Manifold Denoising by Nonlinear Robust Principal Component Analysis.
Ontology highlight
ABSTRACT:
SUBMITTER: Lyu H
PROVIDER: S-EPMC8297813 | biostudies-literature | 2019 Dec
REPOSITORIES: biostudies-literature
Publications
Manifold Denoising by Nonlinear Robust Principal Component Analysis.
Lyu He H Sha Ningyu N Qin Shuyang S Yan Ming M Xie Yuying Y Wang Rongrong R
Advances in neural information processing systems 20191201
This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to separate them by using similar ideas as RPCA? Is there any benefit in treating the manifold as a whole as opposed to treating each local region independently? We answer these two questions affirmatively by proposing and analyzing an optimization framework that separa ...[more]
Similar Datasets
Project description:Fluorescence Lifetime Imaging Microscopy (FLIM) quantifies the autofluorescence lifetime to measure cellular metabolism, therapeutic efficacy, and disease progression. These dynamic processes are intrinsically heterogeneous, increasing the complexity of the signal analysis. Often noise reduction strategies that combine thresholding and non-selective data smoothing filters are applied. These can result in error introduction and data loss. To mitigate these issues, we develop noise-corrected principal component analysis (NC-PCA). This approach isolates the signal of interest by selectively identifying and removing the noise. To validate NC-PCA, a secondary analysis of FLIM images of patient-derived colorectal cancer organoids exposed to a range of therapeutics was performed. First, we demonstrate that NC-PCA decreases the uncertainty up to 4-fold in comparison to conventional analysis with no data loss. Then, using a merged data set, we show that NC-PCA, unlike conventional methods, identifies multiple metabolic states. Thus, NC-PCA provides an enabling tool to advance FLIM analysis across fields.
| S-EPMC11888454 | biostudies-literature
Project description:Numerous approaches have been used to denoise spinal cord functional magnetic resonance imaging (fMRI) data. Principal component analysis (PCA)-based techniques, which derive regressors from a noise region of interest (ROI), have been used in both brain (e.g., CompCor) and spinal cord fMRI. However, spinal cord fMRI denoising methods have yet to be systematically evaluated. Here, we formalize and evaluate a PCA-based technique for deriving nuisance regressors for spinal cord fMRI analysis (SpinalCompCor). In this method, regressors are derived with PCA from a noise ROI, an area defined outside of the spinal cord and cerebrospinal fluid. A parallel analysis is used to systematically determine how many components to retain as regressors for modeling; this designated a median of 11 regressors across three fMRI datasets: motor task (n=26), breathing task (n=27), and resting state (n=10). First-level fMRI modeling demonstrated that principal component regressors did fit noise (e.g., physiological noise from blood vessels), particularly in the resting state fMRI dataset. However, group-level motor task activation maps themselves did not show a clear benefit from including SpinalCompCor regressors over our original denoising model. The potential for collinearity of principal component regressors with the task may be a concern, and this should be considered in future implementations for which task-correlated noise is anticipated.
| S-EPMC11785179 | biostudies-literature
Project description:PurposeMulti-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.MethodsPCA 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.ResultsDenoising 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.ConclusionExperimental 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:Purposeto propose a two-step non-local principal component analysis (PCA) method and demonstrate its utility for denoising diffusion tensor MRI (DTI) with a few diffusion directions.MethodsA two-step denoising pipeline was implemented to ensure accurate patch selection even with high noise levels and was coupled with data preprocessing for g-factor normalization and phase stabilization before data denoising with a non-local PCA algorithm. At the heart of our proposed pipeline was the use of a data-driven optimal shrinkage algorithm to manipulate the singular values in a way that would optimally estimate the noise-free signal. Our approach's denoising performances were evaluated using simulation and in-vivo human data experiments. The results were compared to those obtained with existing local-PCA-based methods.ResultsIn both simulation and human data experiments, our approach substantially enhanced image quality relative to the noisy counterpart, yielding improved performances for estimation of relevant DTI metrics. It also outperformed existing local-PCA-based methods in reducing noise while preserving anatomic details. It also led to improved whole-brain tractography relative to the noisy counterpart.ConclusionThe proposed denoising method has the utility for improving image quality for DTI with reduced diffusion directions and is believed to benefit many applications especially those aiming to achieve quality parametric mapping using only a few image volumes.
| S-EPMC11565869 | 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: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: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: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