Manifold Denoising by Nonlinear Robust Principal Component Analysis.
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ABSTRACT:
SUBMITTER: Lyu H
PROVIDER: S-EPMC8297813 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:PURPOSE:Multi-exponential relaxometry is a powerful tool for characterizing tissue, but generally requires high image signal-to-noise ratio (SNR). This work evaluates the use of principal-component-analysis (PCA) denoising to mitigate these SNR demands and improve the precision of relaxometry measures. METHODS:PCA denoising was evaluated using both simulated and experimental MRI data. Bi-exponential transverse relaxation signals were simulated for a wide range of acquisition and sample parameters, and experimental data were acquired from three excised and fixed mouse brains. In both cases, standard relaxometry analysis was performed on both original and denoised image data, and resulting estimated signal parameters were compared. RESULTS:Denoising reduced the root-mean-square-error of parameters estimated from multi-exponential relaxometry by factors of ≈3×, for typical acquisition and sample parameters. Denoised images and subsequent parameter maps showed little or no signs of spatial artifact or loss of resolution. CONCLUSION:Experimental studies and simulations demonstrate that PCA denoising of MRI relaxometry data is an effective method of improving parameter precision without sacrificing image resolution. This simple yet important processing step thus paves the way for broader applicability of multi-exponential MRI relaxometry.
| S-EPMC6955240 | biostudies-literature
Project description:MotivationPopulation stratification (PS) is a major confounder in genome-wide association studies (GWAS) and can lead to false-positive associations. To adjust for PS, principal component analysis (PCA)-based ancestry prediction has been widely used. Simple projection (SP) based on principal component loadings and the recently developed data augmentation, decomposition and Procrustes (ADP) transformation, such as LASER and TRACE, are popular methods for predicting PC scores. However, the predicted PC scores from SP can be biased toward NULL. On the other hand, ADP has a high computation cost because it requires running PCA separately for each study sample on the augmented dataset.ResultsWe develop and propose two alternative approaches: bias-adjusted projection (AP) and online ADP (OADP). Using random matrix theory, AP asymptotically estimates and adjusts for the bias of SP. OADP uses a computationally efficient online singular value decomposition algorithm, which can greatly reduce the computation cost of ADP. We carried out extensive simulation studies to show that these alternative approaches are unbiased and the computation speed can be 16-16 000 times faster than ADP. We applied our approaches to the UK Biobank data of 488 366 study samples with 2492 samples from the 1000 Genomes data as the reference. AP and OADP required 0.82 and 21 CPU hours, respectively, while the projected computation time of ADP was 1628 CPU hours. Furthermore, when inferring sub-European ancestry, SP clearly showed bias, unlike the proposed approaches.Availability and implementationThe OADP and AP methods, as well as SP and ADP, have been implemented in the open-source Python software FRAPOSA, available at github.com/daviddaiweizhang/fraposa.Contactleeshawn@umich.edu.Supplementary informationSupplementary data are available at Bioinformatics online.
| S-EPMC7267814 | biostudies-literature
Project description:The purpose of this paper for four-dimensional (4D) computed tomography (CT) is threefold. (1) A new spatiotemporal model is presented from the matrix perspective with the row dimension in space and the column dimension in time, namely the robust PCA (principal component analysis)-based 4D CT model. That is, instead of viewing the 4D object as a temporal collection of three-dimensional (3D) images and looking for local coherence in time or space independently, we perceive it as a mixture of low-rank matrix and sparse matrix to explore the maximum temporal coherence of the spatial structure among phases. Here the low-rank matrix corresponds to the 'background' or reference state, which is stationary over time or similar in structure; the sparse matrix stands for the 'motion' or time-varying component, e.g., heart motion in cardiac imaging, which is often either approximately sparse itself or can be sparsified in the proper basis. Besides 4D CT, this robust PCA-based 4D CT model should be applicable in other imaging problems for motion reduction or/and change detection with the least amount of data, such as multi-energy CT, cardiac MRI, and hyperspectral imaging. (2) A dynamic strategy for data acquisition, i.e. a temporally spiral scheme, is proposed that can potentially maintain similar reconstruction accuracy with far fewer projections of the data. The key point of this dynamic scheme is to reduce the total number of measurements, and hence the radiation dose, by acquiring complementary data in different phases while reducing redundant measurements of the common background structure. (3) An accurate, efficient, yet simple-to-implement algorithm based on the split Bregman method is developed for solving the model problem with sparse representation in tight frames.
| S-EPMC3395474 | biostudies-literature
Project description:BackgroundModern developments in single-cell sequencing technologies enable broad insights into cellular state. Single-cell RNA sequencing (scRNA-seq) can be used to explore cell types, states, and developmental trajectories to broaden our understanding of cellular heterogeneity in tissues and organs. Analysis of these sparse, high-dimensional experimental results requires dimension reduction. Several methods have been developed to estimate low-dimensional embeddings for filtered and normalized single-cell data. However, methods have yet to be developed for unfiltered and unnormalized count data that estimate uncertainty in the low-dimensional space. We present a nonlinear latent variable model with robust, heavy-tailed error and adaptive kernel learning to estimate low-dimensional nonlinear structure in scRNA-seq data.ResultsGene expression in a single cell is modeled as a noisy draw from a Gaussian process in high dimensions from low-dimensional latent positions. This model is called the Gaussian process latent variable model (GPLVM). We model residual errors with a heavy-tailed Student's t-distribution to estimate a manifold that is robust to technical and biological noise found in normalized scRNA-seq data. We compare our approach to common dimension reduction tools across a diverse set of scRNA-seq data sets to highlight our model's ability to enable important downstream tasks such as clustering, inferring cell developmental trajectories, and visualizing high throughput experiments on available experimental data.ConclusionWe show that our adaptive robust statistical approach to estimate a nonlinear manifold is well suited for raw, unfiltered gene counts from high-throughput sequencing technologies for visualization, exploration, and uncertainty estimation of cell states.
| S-EPMC7374962 | biostudies-literature
Project description:Despite the utility of tumour characterisation using quantitative parameter maps from multi-b-value diffusion-weighted MRI (DWI), clinicians often prefer the use of the image with highest diffusion-weighting (b-value), for instance for defining regions of interest (ROIs). However, these images are typically degraded by noise, as they do not utilize the information from the full acquisition. We present a principal component analysis (PCA) approach for model-free denoising of DWI data. PCA-denoising was compared to synthetic MRI, where a diffusion model is fitted for each voxel and a denoised image at a given b-value is generated from the model fit. A quantitative comparison of systematic and random errors was performed on data simulated using several diffusion models (mono-exponential, bi-exponential, stretched-exponential and kurtosis). A qualitative visual comparison was also performed for in vivo images in six healthy volunteers and three pancreatic cancer patients. In simulations, the reduction in random errors from PCA-denoising was substantial (up to 55%) and similar to synthetic MRI (up to 53%). Model-based synthetic MRI denoising resulted in substantial (up to 29% of signal) systematic errors, whereas PCA-denoising was able to denoise without introducing systematic errors (less than 2%). In vivo, the signal-to-noise ratio (SNR) and sharpness of PCA-denoised images were superior to synthetic MRI, resulting in clearer tumour boundaries. In the presence of motion, PCA-denoising did not cause image blurring, unlike image averaging or synthetic MRI. Multi-b-value MRI can be denoised model-free with our PCA-denoising strategy that reduces noise to a level similar to synthetic MRI, but without introducing systematic errors associated with the synthetic MRI method.
| S-EPMC7655121 | biostudies-literature
Project description:Constructing a robust emotion-aware analytical framework using non-invasively recorded electroencephalogram (EEG) signals has gained intensive attentions nowadays. However, as deploying a laboratory-oriented proof-of-concept study toward real-world applications, researchers are now facing an ecological challenge that the EEG patterns recorded in real life substantially change across days (i.e., day-to-day variability), arguably making the pre-defined predictive model vulnerable to the given EEG signals of a separate day. The present work addressed how to mitigate the inter-day EEG variability of emotional responses with an attempt to facilitate cross-day emotion classification, which was less concerned in the literature. This study proposed a robust principal component analysis (RPCA)-based signal filtering strategy and validated its neurophysiological validity and machine-learning practicability on a binary emotion classification task (happiness vs. sadness) using a five-day EEG dataset of 12 subjects when participated in a music-listening task. The empirical results showed that the RPCA-decomposed sparse signals (RPCA-S) enabled filtering off the background EEG activity that contributed more to the inter-day variability, and predominately captured the EEG oscillations of emotional responses that behaved relatively consistent along days. Through applying a realistic add-day-in classification validation scheme, the RPCA-S progressively exploited more informative features (from 12.67 ± 5.99 to 20.83 ± 7.18) and improved the cross-day binary emotion-classification accuracy (from 58.31 ± 12.33% to 64.03 ± 8.40%) as trained the EEG signals from one to four recording days and tested against one unseen subsequent day. The original EEG features (prior to RPCA processing) neither achieved the cross-day classification (the accuracy was around chance level) nor replicated the encouraging improvement due to the inter-day EEG variability. This result demonstrated the effectiveness of the proposed method and may shed some light on developing a realistic emotion-classification analytical framework alleviating day-to-day variability.
| S-EPMC5515900 | biostudies-other
Project description:BackgroundHigh throughput RNA sequencing is a powerful approach to study gene expression. Due to the complex multiple-steps protocols in data acquisition, extreme deviation of a sample from samples of the same treatment group may occur due to technical variation or true biological differences. The high-dimensionality of the data with few biological replicates make it challenging to accurately detect those samples, and this issue is not well studied in the literature currently. Robust statistics is a family of theories and techniques aim to detect the outliers by first fitting the majority of the data and then flagging data points that deviate from it. Robust statistics have been widely used in multivariate data analysis for outlier detection in chemometrics and engineering. Here we apply robust statistics on RNA-seq data analysis.ResultsWe report the use of two robust principal component analysis (rPCA) methods, PcaHubert and PcaGrid, to detect outlier samples in multiple simulated and real biological RNA-seq data sets with positive control outlier samples. PcaGrid achieved 100% sensitivity and 100% specificity in all the tests using positive control outliers with varying degrees of divergence. We applied rPCA methods and classical principal component analysis (cPCA) on an RNA-Seq data set profiling gene expression of the external granule layer in the cerebellum of control and conditional SnoN knockout mice. Both rPCA methods detected the same two outlier samples but cPCA failed to detect any. We performed differentially expressed gene detection before and after outlier removal as well as with and without batch effect modeling. We validated gene expression changes using quantitative reverse transcription PCR and used the result as reference to compare the performance of eight different data analysis strategies. Removing outliers without batch effect modeling performed the best in term of detecting biologically relevant differentially expressed genes.ConclusionsrPCA implemented in the PcaGrid function is an accurate and objective method to detect outlier samples. It is well suited for high-dimensional data with small sample sizes like RNA-seq data. Outlier removal can significantly improve the performance of differential gene detection and downstream functional analysis.
| S-EPMC7324992 | biostudies-literature
Project description:Principal component regression uses principal components (PCs) as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We introduce a Bayesian approach that is robust to outliers in both the dependent variable and the covariates. Outliers can be thought of as observations that are not in line with the general trend. The proposed approach automatically penalises these observations so that their impact on the posterior gradually vanishes as they move further and further away from the general trend, corresponding to a concept in Bayesian statistics called whole robustness. The predictions produced are thus consistent with the bulk of the data. The approach also exploits the geometry of PCs to efficiently identify those that are significant. Individual predictions obtained from the resulting models are consolidated according to model-averaging mechanisms to account for model uncertainty. The approach is evaluated on real data and compared to its nonrobust Bayesian counterpart, the traditional frequentist approach and a commonly employed robust frequentist method. Detailed guidelines to automate the entire statistical procedure are provided. All required code is made available, see ArXiv:1711.06341.
| S-EPMC9042041 | biostudies-literature
Project description:Although principal component analysis is frequently used in multivariate/ analysis, it has disadvantages when applied to experimental or diagnostic data. First, the identified principal components have poor generality; since the size and directions of the components are dependent on the particular data set, the components are valid only within the set. Second, the method is sensitive to experimental noise and bias between sample groups, since it cannot reflect the design of experiments; rather, it estimates the same weight and independence of all the samples in the matrix. Third, the resulting components are often difficult to interpret. To address these issues, several options were introduced to the methodology. The resulting components were scaled to unify their size unit. Also, the principal axes were identified using training data sets and shared among experiments. This training data reflects the design of experiments, and its preparation allows noise to be reduced and group bias to be removed. The effects of these options were observed in microarray experiments, and showed an improvement in the separation of groups and robustness to noise. Additionally, unknown samples were appropriately classified using pre-arranged axes, and principal axes well reflected the characteristics of groups in the experiments. This SuperSeries is composed of the SubSeries listed below.
2011-08-15 | GSE31375 | GEO
Project description:Over the past several years, significant efforts have been made to improve the spatial resolution of diffusion-weighted imaging (DWI), aiming at better detecting subtle lesions and more reliably resolving white-matter fiber tracts. A major concern with high-resolution DWI is the limited signal-to-noise ratio (SNR), which may significantly offset the advantages of high spatial resolution. Although the SNR of DWI data can be improved by denoising in post-processing, existing denoising procedures may potentially reduce the anatomic resolvability of high-resolution imaging data. Additionally, non-Gaussian noise induced signal bias in low-SNR DWI data may not always be corrected with existing denoising approaches. Here we report an improved denoising procedure, termed diffusion-matched principal component analysis (DM-PCA), which comprises 1) identifying a group of (not necessarily neighboring) voxels that demonstrate very similar magnitude signal variation patterns along the diffusion dimension, 2) correcting low-frequency phase variations in complex-valued DWI data, 3) performing PCA along the diffusion dimension for real- and imaginary-components (in two separate channels) of phase-corrected DWI voxels with matched diffusion properties, 4) suppressing the noisy PCA components in real- and imaginary-components, separately, of phase-corrected DWI data, and 5) combining real- and imaginary-components of denoised DWI data. Our data show that the new two-channel (i.e., for real- and imaginary-components) DM-PCA denoising procedure performs reliably without noticeably compromising anatomic resolvability. Non-Gaussian noise induced signal bias could also be reduced with the new denoising method. The DM-PCA based denoising procedure should prove highly valuable for high-resolution DWI studies in research and clinical uses.
| S-EPMC5918820 | biostudies-literature