique had the least errors (2.96% at AF = 5, 4.24% at AF = 10) and the smallest variance from the reference T1ρ estimates. DATA CONCLUSION: This study demonstrates the use of different CS algorithms that may be useful in reducing the scan time required to perform volumetric T1ρ mapping of the brain. LEVEL OF EVIDENCE: 2. TECHNICAL EFFICACY STAGE: 1.

Intravoxel B0 inhomogeneity corrected reconstruction using a low-rank encoding operator.

PURPOSE: To present a general and efficient method for macroscopic intravoxel B0 inhomogeneity corrected reconstruction from multi-TE acquisitions. THEORY AND METHODS: A signal encoding model for multi-TE gradient echo (GRE) acquisitions that incorporates 3D intravoxel B0 field variations is derived, and a low-rank approximation to the encoding operator is introduced under piecewise linear B0 assumption. The low-rank approximation enables very efficient computation and memory usage, and allows the proposed signal model to be integrated into general inverse problem formulations that are compatible with multi-coil and undersampling acquisitions as well as different regularization functions. RESULTS: Experimental multi-echo GRE data were acquired to evaluate the proposed method. Effective reduction of macroscopic intravoxel B0 inhomogeneity induced artifacts was demonstrated. Improved R2∗ estimation from the corrected reconstruction over standard Fourier reconstruction has also been obtained. CONCLUSIONS: The proposed method can effectively correct the effects of intravoxel B0 inhomogeneity, and can be useful for various imaging applications involving GRE-based acquisitions, including fMRI, quantitative R2∗ and susceptibility mapping, and MR spectroscopic imaging.

Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning.

The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

Accelerating 3D-T1ρ mapping of cartilage using compressed sensing with different sparse and low rank models.

PURPOSE: To evaluate the feasibility of using compressed sensing (CS) to accelerate 3D-T1ρ mapping of cartilage and to reduce total scan times without degrading the estimation of T1ρ relaxation times. METHODS: Fully sampled 3D-T1ρ datasets were retrospectively undersampled by factors 2-10. CS reconstruction using 12 different sparsifying transforms were compared, including finite differences, temporal and spatial wavelets, learned transforms using principal component analysis (PCA) and K-means singular value decomposition (K-SVD), explicit exponential models, low rank and low rank plus sparse models. Spatial filtering prior to T1ρ parameter estimation was also tested. Synthetic phantom (n = 6) and in vivo human knee cartilage datasets (n = 7) were included. RESULTS: Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative T1ρ error lower than 4.5%. Some sparsifying transforms, such as spatiotemporal finite difference (STFD), exponential dictionaries (EXP) and low rank combined with spatial finite difference (L+S SFD) significantly improved this performance, reaching average relative T1ρ error below 6.5% on T1ρ relaxation times with AF up to 10, when spatial filtering was used before T1ρ fitting, at the expense of smoothing the T1ρ maps. The STFD achieved 5.1% error at AF = 10 with spatial filtering prior to T1ρ fitting. CONCLUSION: Accelerating 3D-T1ρ mapping of cartilage with CS is feasible up to AF of 10 when using STFD, EXP or L+S SFD regularizers. These three best CS methods performed satisfactorily on synthetic phantom and in vivo knee cartilage for AFs up to 10, with T1ρ error of 6.5%.

Streaming PCA and Subspace Tracking: The Missing Data Case.

For many modern applications in science and engineering, data are collected in a streaming fashion carrying time-varying information, and practitioners need to process them with a limited amount of memory and computational resources in a timely manner for decision making. This often is coupled with the missing data problem, such that only a small fraction of data attributes are observed. These complications impose significant, and unconventional, constraints on the problem of streaming Principal Component Analysis (PCA) and subspace tracking, which is an essential building block for many inference tasks in signal processing and machine learning. This survey article reviews a variety of classical and recent algorithms for solving this problem with low computational and memory complexities, particularly those applicable in the big data regime with missing data. We illustrate that streaming PCA and subspace tracking algorithms can be understood through algebraic and geometric perspectives, and they need to be adjusted carefully to handle missing data. Both asymptotic and non-asymptotic convergence guarantees are reviewed. Finally, we benchmark the performance of several competitive algorithms in the presence of missing data for both well-conditioned and ill-conditioned systems.

Compartmentalized low-rank recovery for high-resolution lipid unsuppressed MRSI.

PURPOSE: To introduce a novel algorithm for the recovery of high-resolution magnetic resonance spectroscopic imaging (MRSI) data with minimal lipid leakage artifacts, from dual-density spiral acquisition. METHODS: The reconstruction of MRSI data from dual-density spiral data is formulated as a compartmental low-rank recovery problem. The MRSI dataset is modeled as the sum of metabolite and lipid signals, each of which is support limited to the brain and extracranial regions, respectively, in addition to being orthogonal to each other. The reconstruction problem is formulated as an optimization problem, which is solved using iterative reweighted nuclear norm minimization. RESULTS: The comparisons of the scheme against dual-resolution reconstruction algorithm on numerical phantom and in vivo datasets demonstrate the ability of the scheme to provide higher spatial resolution and lower lipid leakage artifacts. The experiments demonstrate the ability of the scheme to recover the metabolite maps, from lipid unsuppressed datasets with echo time (TE) = 55 ms. CONCLUSION: The proposed reconstruction method and data acquisition strategy provide an efficient way to achieve high-resolution metabolite maps without lipid suppression. This algorithm would be beneficial for fast metabolic mapping and extension to multislice acquisitions. Magn Reson Med 78:1267-1280, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Low-rank regression models for multiple binary responses and their applications to cancer cell-line encyclopedia data.

In this paper, we study high-dimensional multivariate logistic regression models in which a common set of covariates is used to predict multiple binary outcomes simultaneously. Our work is primarily motivated from many biomedical studies with correlated multiple responses such as the cancer cell-line encyclopedia project. We assume that the underlying regression coefficient matrix is simultaneously low-rank and row-wise sparse. We propose an intuitively appealing selection and estimation framework based on marginal model likelihood, and we develop an efficient computational algorithm for inference. We establish a novel high-dimensional theory for this nonlinear multivariate regression. Our theory is general, allowing for potential correlations between the binary responses. We propose a new type of nuclear norm penalty using the smooth clipped absolute deviation, filling the gap in the related non-convex penalization literature. We theoretically demonstrate that the proposed approach improves estimation accuracy by considering multiple responses jointly through the proposed estimator when the underlying coefficient matrix is low-rank and row-wise sparse. In particular, we establish the non-asymptotic error bounds, and both rank and row support consistency of the proposed method. Moreover, we develop a consistent rule to simultaneously select the rank and row dimension of the coefficient matrix. Furthermore, we extend the proposed methods and theory to a joint Ising model, which accounts for the dependence relationships. In our analysis of both simulated data and the cancer cell line encyclopedia data, the proposed methods outperform the existing methods in better predicting responses.

A representation transfer learning approach for enhanced prediction of growth hormone binding proteins.

Growth hormone binding proteins (GHBPs) are soluble proteins that play an important role in the modulation of signaling pathways pertaining to growth hormones. GHBPs are selective and bind non-covalently with growth hormones, but their functions are still not fully understood. Identification and characterization of GHBPs are the preliminary steps for understanding their roles in various cellular processes. As wet lab based experimental methods involve high cost and labor, computational methods can facilitate in narrowing down the search space of putative GHBPs. Performance of machine learning algorithms largely depends on the quality of features that it feeds on. Informative and non-redundant features generally result in enhanced performance and for this purpose feature selection algorithms are commonly used. In the present work, a novel representation transfer learning approach is presented for prediction of GHBPs. For their accurate prediction, deep autoencoder based features were extracted and subsequently SMO-PolyK classifier is trained. The prediction model is evaluated by both leave one out cross validation (LOOCV) and hold out independent testing set. On LOOCV, the prediction model achieved 89.8%% accuracy, with 89.4% sensitivity and 90.2% specificity and accuracy of 93.5%, sensitivity of 90.2% and specificity of 96.8% is attained on the hold out testing set. Further a comparison was made between the full set of sequence-based features, top performing sequence features extracted using feature selection algorithm, deep autoencoder based features and generalized low rank model based features on the prediction accuracy. Principal component analysis of the representative features along with t-sne visualization demonstrated the effectiveness of deep features in prediction of GHBPs. The present method is robust and accurate and may complement other wet lab based methods for identification of novel GHBPs.

Modeling Massive Spatial Datasets Using a Conjugate Bayesian Linear Modeling Framework.

Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models have been proposed that can be easily embedded within a hierarchical modeling framework to carry out Bayesian inference. While the focus of statistical research has mostly been directed toward innovative and more complex model development, relatively limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article discusses how point-referenced spatial process models can be cast as a conjugate Bayesian linear regression that can rapidly deliver inference on spatial processes. The approach allows exact sampling directly (avoids iterative algorithms such as Markov chain Monte Carlo) from the joint posterior distribution of regression parameters, the latent process and the predictive random variables, and can be easily implemented on statistical programming environments such as R.

Meta-Kriging: Scalable Bayesian Modeling and Inference for Massive Spatial Datasets.

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations becomes large. There is a burgeoning literature on approaches for analyzing large spatial datasets. In this article, we propose a divide-and-conquer strategy within the Bayesian paradigm. We partition the data into subsets, analyze each subset using a Bayesian spatial process model and then obtain approximate posterior inference for the entire dataset by combining the individual posterior distributions from each subset. Importantly, as often desired in spatial analysis, we offer full posterior predictive inference at arbitrary locations for the outcome as well as the residual spatial surface after accounting for spatially oriented predictors. We call this approach "Spatial Meta-Kriging" (SMK). We do not need to store the entire data in one processor, and this leads to superior scalability. We demonstrate SMK with various spatial regression models including Gaussian processes and tapered Gaussian processes. The approach is intuitive, easy to implement, and is supported by theoretical results presented in the supplementary material available online. Empirical illustrations are provided using different simulation experiments and a geostatistical analysis of Pacific Ocean sea surface temperature data.