Dimensionality Reduction Method Research Articles

Spherical random projection

Abstract We propose a new method for dimension reduction of high-dimensional spherical data based on the nonlinear projection of sphere-valued data to a randomly chosen subsphere. The proposed method, spherical random projection, leads to a probabilistic lower-dimensional mapping of spherical data into a subsphere of the original. In this paper, we investigate some properties of spherical random projection, including expectation preservation and distance concentration, from which we derive an analogue of the Johnson–Lindenstrauss Lemma for spherical random projection. Clustering model selection is discussed as an application of spherical random projection, and numerical experiments are conducted using real and simulated data.

Interpretation of autoencoder-learned collective variables using Morse-Smale complex and sublevelset persistent homology: An application on molecular trajectories.

Dimensionality reduction often serves as the first step toward a minimalist understanding of physical systems as well as the accelerated simulations of them. In particular, neural network-based nonlinear dimensionality reduction methods, such as autoencoders, have shown promising outcomes in uncovering collective variables (CVs). However, the physical meaning of these CVs remains largely elusive. In this work, we constructed a framework that (1) determines the optimal number of CVs needed to capture the essential molecular motions using an ensemble of hierarchical autoencoders and (2) provides topology-based interpretations to the autoencoder-learned CVs with Morse-Smale complex and sublevelset persistent homology. This approach was exemplified using a series of n-alkanes and can be regarded as a general, explainable nonlinear dimensionality reduction method.

Data dimensionality reduction for an optimal switching mode classification applied to a step-down power converter

Abstract A dimensional reduction algorithm is applied to an intelligent classification model with the purpose of improving the efficiency and accuracy. The proposed classification model, used to distinguish the operating mode: Hard- and Soft-Switching, is presented and an analysis of the synchronized rectified step-down converter is done. With the aim of improving the accuracy and reducing the computational cost of the model, three different methods for dimensional reduction are applied to the input dataset of the model: self-organizing maps, principal component analysis and correlation matrix. The obtained results show how the number of variable is highly reduced and the performance of the classification model is boosted: the results manifest an improve in the accuracy and efficiency of the classification.

GFLASSO-LR: Logistic Regression with Generalized Fused LASSO for Gene Selection in High-Dimensional Cancer Classification

Advancements in genomic technologies have paved the way for significant breakthroughs in cancer diagnostics, with DNA microarray technology standing at the forefront of identifying genetic expressions associated with various cancer types. Despite its potential, the vast dimensionality of microarray data presents a formidable challenge, necessitating efficient dimension reduction and gene selection methods to accurately identify cancerous tumors. In response to this challenge, this study introduces an innovative strategy for microarray data dimension reduction and crucial gene set selection, aiming to enhance the accuracy of cancerous tumor identification. Leveraging DNA microarray technology, our method focuses on pinpointing significant genes implicated in tumor development, aiding the development of sophisticated computerized diagnostic tools. Our technique synergizes gene selection with classifier training within a logistic regression framework, utilizing a generalized Fused LASSO (GFLASSO-LR) regularizer. This regularization incorporates two penalties: one for selecting pertinent genes and another for emphasizing adjacent genes of importance to the target class, thus achieving an optimal trade-off between gene relevance and redundancy. The optimization challenge posed by our approach is tackled using a sub-gradient algorithm, designed to meet specific convergence prerequisites. We establish that our algorithm’s objective function is convex, Lipschitz continuous, and possesses a global minimum, ensuring reliability in the gene selection process. A numerical evaluation of the method’s parameters further substantiates its effectiveness. Experimental outcomes affirm the GFLASSO-LR methodology’s high efficiency in processing high-dimensional microarray data for cancer classification. It effectively identifies compact gene subsets, significantly enhancing classification performance and demonstrating its potential as a powerful tool in cancer research and diagnostics.

Dimension reduction of microbiome data linked Bifidobacterium and Prevotella to allergic rhinitis

Dimension reduction has been used to visualise the distribution of multidimensional microbiome data, but the composite variables calculated by the dimension reduction methods have not been widely used to investigate the relationship of the human gut microbiome with lifestyle and disease. In the present study, we applied several dimension reduction methods, including principal component analysis, principal coordinate analysis (PCoA), non-metric multidimensional scaling (NMDS), and non-negative matrix factorization, to a microbiome dataset from 186 subjects with symptoms of allergic rhinitis (AR) and 106 controls. All the dimension reduction methods supported that the distribution of microbial data points appeared to be continuous rather than discrete. Comparison of the composite variables calculated from the different dimension reduction methods showed that the characteristics of the composite variables differed depending on the distance matrices and the dimension reduction methods. The first composite variables calculated from PCoA and NMDS with the UniFrac distance were strongly associated with AR (FDR adjusted P = 2.4 × 10–4 for PCoA and P = 2.8 × 10–4 for NMDS), and also with the relative abundance of Bifidobacterium and Prevotella. The abundance of Bifidobacterium was also linked to intake of several nutrients, including carbohydrate, saturated fat, and alcohol via composite variables. Notably, the association between the composite variables and AR was much stronger than the association between the relative abundance of individual genera and AR. Our results highlight the usefulness of the dimension reduction methods for investigating the association of microbial composition with lifestyle and disease in clinical research.

Functional sufficient dimension reduction through information maximization with application to classification

Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss mutual information. Compared to the classical FSDR methods, such as functional sliced inverse regression and functional sliced average variance estimation, the proposed methods are appealing because they are capable of estimating multiple effective dimension reduction directions in the case of a relatively small number of categories, especially for the binary response. Moreover, the proposed methods do not require the restrictive linear conditional mean assumption and the constant covariance assumption. They avoid the inverse problem of the covariance operator which is often encountered in the functional sufficient dimension reduction. The functional principal component analysis with truncation be used as a regularization mechanism. Under some mild conditions, the statistical consistency of the proposed methods is established. Simulation studies and real data analyzes are used to evaluate the finite sample properties of our methods.

Image enhancement in palmprint recognition: a novel approach for improved biometric authentication

Several researchers have used image enhancement methods to reduce detection errors and increase verification accuracy in palmprint identification. Divergent opinions exist among experts regarding the best method of image filtering to improve image palmprint recognition. Because of the unique characteristics of palmprints and the difficulties in preventing counterfeiting, image-filtering techniques are the subject of this current research. Researchers hope to create the best biometric system possible by utilizing various techniques. These techniques include image enhancement, Gabor orientation scales, dimension reduction techniques, and appropriate matching strategies. This study investigates how different filtering approaches might be combined to improve images. The palmprint identification system uses a 3W filter, which combines wavelet, Wiener, and weighted filters. Optimizing results entails coordinating the 3W filter with Gabor orientation scales, matching processes, and dimension reduction methods. The research shows that accuracy may be considerably increased using a 3W filter with a Gabor orientation scale of [8×7], the kernel principal component analysis (KPCA) dimension reduction methodology, and a cosine matching method. Specifically, a value of 99.722% can be achieved. These results highlight the importance of selecting appropriate settings and techniques for palmprint recognition systems.

Reliability and sensitivity analyses of porous functionally graded graphene platelet reinforced composite plate

The performance of composite is seriously influenced by numerous uncertain factors, in which the uncertainty analysis plays a vital role in composite materials analysis by providing a comprehensive understanding of uncertain factors and their influence on design and performance. In this study, uncertain behaviors of porous functionally graded graphene platelets reinforced composite (FG-GPLRC) plates are first investigated for assessing the safety under bending deformation. The mechanical model for static analysis of the porous FG-GPLRC plate is formulated by Reddy’s higher-order shear deformation theory, and the bending responses are derived by Hamilton’s principle and the Navier method. Material properties and loads are deemed as random variables, and the performance function is determined by the Tsai-Wu criterion. The univariate dimension reduction method and maximum entropy method are employed to estimate the reliability of porous FG-GPLRC plates with diverse distribution patterns. Additionally, the analytical sensitivities of failure probability with respect to material parameters are derived. The analysis results illustrate that the existence of uncertain factors significantly influences the performance and reliability of composites, and the structural reliability can be improved by adding appropriate pores and graphene platelets at the edge layer of the composite plate.

Identification of control equations using low-dimensional flow representations of pitching airfoil

This study investigates the application of data-driven modeling techniques for understanding the complex dynamics of pitching airfoils at low Reynolds numbers and high angles of attack. Linear and nonlinear dimensionality reduction methods, namely principal component analysis (PCA) and isometric mapping (ISOMAP), are employed to obtain low-dimensional representations of the flow field. Subsequently, sparse identification of nonlinear dynamics (SINDy) is utilized to model the governing equations. The key findings are as follows: PCA primarily captures linear information, with the first two to three dimensions maintaining relatively low reconstruction errors. In contrast, ISOMAP excels in capturing nonlinear features, exhibiting noticeably smaller reconstruction errors. The main information is concentrated in the two-dimensional plane constructed by PCA1 and PCA2 (or ISOMAP1 and ISOMAP2). Differences in trajectory planes formed by combinations of other axes reflect flow field disparities. ISOMAP provides a nonlinear low-dimensional representation, advantageous for capturing nonlinear relationships between flow field characteristics and governing equations. The combination of ISOMAP and SINDy yields virtually no errors in identifying governing equations. Conversely, PCA and SINDy result in significantly different linear trajectories, leading to higher reconstruction errors. The identified governing equations using ISOMAP and SINDy remain consistent across different datasets, demonstrating the method's stability and robustness in accurately characterizing flow field properties under similar conditions.

Variations in the Cadherin 23 Gene Associated With Noise-Induced Hearing Loss.

The relationship between CDH23 gene variants and NIHL is unclear. This study investigates the association between cadherin 23 (CDH23) gene variants and noise-induced hearing loss (NIHL). This is a case-control study. Workers who were exposed to noise from a steel factory in North China were recruited and divided into two groups: the case group (both ears' high-frequency threshold average [BHFTA] ≥40dB) and the control group (BHFTA ≤25 dB). This study used the generalised multifactor dimensionality reduction method to analyse the association among 18 single-nucleotide polymorphisms (SNPs) in CDH23 and NIHL. Logistic regression was performed to investigate the main effects of SNPs and the interactions between cumulative noise exposure (CNE) and SNPs. Furthermore, CNE was adjusted for age, gender, smoking, drinking, physical exercise and hypertension. This study recruited 1,117 participants. The results showed that for rs11592462, participants who carried the GG genotype showed an association with NIHL greater than that of those who carried the CC genotype. Accordingly, genetic variation in the CDH23 gene could play an essential role in determining individual susceptibility to NIHL. Genetic variations in the CDH23 gene may play an important role in determining individual susceptibility to NIHL. These results provide new insight into the pathogenesis and early prevention of NIHL.

A Compound Approach for Monitoring the Variation in Wind Turbine Power Performance with SCADA Data

The performance of wind turbines directly determines the profitability of wind farms. However, the complex environmental conditions and influences of various uncertain factors make it difficult to accurately assess and monitor the actual power generation performance of wind turbines. A data-driven approach is proposed to intelligently monitor the power generation performance evolution of wind turbines based on operational data. Considering the inherent nonlinearity and structural complexity of wind turbine systems, a data-derived characteristic construction and dimensionality reduction method based on KPCA is adopted as a prerequisite. Additionally, an AdaBoost-enhanced regressor is applied to wind power prediction with adequate inputs, and day-oriented deviation indicators are further constructed for quantifying performance fluctuations. The final validation phase includes two application cases: In the first case, the results show that the proposed method is sensitive enough to capture the early characteristics of blade damage faults. In the second case, an uncertainty error within ±0.5% demonstrates that the proposed method has high-level accuracy in the quantitative assessment of the power performance and good practical effectiveness in real engineering applications.

Geometric space construction method combined of a spline-skinning based geometric variation method and PCA dimensionality reduction for ship hull form optimization

In the construction stage of ship hull geometric space, the representation and variation of hull forms pose challenges due to the complex nature of the geometry and the necessity for enhanced flexibility in space. In this study, we utilize T-spline technology for the representation of ship hulls, enabling a unified parameter domain with a reduced number of control points to effectively depict the entire hull surface. Furthermore, we introduce a method for geometric variation based on the T-spline parameter domain, which permits both local and global alterations, thus offering greater flexibility in modifying the geometry. By leveraging the T-spline representation and the geometric variation method, we developed a hybrid geometric approach for constructing the geometric space, which significantly increased the geometric flexibility in ship hull optimization. A geometric space characterized by a high degree of geometric freedom typically requires the use of numerous optimization variables and incurs considerable computational resource consumption. In this research, we apply a linear dimensionality reduction method, principal component analysis, to decrease the dimensionality of the geometric space. This method effectively preserves the original geometric design space, thereby eliminating the need for performance analyses. The numerical optimization results clearly indicate that the proposed method significantly enhances optimization efficiency.

Online Detection of Laser Welding Penetration Depth Based on Multi-Sensor Features.

The accurate online detection of laser welding penetration depth has been a critical problem to which the industry has paid the most attention. Aiming at the laser welding process of TC4 titanium alloy, a multi-sensor monitoring system that obtained the keyhole/molten pool images and laser-induced plasma spectrum was built. The influences of laser power on the keyhole/molten pool morphologies and plasma thermo-mechanical characteristics were investigated. The results showed that there were significant correlations among the variations of the keyhole-molten pool, plasma spectrum, and penetration depth. The image features and spectral features were extracted by image processing and dimension-reduction methods, respectively. Moreover, several penetration depth prediction models based on single-sensor features and multi-sensor features were established. The mean square error of the neural network model built by multi-sensor features was 0.0162, which was smaller than that of the model built by single-sensor features. The established high-precision model provided a theoretical basis for real-time feedback control of the penetration depth in the laser welding process.

ScCRT: a contrastive-based dimensionality reduction model for scRNA-seq trajectory inference.

Trajectory inference is a crucial task in single-cell RNA-sequencing downstream analysis, which can reveal the dynamic processes of biological development, including cell differentiation. Dimensionality reduction is an important step in the trajectory inference process. However, most existing trajectory methods rely on cell features derived from traditional dimensionality reduction methods, such as principal component analysis and uniform manifold approximation and projection. These methods are not specifically designed for trajectory inference and fail to fully leverage prior information from upstream analysis, limiting their performance. Here, we introduce scCRT, a novel dimensionality reduction model for trajectory inference. In order to utilize prior information to learn accurate cells representation, scCRT integrates two feature learning components: a cell-level pairwise module and a cluster-level contrastive module. The cell-level module focuses on learning accurate cell representations in a reduced-dimensionality space while maintaining the cell-cell positional relationships in the original space. The cluster-level contrastive module uses prior cell state information to aggregate similar cells, preventing excessive dispersion in the low-dimensional space. Experimental findings from 54 real and 81 synthetic datasets, totaling 135 datasets, highlighted the superior performance of scCRT compared with commonly used trajectory inference methods. Additionally, an ablation study revealed that both cell-level and cluster-level modules enhance the model's ability to learn accurate cell features, facilitating cell lineage inference. The source code of scCRT is available at https://github.com/yuchen21-web/scCRT-for-scRNA-seq.

From NMR to AI: Designing a Novel Chemical Representation to Enhance Machine Learning Predictions of Physicochemical Properties.

A novel approach to the utilization of nuclear magnetic resonance (NMR) spectroscopy data in the prediction of logD through machine learning algorithms is shown. In the analysis, a data set of 754 chemical compounds, organized into 30 clusters, was evaluated using advanced machine learning models, such as Support Vector Regression (SVR), Gradient Boosting, and AdaBoost, and comprehensive validation and testing methods were employed, including 10-fold cross-validation, bootstrapping, and leave-one-out. The study revealed the superior performance of the Bucket Integration method for dimensionality reduction, consistently yielding the lowest root mean square error (RMSE) across all data sets and normalization schemes. The SVR prediction models demonstrated remarkable computational efficiency and low cost, with the best RMSE value reaching 0.66. Our best model outperformed existing tools like JChem Suite's logD Predictor (0.91) and CplogD (1.27), and a comparison with traditional molecular representations yielded a comparable RMSE (0.50), emphasizing the robustness of our NMR data integration. The widespread availability of NMR data in pharmaceutical and industrial research presents an untapped resource for predictive modeling, highlighting the need for accessible methodologies like ours that complement the analytical toolbox beyond conventional 2D approaches. Our approach, designed to leverage the rich spatial data from NMR spectroscopy, provides additional insights and enriches drug discovery and computational chemistry with a freely accessible tool.

Enhancement of Classifier Performance with Adam and RanAdam Hyper-Parameter Tuning for Lung Cancer Detection from Microarray Data-In Pursuit of Precision.

Microarray gene expression analysis is a powerful technique used in cancer classification and research to identify and understand gene expression patterns that can differentiate between different cancer types, subtypes, and stages. However, microarray databases are highly redundant, inherently nonlinear, and noisy. Therefore, extracting meaningful information from such a huge database is a challenging one. The paper adopts the Fast Fourier Transform (FFT) and Mixture Model (MM) for dimensionality reduction and utilises the Dragonfly optimisation algorithm as the feature selection technique. The classifiers employed in this research are Nonlinear Regression, Naïve Bayes, Decision Tree, Random Forest and SVM (RBF). The classifiers' performances are analysed with and without feature selection methods. Finally, Adaptive Moment Estimation (Adam) and Random Adaptive Moment Estimation (RanAdam) hyper-parameter tuning techniques are used as improvisation techniques for classifiers. The SVM (RBF) classifier with the Fast Fourier Transform Dimensionality Reduction method and Dragonfly feature selection achieved the highest accuracy of 98.343% with RanAdam hyper-parameter tuning compared to other classifiers.

Laplacian adaptive weighted discriminant analysis for semi-supervised multi-class classification

A multi-class discriminant analysis via adaptive weighted scheme (MDAAWS) has been proposed for supervised learning, which can deal with the issue that some classes may be vanished in the subspace. However, the acquisition of labeled data is expensive and time-consuming, while the unlabeled data is easy to obtained. To achieve a wide application, we propose a novel semi-supervised multi-class dimensionality reduction method based on MDAAWS, named Laplacian adaptive weighted discriminant analysis (LapAWDA), by applying manifold regularization to labeled and unlabeled data. This method inherits the merit of MDAAWS, assigning each pairwise class with an adaptive weight to avoid the issue of class vanishing. To enhance the robustness, we introduce the ℓ2,1 norm into LapAWDA to obtain a sparse discriminant projection matrix. Moreover, an alternative and iterative scheme is designed to find the solution of LapAWDA. Extensive experiments on several synthetic and real-world datasets demonstrate the excellent performance of LapAWDA.

Use of t‐distributed stochastic neighbour embedding in vibrational spectroscopy

AbstractThe t‐distributed stochastic neighbour embedding algorithm or t‐SNE is a non‐linear dimension reduction method used to visualise multivariate data. It enables a high‐dimensional dataset, such as a set of infrared spectra, to be represented on a single, typically two‐dimensional graph, revealing its global and local structure. t‐SNE is very popular in the machine learning community and has been applied in many fields, generally with the aim of visualising large datasets. In vibrational spectroscopy, t‐SNE is gaining notoriety but principal component analysis (PCA) remains by far the reference method for exploratory analysis and dimension reduction. However, t‐SNE may represent a real aid in the analysis of vibrational spectroscopic datasets. It provides an at‐a‐glance global view of the dataset allowing to distinguish the main factors influencing the spectral signal and the hierarchy between these factors, and gives an indication on the possibility of performing predictive modelling. It can also provide great support in the choice of the pre‐processing, by comparing rapidly different general pre‐processing approaches according to their effect on the variable of interest. Here we propose to illustrate these advantages using different datasets. We also propose an approach based on a synergy between the t‐SNE and PCA methods, allowing respective advantages of each to be exploited.

Learning manifolds from non-stationary streams

Streaming adaptations of manifold learning based dimensionality reduction methods, such as Isomap, are based on the assumption that a small initial batch of observations is enough for exact learning of the manifold, while remaining streaming data instances can be cheaply mapped to this manifold. However, there are no theoretical results to show that this core assumption is valid. Moreover, such methods typically assume that the underlying data distribution is stationary and are not equipped to detect, or handle, sudden changes or gradual drifts in the distribution that may occur when the data is streaming. We present theoretical results to show that the quality of a manifold asymptotically converges as the size of data increases. We then show that a Gaussian Process Regression (GPR) model, that uses a manifold-specific kernel function and is trained on an initial batch of sufficient size, can closely approximate the state-of-art streaming Isomap algorithms, and the predictive variance obtained from the GPR prediction can be employed as an effective detector of changes in the underlying data distribution. Results on several synthetic and real data sets show that the resulting algorithm can effectively learn lower dimensional representation of high dimensional data in a streaming setting, while identifying shifts in the generative distribution. For instance, key findings on a Gas sensor array data set show that our method can detect changes in the underlying data stream, triggered due to real-world factors, such as introduction of a new gas in the system, while efficiently mapping data on a low-dimensional manifold.

Abstract 4927: Combining single-cell ATAC and RNA sequencing for supervised cell annotation

Abstract Background: Analysis of samples at the single-cell level offers insights into cellular heterogeneity and cell function. Cell type annotation is the first critical step for performing such an analysis. While current methods primarily utilize single-cell RNA sequencing (scRNA-seq) for annotation, several studies have demonstrated improved classification accuracy by combining scRNA-seq with transposase-accessible chromatin sequencing (ATAC-seq) using unsupervised methods. However, the utility of ATAC-seq features for supervised cell-type annotation has not been explored. Aims/Objectives: The objective of this study was to evaluate the relative performance of supervised cell-type classification using scRNA-seq alone vs. in multimodal combination with ATAC-seq; and how these data interplay with choice of classification and dimensionality reduction methods. Methods: A peripheral-blood mononuclear cell multi-omic dataset from a single, healthy female donor wasanalysed in this study. Ground truth annotations were generated using unsupervised annotation with the weighted nearest neighbour clustering method. Two dimensionality reduction methods (principal component analysis (PCA), single-cell Variational Inference (scVI) autoencoder) and four classification models (logistic regression, random forest, support vector machine (SVM)) were implemented and performance metrics (F1 score, precision, and recall) were compared over 10 bootstrap samples. Results: ATAC-seq features improved annotation quality and prediction confidence when using scVI embeddings, independent of the classifier. The best-performing model (SVM with scVI embeddings) showed an increase from a median macro F1 score of 0.907 (IQR = [0.902, 0.910]) using scRNA-seq alone to 0.946 (IQR = [0.940, 0.949], p <0.05) with ATAC-seq added. For PCA embeddings, improvements in macro F1 score were insignificant. All cell types (B, T, monocytes, natural killer and dendritic cells) showed significant improvements when using ATAC-seq with scVI embeddings. CD4 T effector memory cells showed the largest gain in F1 score (0.112, p <0.01), whilst type-2 conventional dendritic cells showed the smallest improvement (0.006, p <0.05). Prediction confidence was improved in B cells, monocytes, natural killer cells, CD4 and CD8 naïve cells, CD4 T central memory cells and CD8 T effector memory cells. Improvements in F1 scores were lost when only classifying major cell types rather than subtypes. Conclusions: Employing ATAC-seq embeddings with scVI autoencoder enhances supervised annotation quality over scRNA-only methods. Further studies should explore the use of ATAC to improve the annotation of highly heterogeneous tissues such as tumours. Citation Format: Jaidip Gill, Abhijit Dasgupta, Brychan Manry, Natasha Markuzon. Combining single-cell ATAC and RNA sequencing for supervised cell annotation [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 4927.