High-dimensional Data Analysis Research Articles

A State-Migration Particle Swarm Optimizer for Adaptive Latent Factor Analysis of High-Dimensional and Incomplete Data

A State-Migration Particle Swarm Optimizer for Adaptive Latent Factor Analysis of High-Dimensional and Incomplete Data

Practical Screening Method for Cancer Gene Diagnosis -How to Choose Cancer and Normal Patients by four Principles

We developed a new theory of discriminant analysis (Theory1). Physicians can use it for practical medical diagnoses. Only Revised IP Optimal-LDF (RIP) obtains the minimum number of misclassification (MNM). RIP can discriminate linearly separable data (LSD) theoretically. It discriminated against 169 microarrays with two classes and found that 169 MNMs are zero and LSD. It can split high-dimensional arrays into many small LSD with less than n (patient’s number) genes that are the candidates of multivariate oncogenes. We completed a new theory of high-dimensional gene data analysis (Theory2). A 100-fold Cross-Validation (Method1) can rank all candidates for the importance of diagnosis. Thus, if physicians firstly use Theory2 as the screening method, they can start their medical studies with the correct small sizes of candidates. This paper analyzes four arrays in detail and proposes correctly choosing cancer and normal patients using four principles.

Application of mass cytometry in multiparametric characterization of precancerous cervical lesions.

Cervical cancer (CC) is the fourth most common malignant tumor in women worldwide. Detecting different biomarkers together on single cells by novel method mass cytometry could contribute to more precise screening. Liquid-based cytology (LBC) cervical samples were collected (N = 53) from women categorized as normal and precancerous lesions. Human papillomavirus was genotyped by polymerase chain reaction, while simultaneous examination of the expression of 29 proteins was done by mass cytometry (CyTOF). Differences in cluster abundances were assessed with Spearman's rank correlation as well as high dimensional data analysis (t-SNE, FlowSOM). Cytokeratin (ITGA6, Ck5, Ck10/13, Ck14, Ck7) expression patterns allowed determining the presence of different cells in the cervical epithelium. FlowSOM analysis enabled to phenotype cervical cells in five different metaclusters and find new markers that could be important in CC screening. The markers Ck18, Ck18, and CD63 (Metacluster 3) showed significantly increasing associated with severity of the precancerous lesions (Spearman rank correlation rho 0.304, p = 0.0271), while CD71, KLF4, LRIG1, E-cadherin, Nanog and p53 (Metacluster 1) decreased with severity of the precancerous lesions (Spearman rank correlation rho -0.401, p = 0.0029). Other metaclusters did not show significant correlation, but metacluster 2 (Ck17, MCM, MMP7, CD29, E-cadherin, Nanog, p53) showed higher abundance in low- and high-grade intraepithelial lesion cases. CyTOF appears feasible and should be considered when examining novel biomarkers on cervical LBC samples. This study enabled us to characterize different cells in the cervical epithelium and find markers and populations that could distinguish precancerous lesions.

Conditional sufficient variable selection with prior information

AbstractDimension reduction and variable selection play crucial roles in high-dimensional data analysis. Numerous existing methods have been demonstrated to attain either or both of these goals. The Minimum Average Variance Estimation (MAVE) method and its variants are effective approaches to estimate directions on the Central Mean Subspace (CMS). The Sparse Minimum Average Variance Estimation (SMAVE) combines the concepts of sufficient dimension reduction and variable selection and has been demonstrated to exhaustively estimate CMS while simultaneously selecting informative variables using LASSO without assuming any specific model or distribution on the predictor variables. In many applications, however, researchers typically possess prior knowledge for a set of predictors that is associated with response. In the presence of a known set of variables, the conditional contribution of additional predictors provides a natural evaluation of the relative importance. Based on this concept, we propose the Conditional Sparse Minimum Average Variance Estimation (CSMAVE) method. By utilizing prior information and creating a meaningful conditioning set for SMAVE, we intend to select variables that will result in a more parsimonious model and a more accurate interpretation than SMAVE. We evaluate our strategy by analyzing simulation examples and comparing them to the SMAVE method. And a real-world dataset validates the applicability and efficiency of our method.

The Effect of Regularized Regression and Tree-Based Missing Data Imputation Methods on Classification Performance in High Dimensional Data

Missing data is an important problem in the analysis and classification of high dimensional data. The aim of this study is to compare the effects of four different missing data imputation methods on classification performance in high dimensional data. In this study, missing data imputation methods were evaluated using data sets, whose independent variables between mixed correlated with each other, for binary dependent variable, p=500 independent variables, n=150 units and 1000 times running simulation. Missing data structures were created according to different missing rates. Different datasets were obtained by imputing the missing values using different methods. Regularized regression methods such as lasso and elastic net regression were used for imputation, as well as tree-based methods such as support vector machine and classification and regression trees. At the end of simulation, the classification scores of the methods were obtained by gradient boosting machines and the missing data prediction performances were evaluated according to the distance of these scores from the reference. Our simulation demonstrates that regularized regression methods outperform tree-based methods in classifying high dimensional datasets. Additionally, it was found that the increase in the amount of missing values reduced the classification performance of the methods in high dimensional data.

FPR1 signaling aberrantly regulates S100A8/A9 production by CD14+FCN1hi macrophages and aggravates pulmonary pathology in severe COVID-19

Excessive alarmins S100A8/A9 escalate the inflammation and even exacerbate immune-driven thrombosis and multi-organ damage. However, the regulatory mechanisms of S100A8/A9 expression in infectious diseases remain unclear. In this study, high-dimensional transcriptomic data analyses revealed a high proportion of CD14+FCN1hi macrophages within the pulmonary niche post-severe SARS-CoV-2 infection. By constructing the S100-coexpression gene list and supervised module scoring, we found that CD14+FCN1hi macrophages presented the highest scores of alarmin S100, and possibly served as the trigger and amplifier of inflammation in severe COVID-19. These CD14+FCN1hi cells lacked the positive regulatory activity of transcription factor PPARγ, and lost their differentiation ability towards mature macrophages. Ex vivo experiments further validated that the epithelial cells with high ORF-3a expression promoted the expression and secretion of S100A8/A9 through ANXA1/SAA1-FPR1 signaling. S100A8/A9 heterodimers, as well as the co-localization of S100A8/A9 with microtubules, were both diminished by the FPR1 inhibitor. Phospho-kinase protein array indicated that STAT3 promoted transcription, and PLC-γ and ERK1/2 pathways were involved in the hetero-dimerization and unconventional secretion of S100A8/A9. Our study highlights the pivotal role of FPR1 signaling in the excessive production of S100A8/A9 and provides a promising target for the prevention and control of severe COVID-19 and post-acute COVID-19 sequelae.

Information entropy-assisted intuitionistic fuzzy rough feature subset selection

Fuzzy-rough set (FRS) has been effectively implemented as a powerful pre-processing tool to cope with the issues such as vagueness, imprecision, noise and uncertainty in high-dimensional data analysis. However, FRS fails to handle the uncertainty due to identification, which is very much common in heterogeneous data. Moreover, it is always challenging to handle different issues such as vagueness, uncertainty, and noise during elimination of irrelevant and redundant features. This paper investigates an intuitionistic fuzzy rough set (IFRS)-aided feature selection method by using information entropy notion to tackle these issues simultaneously. We establish an intuitionistic fuzzy (IF) similarity relation. Then IFRS model is discussed based on this relation. Next, we present a novel IF granular structure. Based on the granular structure, we present lambda-conditional entropy for IF framework. Further, relevant mathematical theorems are proved to justify the theoretical aspect of the models. Moreover, a positive region preserved attribute selection method is proposed. A comprehensive experimental study is discussed to demonstrate the effectiveness and practical validation of the proposed method. Finally, a methodology is developed based on proposed models, which increases accuracy for the minority RNA silencing suppressors against majority class non-suppressors as evident from better sensitivity and G-means metrics.

Support vector machine based on the quadratic unconstrained binary optimization model

Abstract Support vector machine (SVM) is a powerful supervised machine learning model that is often used in binary classification algorithms. As Moore’s Law approaches its theoretical limits and the demand for machine learning to handle large-scale, high-dimensional data analysis intensifies, the necessity of adopting non-traditional computational approaches becomes evident. Quantum computing, in particular, emerges as a vital solution for the effective training of SVM models, providing capabilities beyond those of classical computing systems. To solve the above problems, a QUBO (quadratic unconstrained binary optimization) model is proposed to transform the SVM machine learning model into a quadratic unconstrained binary optimization problem so that they can be effectively trained on the D-Wave platform using adiabatic quantum computer. The results show that the QUBO model can transform the SVM model into a simple quadratic programming problem, which makes it suitable for adiabatic quantum computer processing. When processing large-scale and high-dimensional data, this transformation shows a natural advantage and significantly improves computational efficiency. The application potential of this transformation technology is huge in the medical field.

Thinking points for effective batch correction on biomedical data.

Batch effects introduce significant variability into high-dimensional data, complicating accurate analysis and leading to potentially misleading conclusions if not adequately addressed. Despite technological and algorithmic advancements in biomedical research, effectively managing batch effects remains a complex challenge requiring comprehensive considerations. This paper underscores the necessity of a flexible and holistic approach for selecting batch effect correction algorithms (BECAs), advocating for proper BECA evaluations and consideration of artificial intelligence-based strategies. We also discuss key challenges in batch effect correction, including the importance of uncovering hidden batch factors and understanding the impact of design imbalance, missing values, and aggressive correction. Our aim is to provide researchers with a robust framework for effective batch effects management and enhancing the reliability of high-dimensional data analyses.

The spike-and-slab quantile LASSO for robust variable selection in cancer genomics studies.

Data irregularity in cancer genomics studies has been widely observed in the form of outliers and heavy-tailed distributions in the complex traits. In the past decade, robust variable selection methods have emerged as powerful alternatives to the nonrobust ones to identify important genes associated with heterogeneous disease traits and build superior predictive models. In this study, to keep the remarkable features of the quantile LASSO and fully Bayesian regularized quantile regression while overcoming their disadvantage in the analysis of high-dimensional genomics data, we propose the spike-and-slab quantile LASSO through a fully Bayesian spike-and-slab formulation under the robust likelihood by adopting the asymmetric Laplace distribution (ALD). The proposed robust method has inherited the prominent properties of selective shrinkage and self-adaptivity to the sparsity pattern from the spike-and-slab LASSO (Roc̆ková and George, J Am Stat Associat, 2018, 113(521): 431-444). Furthermore, the spike-and-slab quantile LASSO has a computational advantage to locate the posterior modes via soft-thresholding rule guided Expectation-Maximization (EM) steps in the coordinate descent framework, a phenomenon rarely observed for robust regularization with nondifferentiable loss functions. We have conducted comprehensive simulation studies with a variety of heavy-tailed errors in both homogeneous and heterogeneous model settings to demonstrate the superiority of the spike-and-slab quantile LASSO over its competing methods. The advantage of the proposed method has been further demonstrated in case studies of the lung adenocarcinomas (LUAD) and skin cutaneous melanoma (SKCM) data from The Cancer Genome Atlas (TCGA).

Feature selection by replicate reproducibility and non-redundancy.

A fundamental step in many analyses of high-dimensional data is dimension reduction. Two basic approaches are introduction of new synthetic coordinates and selection of extant features. Advantages of the latter include interpretability, simplicity, transferability, and modularity. A common criterion for unsupervized feature selection is variance or dynamic range. However, in practice, it can occur that high-variance features are noisy, that important features have low variance, or that variances are simply not comparable across features because they are measured in unrelated numeric scales or physical units. Moreover, users may want to include measures of signal-to-noise ratio and non-redundancy into feature selection. Here, we introduce the RNR algorithm, which selects features based on (i) the reproducibility of their signal across replicates and (ii) their non-redundancy, measured by linear dependence. It takes as input a typically large set of features measured on a collection of objects with two or more replicates per object. It returns an ordered list of features, i1,i2,…,ik, where feature i1 is the one with the highest reproducibility across replicates, i2 that with the highest reproducibility across replicates after projecting out the dimension spanned by i1, and so on. Applications to microscopy-based imaging of cells and proteomics highlight benefits of the approach. The RNR method is available via Bioconductor (Huber W, Carey VJ, Gentleman R et al. (Orchestrating high-throughput genomic analysis with bioconductor. Nat Methods 2015;12:115-21.) in the R package FeatSeekR. Its source code is also available at https://github.com/tcapraz/FeatSeekR under the GPL-3 open source license.

Higher-order correction of persistent batch effects in correlation networks.

Systems biology analyses often use correlations in gene expression profiles to infer co-expression networks that are then used as input for gene regulatory network inference or to identify functional modules of co-expressed or putatively co-regulated genes. While systematic biases, including batch effects, are known to induce spurious associations and confound differential gene expression analyses (DE), the impact of batch effects on gene co-expression has not been fully explored. Methods have been developed to adjust expression values, ensuring conditional independence of mean and variance from batch or other covariates for each gene, resulting in improved fidelity of DE analysis. However, such adjustments do not address the potential for spurious differential co-expression (DC) between groups. Consequently, uncorrected, artifactual DC can skew the correlation structure, leading to the identification of false, non-biological associations, even when the input data are corrected using standard batch correction. In this work, we demonstrate the persistence of confounders in covariance after standard batch correction using synthetic and real-world gene expression data examples. We then introduce Co-expression Batch Reduction Adjustment (COBRA), a method for computing a batch-corrected gene co-expression matrix based on estimating a conditional covariance matrix. COBRA estimates a reduced set of parameters expressing the co-expression matrix as a function of the sample covariates, allowing control for continuous and categorical covariates. COBRA is computationally efficient, leveraging the inherently modular structure of genomic data to estimate accurate gene regulatory associations and facilitate functional analysis for high-dimensional genomic data. COBRA is available under the GLP3 open source license in R and Python in netZoo (https://netzoo.github.io).

A unique human cord blood CD8+CD45RA+CD27+CD161+ T-cell subset identified by flow cytometric data analysis using Seurat.

Advances in single-cell level analytical techniques, especially cytometric approaches, have led to profound innovation in biomedical research, particularly in the field of clinical immunology. This has resulted in an expansion of high-dimensional data, posing great challenges for comprehensive and unbiased analysis. Conventional manual analysis is thus becoming untenable to handle these challenges. Furthermore, most newly developed computational methods lack flexibility and interoperability, hampering their accessibility and usability. Here, we adapted Seurat, an R package originally developed for single-cell RNA sequencing (scRNA-seq) analysis, for high-dimensional flow cytometric data analysis. Based on a 20-marker antibody panel and analyses of T-cell profiles in both adult blood and cord blood (CB), we showcased the robust capacity of Seurat in flow cytometric data analysis, which was further validated by Spectre, another high-dimensional cytometric data analysis package, and conventional manual analysis. Importantly, we identified a unique CD8+ T-cell population defined as CD8+CD45RA+CD27+CD161+ T cell that was predominantly present in CB. We characterised its IFN-γ-producing and potential cytotoxic properties using flow cytometry experiments and scRNA-seq analysis from a published dataset. Collectively, we identified a unique human CB CD8+CD45RA+CD27+CD161+ T-cell subset and demonstrated that Seurat, a widely used package for scRNA-seq analysis, possesses great potential to be repurposed for cytometric data analysis. This facilitates an unbiased and thorough interpretation of complicated high-dimensional data using a single analytical pipeline and opens a novel avenue for data-driven investigation in clinical immunology.

Newton-Raphson Meets Sparsity: Sparse Learning Via a Novel Penalty and a Fast Solver.

In machine learning and statistics, the penalized regression methods are the main tools for variable selection (or feature selection) in high-dimensional sparse data analysis. Due to the nonsmoothness of the associated thresholding operators of commonly used penalties such as the least absolute shrinkage and selection operator (LASSO), the smoothly clipped absolute deviation (SCAD), and the minimax concave penalty (MCP), the classical Newton-Raphson algorithm cannot be used. In this article, we propose a cubic Hermite interpolation penalty (CHIP) with a smoothing thresholding operator. Theoretically, we establish the nonasymptotic estimation error bounds for the global minimizer of the CHIP penalized high-dimensional linear regression. Moreover, we show that the estimated support coincides with the target support with a high probability. We derive the Karush-Kuhn-Tucker (KKT) condition for the CHIP penalized estimator and then develop a support detection-based Newton-Raphson (SDNR) algorithm to solve it. Simulation studies demonstrate that the proposed method performs well in a wide range of finite sample situations. We also illustrate the application of our method with a real data example.

Similarity Metrics for Subcellular Analysis of FRET Microscopy Videos.

Understanding the heterogeneity of molecular environments within cells is an outstanding challenge of great fundamental and technological interest. Cells are organized into specialized compartments, each with distinct functions. These compartments exhibit dynamic heterogeneity under high-resolution microscopy, which reflects fluctuations in molecular populations, concentrations, and spatial distributions. To enhance our comprehension of the spatial relationships among molecules within cells, it is crucial to analyze images of high-resolution microscopy by clustering individual pixels according to their visible spatial properties and their temporal evolution. Here, we evaluate the effectiveness of similarity metrics based on their ability to facilitate fast and accurate data analysis in time and space. We discuss the capability of these metrics to differentiate subcellular localization, kinetics, and structures of protein-RNA interactions in Forster resonance energy transfer (FRET) microscopy videos, illustrated by a practical example from recent literature. Our results suggest that using the correlation similarity metric to cluster pixels of high-resolution microscopy data should improve the analysis of high-dimensional microscopy data in a wide range of applications.

A review on advancements in feature selection and feature extraction for high-dimensional NGS data analysis.

Recent advancements in biomedical technologies and the proliferation of high-dimensional Next Generation Sequencing (NGS) datasets have led to significant growth in the bulk and density of data. The NGS high-dimensional data, characterized by a large number of genomics, transcriptomics, proteomics, and metagenomics features relative to the number of biological samples, presents significant challenges for reducing feature dimensionality. The high dimensionality of NGS data poses significant challenges for data analysis, including increased computational burden, potential overfitting, and difficulty in interpreting results. Feature selection and feature extraction are two pivotal techniques employed to address these challenges by reducing the dimensionality of the data, thereby enhancing model performance, interpretability, and computational efficiency. Feature selection and feature extraction can be categorized into statistical and machine learning methods. The present study conducts a comprehensive and comparative review of various statistical, machine learning, and deep learning-based feature selection and extraction techniques specifically tailored for NGS and microarray data interpretation of humankind. A thorough literature search was performed to gather information on these techniques, focusing on array-based and NGS data analysis. Various techniques, including deep learning architectures, machine learning algorithms, and statistical methods, have been explored for microarray, bulk RNA-Seq, and single-cell, single-cell RNA-Seq (scRNA-Seq) technology-based datasets surveyed here. The study provides an overview of these techniques, highlighting their applications, advantages, and limitations in the context of high-dimensional NGS data. This review provides better insights for readers to apply feature selection and feature extraction techniques to enhance the performance of predictive models, uncover underlying biological patterns, and gain deeper insights into massive and complex NGS and microarray data.

Exploring the response and prediction of phytoplankton to environmental factors in eutrophic marine areas using interpretable machine learning methods

Coastal marine areas are frequently affected by human activities and face ecological and environmental threats, such as algal blooms and climate change. The community structure of phytoplankton—primary producers in marine ecosystems—is highly sensitive to environmental factors, such as temperature, salinity, and nutrients. However, traditional methods for exploring the relationship between phytoplankton communities and environmental factors in eutrophic marine areas are limited by various factors. Therefore, this study employed interpretable machine learning models, integrating high-dimensional data analysis and complex system modeling, to quantitatively and thoroughly analyze the dynamic relationship between phytoplankton communities and environmental variables in high-frequency samples collected over 53 weeks from eutrophic marine areas. The cell abundance of phytoplankton exhibited a distinct “two-peak pattern” variation. Interpretable machine learning model analysis revealed the dynamic contributions of different environmental factors during changes in the phytoplankton community structure. The results showed that temperature was a key environmental factor that affected phytoplankton growth during peak periods. In addition, the contribution of salinity increased during the second peak in phytoplankton abundance, highlighting its central role in the ecological dynamics of this phase. During green tide outbreaks, particularly in Area 01, the contributions of factors such as temperature and salinity increased, whereas those of phosphates and silicates decreased, indicating that green tide outbreaks substantially altered the nutritional dynamics of the ecosystem. Furthermore, different phytoplankton species, such as Skeletonema costatum, Thalassiosira spp., and Nitzschia spp., exhibit varying responses to environmental factors. Hence, the predictions made using random forest and generalized additive models for phytoplankton cell abundance in two marine areas revealed complex nonlinear relationships between environmental factors, such as temperature, salinity, and phytoplankton abundance.

Statistical inference on kurtosis of independent component model

Independent component model (ICM) is a widely-used population distribution in high-dimensional data analysis and random matrix theory. In this work, we study the kurtosis of the ICM, which is an important parameter in asymptotic distributions of many commonly used statistics and is also an important criterion for measuring the heavy-tailed nature of the data. Based on U-statistics, we develop an estimation method. Theoretically, we show that the proposed estimator is consistent under regular conditions, especially we relax the restriction that the data dimension and the sample size are of the same order. Furthermore, we derive the asymptotic normality of the estimator, which allows us to construct confidence intervals and hypothesis testing statistics. Computationally, we provide a fast and efficient algorithm by leveraging the matrix structure, where the computational complexity is essentially equivalent to computing the sample covariance matrix and the Gram matrix. Finally, the effectiveness of the proposed method is demonstrated through simulated data and real-world data.

Multimodal functional deep learning for multiomics data.

With rapidly evolving high-throughput technologies and consistently decreasing costs, collecting multimodal omics data in large-scale studies has become feasible. Although studying multiomics provides a new comprehensive approach in understanding the complex biological mechanisms of human diseases, the high dimensionality of omics data and the complexity of the interactions among various omics levels in contributing to disease phenotypes present tremendous analytical challenges. There is a great need of novel analytical methods to address these challenges and to facilitate multiomics analyses. In this paper, we propose a multimodal functional deep learning (MFDL) method for the analysis of high-dimensional multiomics data. The MFDL method models the complex relationships between multiomics variants and disease phenotypes through the hierarchical structure of deep neural networks and handles high-dimensional omics data using the functional data analysis technique. Furthermore, MFDL leverages the structure of the multimodal model to capture interactions between different types of omics data. Through simulation studies and real-data applications, we demonstrate the advantages of MFDL in terms of prediction accuracy and its robustness to the high dimensionality and noise within the data.

Censored Least Squares for Imputing Missing Values in PARAFAC Tensor Factorization.

Tensor factorization is a dimensionality reduction method applied to multidimensional arrays. These methods are useful for identifying patterns within a variety of biomedical datasets due to their ability to preserve the organizational structure of experiments and therefore aid in generating meaningful insights. However, missing data in the datasets being analyzed can impose challenges. Tensor factorization can be performed with some level of missing data and reconstruct a complete tensor. However, while tensor methods may impute these missing values, the choice of fitting algorithm may influence the fidelity of these imputations. Previous approaches, based on alternating least squares with prefilled values or direct optimization, suffer from introduced bias or slow computational performance. In this study, we propose that censored least squares can better handle missing values with data structured in tensor form. We ran censored least squares on four different biological datasets and compared its performance against alternating least squares with prefilled values and direct optimization. We used the error of imputation and the ability to infer masked values to benchmark their missing data performance. Censored least squares appeared best suited for the analysis of high-dimensional biological data by accuracy and convergence metrics across several studies.