Sparse Component Research Articles

A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising

Hyperspectral images (HSIs) are frequently corrupted by mixing noise during their acquisition and transmission. Such complicated noise may reduce the quality of the obtained HSIs and limit the accuracy of the subsequent processing. By using the low-rank prior of the tensor formed by spatial and spectral information and further exploring the intrinsic structure of the underlying HSI from noisy observations, in this paper, we propose a new nonconvex low-rank tensor approximation method including optimization model and efficient iterative algorithm to eliminate multiple types of noise. The proposed mathematical model consists of a nonconvex low-rank regularization term using the γ nuclear norm, which is nonconvex surrogate to Tucker rank, and two data fidelity terms representing sparse and Gaussian noise components, which are regularized by the -norm and the Frobenius norm, respectively. To solve this model, we propose an efficient augmented Lagrange multiplier algorithm. We also study the convergence and parameter setting of the algorithm. Extensive experimental results show that the proposed method has better denoising performance than the state-of-the-art competing methods for low-rank tensor approximation and noise modeling.

Evaluating carbon neutrality potential in China based on sparse principal component analysis

The resource endowments, development levels and emission reduction potential of different provinces in China are different. Accurately judging regional differences of carbon neutrality potential of each province is helpful to analyze the low-carbon development strategy. In this research, a comprehensive evaluation index system for carbon neutrality potential is constructed, and the carbon neutrality potential score of China from 2003 to 2019 is calculated by sparse principal components(SPC), and dynamically evaluated by combining time ordered weighted average operator (TOWA operator). The results show that: (1) The evaluation score of carbon neutrality potential is greatly affected by the sustainable driving force, and the overall trend is on the rise. But there is a significant gap between provinces, showing the distribution characteristics of “high in the east and low in the central and western regions”. (2) The upward trend of sustainable driving force is obvious, there is a momentum of accelerated development in recent years. The gap between provinces is large. (3) The resilient driving force showed an increasing trend, but some provinces have experienced a decline since 2017. (4) The growth trend of coordination and transformational resilience is flat. The development of provinces is relatively balanced. This provides a reference for the analysis of each region to formulate low-carbon development strategies tailored to local conditions.

Sparse dimensionality reduction approaches in Mendelian randomisation with highly correlated exposures.

Multivariable Mendelian randomisation (MVMR) is an instrumental variable technique that generalises the MR framework for multiple exposures. Framed as a regression problem, it is subject to the pitfall of multicollinearity. The bias and efficiency of MVMR estimates thus depends heavily on the correlation of exposures. Dimensionality reduction techniques such as principal component analysis (PCA) provide transformations of all the included variables that are effectively uncorrelated. We propose the use of sparse PCA (sPCA) algorithms that create principal components of subsets of the exposures with the aim of providing more interpretable and reliable MR estimates. The approach consists of three steps. We first apply a sparse dimension reduction method and transform the variant-exposure summary statistics to principal components. We then choose a subset of the principal components based on data-driven cutoffs, and estimate their strength as instruments with an adjusted F-statistic. Finally, we perform MR with these transformed exposures. This pipeline is demonstrated in a simulation study of highly correlated exposures and an applied example using summary data from a genome-wide association study of 97 highly correlated lipid metabolites. As a positive control, we tested the causal associations of the transformed exposures on coronary heart disease (CHD). Compared to the conventional inverse-variance weighted MVMR method and a weak instrument robust MVMR method (MR GRAPPLE), sparse component analysis achieved a superior balance of sparsity and biologically insightful grouping of the lipid traits.

Volatile Markers for Cancer in Exhaled Breath-Could They Be the Signature of the Gut Microbiota?

It has been shown that the gut microbiota plays a central role in human health and disease. A wide range of volatile metabolites present in exhaled breath have been linked with gut microbiota and proposed as a non-invasive marker for monitoring pathological conditions. The aim of this study was to examine the possible correlation between volatile organic compounds (VOCs) in exhaled breath and the fecal microbiome by multivariate statistical analysis in gastric cancer patients (n = 16) and healthy controls (n = 33). Shotgun metagenomic sequencing was used to characterize the fecal microbiota. Breath-VOC profiles in the same participants were identified by an untargeted gas chromatography-mass spectrometry (GC-MS) technique. A multivariate statistical approach involving a canonical correlation analysis (CCA) and sparse principal component analysis identified the significant relationship between the breath VOCs and fecal microbiota. This relation was found to differ between gastric cancer patients and healthy controls. In 16 cancer cases, 14 distinct metabolites identified from the breath belonging to hydrocarbons, alcohols, aromatics, ketones, ethers, and organosulfur compounds were highly correlated with 33 fecal bacterial taxa (correlation of 0.891, p-value 0.045), whereas in 33 healthy controls, 7 volatile metabolites belonging to alcohols, aldehydes, esters, phenols, and benzamide derivatives correlated with 17 bacterial taxa (correlation of 0.871, p-value 0.0007). This study suggested that the correlation between fecal microbiota and breath VOCs was effective in identifying exhaled volatile metabolites and the functional effects of microbiome, thus helping to understand cancer-related changes and improving the survival and life expectancy in gastric cancer patients.

Prediction of drug sensitivity based on multi-omics data using deep learning and similarity network fusion approaches.

With the rapid development of multi-omics technologies and accumulation of large-scale bio-datasets, many studies have conducted a more comprehensive understanding of human diseases and drug sensitivity from multiple biomolecules, such as DNA, RNA, proteins and metabolites. Using single omics data is difficult to systematically and comprehensively analyze the complex disease pathology and drug pharmacology. The molecularly targeted therapy-based approaches face some challenges, such as insufficient target gene labeling ability, and no clear targets for non-specific chemotherapeutic drugs. Consequently, the integrated analysis of multi-omics data has become a new direction for scientists to explore the mechanism of disease and drug. However, the available drug sensitivity prediction models based on multi-omics data still have problems such as overfitting, lack of interpretability, difficulties in integrating heterogeneous data, and the prediction accuracy needs to be improved. In this paper, we proposed a novel drug sensitivity prediction (NDSP) model based on deep learning and similarity network fusion approaches, which extracts drug targets using an improved sparse principal component analysis (SPCA) method for each omics data, and construct sample similarity networks based on the sparse feature matrices. Furthermore, the fused similarity networks are put into a deep neural network for training, which greatly reduces the data dimensionality and weakens the risk of overfitting problem. We use three omics of data, RNA sequence, copy number aberration and methylation, and select 35 drugs from Genomics of Drug Sensitivity in Cancer (GDSC) for experiments, including Food and Drug Administration (FDA)-approved targeted drugs, FDA-unapproved targeted drugs and non-specific therapies. Compared with some current deep learning methods, our proposed method can extract highly interpretable biological features to achieve highly accurate sensitivity prediction of targeted and non-specific cancer drugs, which is beneficial for the development of precision oncology beyond targeted therapy.

Optimal Portfolio Using Factor Graphical Lasso

Abstract Graphical models are a powerful tool to estimate a high-dimensional inverse covariance (precision) matrix, which has been applied for a portfolio allocation problem. The assumption made by these models is a sparsity of the precision matrix. However, when stock returns are driven by common factors, such assumption does not hold. We address this limitation and develop a framework, Factor Graphical Lasso (FGL), which integrates graphical models with the factor structure in the context of portfolio allocation by decomposing a precision matrix into low-rank and sparse components. Our theoretical results and simulations show that FGL consistently estimates the portfolio weights and risk exposure and also that FGL is robust to heavy-tailed distributions which makes our method suitable for financial applications. FGL-based portfolios are shown to exhibit superior performance over several prominent competitors including equal-weighted and index portfolios in the empirical application for the S&P500 constituents.

A Smart Battery Management System for Electric Vehicles Using Deep Learning-Based Sensor Fault Detection

Battery sensor data collection and transmission are essential for battery management systems (BMS). Since inaccurate battery data brought on by sensor faults, communication issues, or even cyber-attacks can impose serious harm on BMS and adversely impact the overall dependability of BMS-based applications, such as electric vehicles, it is critical to assess the durability of battery sensor and communication data in BMS. Sensor data are necessary for a BMS to perform every operation. Effective sensor fault detection is crucial for the sustainability and security of electric vehicle battery systems. This research suggests a system for battery data, especially lithium ion batteries, that allows deep learning-based detection and the classification of faulty battery sensor and transmission information. Initially, we collected the sensor data, and preprocessing was carried out using z-score normalization. The features were extracted using sparse principal component analysis (SPCA), and enhanced marine predators algorithm (EMPA) was used for feature selection. The BMS’s safety and dependability may be enhanced by the suggested incipient bat-optimized deep residual network (IB-DRN)-based false battery data identification and classification system. Simulations using MATLAB (2021a), along with statistics, machine learning, and a deep learning toolbox, along with experimental research, were used to show and assess how well the suggested strategy performs. It is shown to be superior to traditional approaches.

A generalized inertial proximal alternating linearized minimization method for nonconvex nonsmooth problems

We propose a general inertial version of the proximal alternating linearized minimization (PALM) (denoted by NiPALM) for a class of nonconvex and nonsmooth minimization problems, whose objective function is the sum of a smooth function of the entire variables and two nonsmooth functions of each variable. NiPALM is general in the sense that it contains the popular PALM, the inertial PALM (iPALM) and Gauss-Seidel type inertial PALM (GiPALM) as special cases. Under mild assumptions, namely, the underlying functions satisfy the Kurdyka-Łojasiewicz (KL) property and some suitable conditions on the parameters, we prove that each bounded sequence generated by NiPALM globally converges to a critical point. We also apply NiPALM to nonnegative matrix factorization, sparse principal component analysis, and weighted low-rank matrix restoration problems. Comparing results with those by PALM, iPALM, and GiPALM demonstrate the robustness and effectiveness of the proposed algorithm.

A Human-Centered Comprehensive Measure of Take-Over Performance Based on Multiple Objective Metrics

For highly automated vehicles, effective take-over performance measures are essential for establishing quantitative take-over models and exploring approaches to improve take-over performance. However, there is a lack of comprehensive take-over performance measures that suitably combine multiple objective metrics based on an average evaluation from human drivers. In this study, we proposed a human-centered comprehensive measure of take-over performance (HCMTP). There are four main building blocks for the HCMTP. First, we adopted sparse principal component analysis to identify the main aspects of take-over performance based on multiple original objective take-over performance metrics. Second, we developed a scale of take-over performance assessment to obtain drivers’ original subjective self-assessments of take-over performance. Third, we established nonlinear individual mapping functions to acquire different drivers’ evaluation criteria for take-over performance. Fourth, we proposed a relabeling algorithm to obtain drivers’ average evaluation of take-over performance. To verify the effectiveness of the HCMTP, we conducted a verification experiment involving 68 participants. The results indicate that the HCMTP is effective and able to reduce the interference of individual differences, stochasticity, and data imbalance. This study contributes to identifying the main aspects of take-over performance, systematically understanding how human drivers subjectively evaluate take-over performance, and evaluating drivers’ take-over performance comprehensively.

Sparse clusterability: testing for cluster structure in high dimensions

BackgroundCluster analysis is utilized frequently in scientific theory and applications to separate data into groups. A key assumption in many clustering algorithms is that the data was generated from a population consisting of multiple distinct clusters. Clusterability testing allows users to question the inherent assumption of latent cluster structure, a theoretical requirement for meaningful results in cluster analysis.ResultsThis paper proposes methods for clusterability testing designed for high-dimensional data by utilizing sparse principal component analysis. Type I error and power of the clusterability tests are evaluated using simulated data with different types of cluster structure in high dimensions. Empirical performance of the new methods is evaluated and compared with prior methods on gene expression, microarray, and shotgun proteomics data. Our methods had reasonably low Type I error and maintained power for many datasets with a variety of structures and dimensions. Cluster structure was not detectable in other datasets with spatially close clusters.ConclusionThis is the first analysis of clusterability testing on both simulated and real-world high-dimensional data.

Feature Selection and Damage Identification for Urban Railway Track Using Bayesian Globally Sparse Principal Component Analysis

Urban railway track infrastructures often suffer from damage that affects their service performance due to a variety of factors. In this study, an unsupervised feature selection and damage identification method based on globally sparse probabilistic principal component analysis (PCA) is proposed for urban railway tracks using the monitoring data of train-induced dynamic responses. A Bayesian framework is proposed for generating principal components on a basis of vectors (original variables) with a global sparseness pattern instead of separate patterns in a traditional sparse PCA. In this framework, a variational expectation-maximization algorithm is employed to obtain the tractable calculation of the marginal likelihood function for learning all uncertain parameters of the Bayesian model. The obtained principal components are linear combinations of the very same set of important variables, making our method better interpretable than the traditional sparse PCA. We can clearly understand which original variables are most relevant for describing the data. The track damage is identified simply by discriminating the corresponding measured dynamic responses using the binary elements of the latent vector inferred from the Bayesian globally sparse PCA algorithm. The usefulness is demonstrated by successfully identifying the track bed plate crack damage through the actual train-induced dynamic responses collected from the structural health monitoring system of an urban railway track infrastructure, where the method is able to achieve F1 scores of 90% or higher for various scenarios.

Joint L2,p-norm and random walk graph constrained PCA for single-cell RNA-seq data

The development and widespread utilization of high-throughput sequencing technologies in biology has fueled the rapid growth of single-cell RNA sequencing (scRNA-seq) data over the past decade. The development of scRNA-seq technology has significantly expanded researchers’ understanding of cellular heterogeneity. Accurate cell type identification is the prerequisite for any research on heterogeneous cell populations. However, due to the high noise and high dimensionality of scRNA-seq data, improving the effectiveness of cell type identification remains a challenge. As an effective dimensionality reduction method, Principal Component Analysis (PCA) is an essential tool for visualizing high-dimensional scRNA-seq data and identifying cell subpopulations. However, traditional PCA has some defects when used in mining the nonlinear manifold structure of the data and usually suffers from over-density of principal components (PCs). Therefore, we present a novel method in this paper called joint -norm and random walk graph constrained PCA (RWPPCA). RWPPCA aims to retain the data’s local information in the process of mapping high-dimensional data to low-dimensional space, to more accurately obtain sparse principal components and to then identify cell types more precisely. Specifically, RWPPCA combines the random walk (RW) algorithm with graph regularization to more accurately determine the local geometric relationships between data points. Moreover, to mitigate the adverse effects of dense PCs, the -norm is introduced to make the PCs sparser, thus increasing their interpretability. Then, we evaluate the effectiveness of RWPPCA on simulated data and scRNA-seq data. The results show that RWPPCA performs well in cell type identification and outperforms other comparison methods.

Optimal Convex Lifted Sparse Phase Retrieval and PCA With an Atomic Matrix Norm Regularizer

We present novel analysis and algorithms for solving sparse phase retrieval and sparse principal component analysis (PCA) with convex lifted matrix formulations. The key innovation is a new mixed atomic matrix norm that, when used as regularization, promotes low-rank matrices with sparse factors. We show that convex programs with this atomic norm as a regularizer provide near-optimal sample complexity and error rate guarantees for sparse phase retrieval and sparse PCA. While we do not know how to solve the convex programs exactly with an efficient algorithm, for the phase retrieval case we carefully analyze the program and its dual and thereby derive a practical heuristic algorithm. We show empirically that this practical algorithm performs similarly to existing state-of-the-art algorithms.

Forecasting the realized volatility of Energy Stock Market: A multimodel comparison

The realized volatility forecasting of energy sector stocks facilitates the establishment of corresponding risk warning mechanisms and investor decisions. In this paper, we collected two different energy sector indices and used different methods, namely principal component analysis (PCA) and sparse principal component analysis (SPCA), to extract features, and combined LSTM and GRU to construct 12 different models. The results show that the SPCA-LSTM model we constructed has the best forecasting performance in the realized volatility forecasting of energy indices, and SPCA has better forecasting results than PCA in the feature extraction stage. The results of the robustness test indicate that our results are robust.

Speckle-noise filtering based on non-local mean sparse principal component analysis method

Speckle-noise filtering is an extensive and key process in coherent interferometric techniques to obtain important and accurate information from the recorded interferogram or fringe pattern. The speckle-noise inherent to these interferograms, recorded by digital image sensors in these optical techniques, is eliminated by an appropriate image processing method. Since the beginning and further development of these techniques, a wide variety of speckle noise filtering methods and techniques have been proposed. The present research work aims to exploit the performance of the non-local sparse principal component analysis (NLS-PCA) method for speckle noise reduction as applied to the interferometric fringe patterns obtained from digital holographic and digital speckle pattern interferometric techniques. The performance of the NLS-PCA is evaluated on numerical simulations using different types of speckle fringe patterns resulting in the method being highly effective in filtering the speckle noise and providing superior results evaluated in terms of peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), Edge preservation Index (EPI), and Equivalent Number of look (ENL), in comparison to widely known methods such as windowed Fourier transform method, Lee filter, Weiner filter. Furthermore, the proposed method maintains the finer details and preserves the fringe edges effectively. The performance of the NLS-PCA method is also demonstrated on experimental speckle fringe patterns and digital holograms.

Genomic patterns linked to gray matter alterations underlying working memory deficits in adults and adolescents with attention-deficit/hyperactivity disorder

Attention-deficit/hyperactivity disorder (ADHD) is a highly heritable neurodevelopmental disorder, with onset in childhood and a considerable likelihood to persist into adulthood. Our previous work has identified that across adults and adolescents with ADHD, gray matter volume (GMV) alteration in the frontal cortex was consistently associated with working memory underperformance, and GMV alteration in the cerebellum was associated with inattention. Recent knowledge regarding ADHD genetic risk loci makes it feasible to investigate genomic factors underlying these persistent GMV alterations, potentially illuminating the pathology of ADHD persistence. Based on this, we applied a sparsity-constrained multivariate data fusion approach, sparse parallel independent component analysis, to GMV variations in the frontal and cerebellum regions and candidate risk single nucleotide polymorphisms (SNPs) data from 341 unrelated adult participants, including 167 individuals with ADHD, 47 unaffected siblings, and 127 healthy controls. We identified one SNP component significantly associated with one GMV component in superior/middle frontal regions and replicated this association in 317 adolescents from ADHD families. The association was stronger in individuals with ADHD than in controls, and stronger in adults and older adolescents than in younger ones. The SNP component highlights 93 SNPs in long non-coding RNAs mainly in chromosome 5 and 21 protein-coding genes that are significantly enriched in human neuron cells. Eighteen identified SNPs have regulation effects on gene expression, transcript expression, isoform percentage, or methylation level in frontal regions. Identified genes highlight MEF2C, CADM2, and CADPS2, which are relevant for modulating neuronal substrates underlying high-level cognition in ADHD, and their causality effects on ADHD persistence await further investigations. Overall, through a multivariate analysis, we have revealed a genomic pattern underpinning the frontal gray matter variation related to working memory deficit in ADHD.

Sparse Component Analysis (SCA) Based on Adaptive Time-Frequency Thresholding for Underdetermined Blind Source Separation (UBSS).

Blind source separation (BSS) recovers source signals from observations without knowing the mixing process or source signals. Underdetermined blind source separation (UBSS) occurs when there are fewer mixes than source signals. Sparse component analysis (SCA) is a general UBSS solution that benefits from sparse source signals which consists of (1) mixing matrix estimation and (2) source recovery estimation. The first stage of SCA is crucial, as it will have an impact on the recovery of the source. Single-source points (SSPs) were detected and clustered during the process of mixing matrix estimation. Adaptive time-frequency thresholding (ATFT) was introduced to increase the accuracy of the mixing matrix estimations. ATFT only used significant TF coefficients to detect the SSPs. After identifying the SSPs, hierarchical clustering approximates the mixing matrix. The second stage of SCA estimated the source recovery using least squares methods. The mixing matrix and source recovery estimations were evaluated using the error rate and mean squared error (MSE) metrics. The experimental results on four bioacoustics signals using ATFT demonstrated that the proposed technique outperformed the baseline method, Zhen's method, and three state-of-the-art methods over a wide range of signal-to-noise ratio (SNR) ranges while consuming less time.

Application of dense neural networks for manifold-based modeling of flame-wall interactions

Artifical neural networks (ANNs) are universal approximators capable of learning any correlation between arbitrary input data with corresponding outputs, which can also be exploited to represent a low-dimensional chemistry manifold in the field of combustion. In this work, a procedure is developed to simulate a premixed methane-air flame undergoing side-wall quenching utilizing an ANN chemistry manifold. In the investigated case, the flame characteristics are governed by two canonical problems: the adiabatic flame propagation in the core flow and the non-adiabatic flame- wall interaction governed by enthalpy losses to the wall. Similar to the tabulation of a Quenching Flamelet-Generated Manifold (QFM), the neural network is trained on a 1D head-on quenching flame database to learn the intrinsic chemistry manifold. The control parameters (i.e. the inputs) of the ANN are identified from thermo-chemical state variables by a sparse principal component analysis (PCA) without using prior knowledge about the flame physics. These input quantities are then transported in the coupled CFD solver and used for manifold access during simulation runtime. The chemical source terms are corrected at the manifold boundaries to ensure bounded- ness of the thermo-chemical state at all times. Finally, the ANN model is assessed by comparison to simulation results of the 2D side-wall quenching (SWQ) configuration with detailed chemistry and with a flamelet-based manifold (QFM).

Finding hidden structure of sparse longitudinal data via functional Eigenfunctions

ABSTRACT In this research, we are interested in finding the hidden dependence structure of sparse longitudinal data. Finding the hidden dependence structure of sparse longitudinal data is difficult due to the starting and end times being different. We propose that finding the directional dependence structure of the eigenfunctions by sparse functional principal component analysis (FPCA) may be a good alternative solution to find the hidden dependence structure of sparse longitudinal data. To verify this idea, we apply sparse FPCA to simulated data and two real datasets, wage sparse longitudinal data and Korea composite stock price index (KOSPI) high-frequency minute tick data and then apply vine copula and copula dynamic conditional correlation with asymmetric GARCH model to the functional eigenfunctions from FPCA.

Development of a Water Quality Index Using Sparse Principal Component Analysis for the Tigris River in Iraq

Development of a Water Quality Index Using Sparse Principal Component Analysis for the Tigris River in Iraq