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We propose an estimator for the population mean θ0=피(Y) under the semi‐supervised learning setting with the Missing at Random (MAR) assumption. This setting assumes that the probability of observing Y$$ Y $$, denoted by πM∗$$ {\pi}_M^{\ast } $$, depends on the total sample size M$$ M $$ and satisfies πM∗=o(1)$$ {\pi}_M^{\ast }=o(1) $$. To efficiently estimate θ0$$ {\theta}_0 $$, we introduce an adaptive estimator based on inverse probability weighting and cross‐fitting. Theoretical analysis reveals that our proposed estimator is consistent and efficient, with a convergence rate of MπM∗$$ \sqrt{M{\pi}_M^{\ast }} $$, slower than the typical M$$ \sqrt{M} $$ rate, due to the diminishing proportion of labelled data as the sample size M$$ M $$ increases in the semi‐supervised setting. We also prove the consistency of inverse probability weighting (IPW)–Nadaraya–Watson density function estimators. Extensive simulations and an application to the Los Angeles homeless data validate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

The estimation of the central space is at the core of the sufficient dimension reduction (SDR) literature. However, it is well known that the finite-sample estimation suffers from collinearity among predictors. Cook, Helland, and Su proposed the predictor envelope method under linear models that can alleviate the problem by targeting a bigger space—which not only envelopes the central information, but also partitions the predictors by finding an uncorrelated set of material and immaterial predictors. One limitation of the predictor envelope is that it has strong distributional and modeling assumptions and therefore, it cannot be readily used in semiparametric settings where SDR usually nests. In this article, we generalize the envelope model by defining the enveloped central space and propose a semiparametric method to estimate it. We derive the entire class of regular and asymptotically linear (RAL) estimators as well as the locally and globally semiparametrically efficient estimators for the enveloped central space. Based on the connection between predictor envelope and partial least square (PLS), our methods can also be used to calculate the PLS space beyond linearity. In the simulations, our methods are shown to be both robust and accurate for estimating the enveloped central space under different settings. Moreover, the downstream analysis using state-of-the-art methods such as machine learning (ML) methods has the potential to achieve much better predictions. We further illustrate our methods in a heart failure study. for this article are available online. [ABSTRACT FROM AUTHOR]

The growing complexity of biological data has spurred the development of innovative computational techniques to extract meaningful information and uncover hidden patterns within vast datasets. Biological networks, such as gene regulatory networks and protein-protein interaction networks, hold critical insights into biological features' connections and functions. Integrating and analyzing high-dimensional data, particularly in gene expression studies, stands prominent among the challenges in deciphering these networks. Clustering methods play a crucial role in addressing these challenges, with spectral clustering emerging as a potent unsupervised technique considering intrinsic geometric structures. However, spectral clustering's user-defined cluster number can lead to inconsistent and sometimes orthogonal clustering regimes. We propose the Multi-layer Bundling (MLB) method to address this limitation, combining multiple prominent clustering regimes to offer a comprehensive data view. We call the outcome clusters "bundles". This approach refines clustering outcomes, unravels hierarchical organization, and identifies bridge elements mediating communication between network components. By layering clustering results, MLB provides a global-to-local view of biological feature clusters enabling insights into intricate biological systems. Furthermore, the method enhances bundle network predictions by integrating the bundle co-cluster matrix with the affinity matrix. The versatility of MLB extends beyond biological networks, making it applicable to various domains where understanding complex relationships and patterns is needed. [ABSTRACT FROM AUTHOR]

Tissue dissociation results in single-cell datasets with limited spatiotemporal context. The predictive power of single-cell RNA sequencing (scRNA-seq) can be improved by complementing with methods that 'anchor' cells in space and time. We assess how the information content produced by various spatial technologies can be used to integrate spatial information into scRNA-seq datasets. We reflect on the initial promises of scRNA-seq and whether complementary spatial data can bring us closer to truly observing plant biology at cellular resolution. Plant scientists are rapidly integrating single-cell RNA sequencing (scRNA-seq) into their workflows. Maximizing the potential of scRNA-seq requires a proper understanding of the spatiotemporal context of cells. However, positional information is inherently lost during scRNA-seq, limiting its potential to characterize complex biological systems. In this review we highlight how current single-cell analysis pipelines cannot completely recover spatial information, which confounds biological interpretation. Various strategies exist to identify the location of RNA, from classical RNA in situ hybridization to spatial transcriptomics. Herein we discuss the possibility of utilizing this spatial information to supervise single-cell analyses. An integrative approach will maximize the potential of each technology, and lead to insights which go beyond the capability of each individual technology. [ABSTRACT FROM AUTHOR]

Functional time series model has been the subject of the most research in recent years, and since functional data is infinite dimensional, dimension reduction is essential for functional time series. However, the majority of the existing dimension reduction methods such as the functional principal component and fixed basis expansion are unsupervised and typically result in information loss. Then, the functional time series model has an urgent need for a supervised dimension reduction method. The functional sufficient dimension reduction method is a supervised technique that adequately exploits the regression structure information, resulting in minimal information loss. Functional sliced inverse regression (FSIR) is the most popular functional sufficient dimension reduction method, but it cannot be applied directly to functional time series model. In this paper, we examine a functional time series model in which the response is a scalar time series and the explanatory variable is functional time series. We propose a novel supervised dimension reduction technique for the regression model by combining the FSIR and blind source separation methods. Furthermore, we propose innovative strategies for selecting the dimensionality of dimension reduction space and the lags of the functional time series. Numerical studies, including simulation studies and a real data analysis are show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

As the concentration of fine dust has recently increased, numerous related studies are being conducted to address this issue. Aerosol optical depth (AOD) is a vital atmospheric parameter for measuring the optical properties of aerosols in the atmosphere, providing crucial information related to fine dust. In this paper, we apply three dimension reduction methods, nonnegative matrix factorization (NMF), empirical orthogonal functions (EOF) analysis and independent component analysis (ICA), to AOD data to analyze the patterns of fine dust in the East Asia region. Through a comparison of three dimension reduction methods, we observe that some patterns are observed in all three method, while some information are only extracted in a specific method. Additionally, we forecast AOD levels based on three methods, and compare the predictive performance of the three methodologies. [ABSTRACT FROM AUTHOR]

Assessment of similarity in species composition or abundance across sampled locations is a common goal in multi‐species monitoring programs. Existing ordination techniques provide a framework for clustering sample locations based on species composition by projecting high‐dimensional community data into a low‐dimensional, latent ecological gradient representing species composition. However, these techniques require specification of the number of distinct ecological communities present in the latent space, which can be difficult to determine in advance.We develop an ordination model capable of simultaneous clustering and ordination that allows for estimation of the number of clusters present in the latent ecological gradient. This model draws latent coordinates for each sample location from a Dirichlet process mixture model, affording researchers with probabilistic statements about the number of clusters present in the latent ecological gradient.The model is compared to existing methods for simultaneous clustering and ordination via simulation and applied to two empirical datasets; JAGS code to fit the proposed model is provided in an appendix. The first dataset concerns presence‐absence records of fish in the Doubs river in eastern France and the second dataset describes presence‐absence records of plant species in Craters of the Moon National Monument and Preserve (CRMO) in Idaho, USA. Results from both analyses align with existing ecological gradients at each location.Development of the Dirichlet process ordination model provides wildlife managers with data‐driven inferences about the number of distinct communities present across monitored locations, allowing for more cost‐effective monitoring and reliable decision‐making for conservation management. [ABSTRACT FROM AUTHOR]

An increasingly common viewpoint is that protein dynamics datasets reside in a nonlinear subspace of low conformational energy. Ideal data analysis tools should therefore account for such nonlinear geometry. The Riemannian geometry setting can be suitable for a variety of reasons. First, it comes with a rich mathematical structure to account for a wide range of geometries that can be modeled after an energy landscape. Second, many standard data analysis tools developed for data in Euclidean space can be generalized to Riemannian manifolds. In the context of protein dynamics, a conceptual challenge comes from the lack of guidelines for constructing a smooth Riemannian structure based on an energy landscape. In addition, computational feasibility in computing geodesics and related mappings poses a major challenge. This work considers these challenges. The first part of the paper develops a local approximation technique for computing geodesics and related mappings on Riemannian manifolds in a computationally feasible manner. The second part constructs a smooth manifold and a Riemannian structure that is based on an energy landscape for protein conformations. The resulting Riemannian geometry is tested on several data analysis tasks relevant for protein dynamics data. In particular, the geodesics with given start- and end-points approximately recover corresponding molecular dynamics trajectories for proteins that undergo relatively ordered transitions with medium-sized deformations. The Riemannian protein geometry also gives physically realistic summary statistics and retrieves the underlying dimension even for large-sized deformations within seconds on a laptop. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the homogenization and dimension reduction for a nonlinear elasticity problem of a textile structure. The structure is represented as a squared piece of cloth and modeled as a woven canvas made of long and thin fibers, crossing each other in a periodic pattern. The squared domain is partially clamped on the left and bottom. The fibers are assumed to be glued, a condition that allows to extend the woven structure to a non-perforate plate. The nonlinear elasticity problem is stated via minimization over the energy functional. The homogenization is made via the periodic unfolding method, with an additional dimension reduction. Since the existence of a minimum of the limit energy functional is not ensured, sufficient conditions for the existence are given by assuming that the material is homogeneous and isotropic. [ABSTRACT FROM AUTHOR]

In this paper, we study the Γ -limit of a properly rescaled family of energies, defined on a narrow strip, as the width of the strip tends to zero. The limit energy is one-dimensional and is able to capture (and penalize) concentrations of the midline curvature. At the best of our knowledge, it is the first paper in the Γ -convergence field for dimension reduction that predicts elastic hinges. In particular, starting from a purely elastic shell model with "smooth" solutions, we obtain a beam model where the derivatives of the displacement and/or of the rotation fields may have jump discontinuities. Mechanically speaking, elastic hinges can occur in the beam. [ABSTRACT FROM AUTHOR]

We consider situations in which the clustering of some multivariate data is desired, which establishes an ordering of the clusters with respect to an underlying latent variable. As our motivating example for a situation where such a technique is desirable, we consider scatterplots of traffic flow and speed, where a pattern of consecutive clusters can be thought to be linked by a latent variable, which is interpretable as traffic density. We focus on latent structures of linear or quadratic shapes, and present an estimation methodology based on expectation–maximization, which estimates both the latent subspace and the clusters along it. The directed clustering approach is summarized in two algorithms and applied to the traffic example outlined. Connections to related methodology, including principal curves, are briefly drawn. [ABSTRACT FROM AUTHOR]

Hypertensive disorders in pregnancy, which include preeclampsia, eclampsia, and chronic hypertension, complicate approximately 10% of all pregnancies in the world, constituting one of the most serious causes of mortality and morbidity in gestation. To help predict the occurrence of hypertensive disorders, a study based on algorithms that help model this health problem using mathematical tools is proposed. This study proposes a fuzzy c-means (FCM) model based on the Takagi–Sugeno (T-S) type of fuzzy rule to predict hypertensive disorders in pregnancy. To test different modeling methodologies, cross-validation comparisons were made between random forest, decision tree, support vector machine, and T-S and FCM methods, which achieved 80.00%, 66.25%, 70.00%, and 90.00%, respectively. The evaluation consisted of calculating the true positive rate (TPR) over the true negative rate (TNR), with equal error rate (EER) curves achieving a percentage of 20%. The learning dataset consisted of a total of 371 pregnant women, of which 13.2% were diagnosed with a condition related to gestational hypertension. The dataset for this study was obtained from the Secretaría de Salud del Estado de Hidalgo (SSEH), México. A random sub-sampling technique was used to adjust the class distribution of the data set, and to eliminate the problem of unbalanced classes. The models were trained using a total of 98 samples. The modeling results indicate that the T-S and FCM method has a higher predictive ability than the other three models in this research. [ABSTRACT FROM AUTHOR]

Manifold learning-based approaches have emerged as prominent techniques for dimensionality reduction. Among these methods, t-Distributed Stochastic Neighbor Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP) stand out as two of the most widely used and effective approaches. While both methods share similar underlying procedures, empirical observations indicate two distinctive properties: global data structure preservation and computational efficiency. However, the underlying mathematical principles behind these distinctions remain elusive. To address this gap, this study presents a comparative analysis of the subprocesses involved in these methods, aiming to elucidate the mathematical mechanisms underlying the observed distinctions. By meticulously examining the equation formulations, the mathematical mechanisms contributing to global data structure preservation and computational efficiency are elucidated. To validate the theoretical analysis, data are collected through a laboratory experiment, and an open-source dataset is utilized for validation across different datasets. The consistent alignment of results obtained from both balanced and unbalanced datasets robustly confirms the study's findings. The insights gained from this study provide a deeper understanding of the mathematical underpinnings of t-SNE and UMAP, enabling more informed and effective use of these dimensionality reduction techniques in various applications, such as anomaly detection, natural language processing, and bioinformatics. [ABSTRACT FROM AUTHOR]

In the Ontology Learning research domain, despite recent advancements, the performance of current non or semi-supervised approaches for concept formation remains sub-optimal, particularly from a single, small-sized corpus for a specialized domain. In order to answer the performance drawback, this paper introduces a novel pipeline, called CO-ISSC (Core Ontology-based Incremental Semi-Supervised Clustering), for concept formation towards ontology learning. This pipeline uses a PLM (Pre-trained Language Model) and combines in an incremental manner a semi-supervised dimension reduction technique and a clustering technique, guided by core concepts as prior knowledge to align results with the ontology domain. Its incremental nature enhances prior knowledge and boosts its performance. The CO-ISSC pipeline's performance is evaluated on the recent and significant AI Act text established by the European Union, which aims to ensure the safety, transparency, and non-discrimination of AI systems. To this end, we manually built a benchmark terminology for the AI Act domain given that no reference model exists yet. The results demonstrate promising performance of the CO-ISSC pipeline, outperforming baseline non-supervised or semi-supervised approaches such as DBSCAN, similarity measure based approaches, support vector machines and ANN. [ABSTRACT FROM AUTHOR]

We show that the linear brittle Griffith energy on a thin rectangle Γ -converges after rescaling to the linear one-dimensional brittle Euler–Bernoulli beam energy. In contrast to the existing literature, we prove a corresponding sharp compactness result, namely a suitable weak convergence after subtraction of piecewise rigid motions with the number of jumps bounded by the energy. [ABSTRACT FROM AUTHOR]

Principal components analysis (PCA) and partial least squares (PLS) have been used for the construction of socioeconomic status (SES) indices to use as a predictor of the well-being status in targeted programs. Generally, these indicators are constructed as a linear combination of the first component. Due to the characteristics of the socioeconomic data, different extensions of PCA and PLS for non-metric variables have been proposed for these applications. In this paper, we compare the predictive performance of SES indices constructed using more than one component. Additionally, for the inclusion of non-metric variables, a variant of the normal mean coding is proposed that takes into account the multivariate nature of the variables, which we call multivariate normal mean coding (MNMC). Using simulations and real data, we found that PLS using MNMC as well as the classical dummy encoding method give the best predictive results with a more parsimonious SES index, both in regression and classification problems. [ABSTRACT FROM AUTHOR]

ANOVA decomposition of a function with random input variables provides ANOVA functionals (AFs), which contain information about the contributions of the input variables on the output variable(s). By embedding AFs into an appropriate reproducing kernel Hilbert space regarding their distributions, we propose an efficient statistical test of independence between the input variables and output variable(s). The resulting test statistic leads to new dependence measures of association between inputs and outputs that allow for i) dealing with any distribution of AFs, including the Cauchy distribution, ii) accounting for the necessary or desirable moments of AFs and the interactions among the input variables. In uncertainty quantification for mathematical models, a number of existing measures are special cases of this framework. We then provide unified and general global sensitivity indices and their consistent estimators, including asymptotic distributions. For Gaussian-distributed AFs, we obtain Sobol' indices and dependent generalized sensitivity indices using quadratic kernels. [ABSTRACT FROM AUTHOR]

Factor models are widely used for dimension reduction in the analysis of multivariate data. This is achieved through decomposition of a p × p covariance matrix into the sum of two components. Through a latent factor representation, they can be interpreted as a diagonal matrix of idiosyncratic variances and a shared variation matrix, that is, the product of a p × k factor loadings matrix and its transpose. If k ≪ p , this defines a parsimonious factorisation of the covariance matrix. Historically, little attention has been paid to incorporating prior information in Bayesian analyses using factor models where, at best, the prior for the factor loadings is order invariant. In this work, a class of structured priors is developed that can encode ideas of dependence structure about the shared variation matrix. The construction allows data-informed shrinkage towards sensible parametric structures while also facilitating inference over the number of factors. Using an unconstrained reparameterisation of stationary vector autoregressions, the methodology is extended to stationary dynamic factor models. For computational inference, parameter-expanded Markov chain Monte Carlo samplers are proposed, including an efficient adaptive Gibbs sampler. Two substantive applications showcase the scope of the methodology and its inferential benefits. [ABSTRACT FROM AUTHOR]

We consider high-dimensional Bayesian inverse problems with arbitrary likelihood and product-form Laplace prior for which we provide a certified approximation of the posterior in the Hellinger distance. The approximate posterior differs from the prior only in a small number of relevant coordinates that contribute the most to the update from the prior to the posterior. We propose and analyze a gradient-based diagnostic to identify these relevant coordinates. Although this diagnostic requires computing an expectation with respect to the posterior, we propose tractable methods for the classical case of a linear forward model with Gaussian likelihood. Our methods can be employed to estimate the diagnostic before solving the Bayesian inverse problem via, e.g., Markov chain Monte Carlo (MCMC) methods. After selecting the coordinates, the approximate posterior can be efficiently inferred since most of its coordinates are only informed by the prior. Moreover, specialized MCMC methods, such as the pseudo-marginal MCMC algorithm, can be used to obtain less correlated samples when sampling the exact posterior. We show the applicability of our method using a 1D signal deblurring problem and a high-dimensional 2D super-resolution problem. [ABSTRACT FROM AUTHOR]

Motivation: Chemical space embedding methods are widely utilized in various research settings for dimensional reduction, clustering and effective visualization. The maps generated by the embedding process can provide valuable insight to medicinal chemists in terms of the relationships between structural, physicochemical and biological properties of compounds. However, these maps are known to be difficult to interpret, and the "landscape" on the map is prone to "rearrangement" when embedding different sets of compounds. Results: In this study we present the Hilbert-Curve Assisted Space Embedding (HCASE) method which was designed to create maps by organizing structures according to a logic familiar to medicinal chemists. First, a chemical space is created with the help of a set of "reference scaffolds". These scaffolds are sorted according to the medicinal chemistry inspired Scaffold-Key algorithm found in prior art. Next, the ordered scaffolds are mapped to a line which is folded into a higher dimensional (here: 2D) space. The intricately folded line is referred to as a pseudo-Hilbert-Curve. The embedding of a compound happens by locating its most similar reference scaffold in the pseudo-Hilbert-Curve and assuming the respective position. Through a series of experiments, we demonstrate the properties of the maps generated by the HCASE method. Subjects of embeddings were compounds of the DrugBank and CANVASS libraries, and the chemical spaces were defined by scaffolds extracted from the ChEMBL database. Scientific contribution: The novelty of HCASE method lies in generating robust and intuitive chemical space embeddings that are reflective of a medicinal chemist's reasoning, and the precedential use of space filling (Hilbert) curve in the process. Availability: https://github.com/ncats/hcase [ABSTRACT FROM AUTHOR]

Thyroid cancer incidences endure to increase even though a large number of inspection tools have been developed recently. Since there is no standard and certain procedure to follow for the thyroid cancer diagnoses, clinicians require conducting various tests. This scrutiny process yields multi-dimensional big data and lack of a common approach leads to randomly distributed missing (sparse) data, which are both formidable challenges for the machine learning algorithms. This paper aims to develop an accurate and computationally efficient deep learning algorithm to diagnose the thyroid cancer. In this respect, randomly distributed missing data stemmed singularity in learning problems is treated and dimensionality reduction with inner and target similarity approaches are developed to select the most informative input datasets. In addition, size reduction with the hierarchical clustering algorithm is performed to eliminate the considerably similar data samples. Four machine learning algorithms are trained and also tested with the unseen data to validate their generalization and robustness abilities. The results yield 100% training and 83% testing preciseness for the unseen data. Computational time efficiencies of the algorithms are also examined under the equal conditions. [ABSTRACT FROM AUTHOR]

A major challenge of precision oncology is the identification and prioritization of suitable treatment options based on molecular biomarkers of the considered tumor. In pursuit of this goal, large cancer cell line panels have successfully been studied to elucidate the relationship between cellular features and treatment response. Due to the high dimensionality of these datasets, machine learning (ML) is commonly used for their analysis. However, choosing a suitable algorithm and set of input features can be challenging. We performed a comprehensive benchmarking of ML methods and dimension reduction (DR) techniques for predicting drug response metrics. Using the Genomics of Drug Sensitivity in Cancer cell line panel, we trained random forests, neural networks, boosting trees and elastic nets for 179 anti-cancer compounds with feature sets derived from nine DR approaches. We compare the results regarding statistical performance, runtime and interpretability. Additionally, we provide strategies for assessing model performance compared with a simple baseline model and measuring the trade-off between models of different complexity. Lastly, we show that complex ML models benefit from using an optimized DR strategy, and that standard models—even when using considerably fewer features—can still be superior in performance. [ABSTRACT FROM AUTHOR]

This paper focuses on the simultaneous homogenization and dimension reduction of periodic composite plates within the framework of non-linear elasticity. The composite plate in its reference (undeformed) configuration consists of a periodic perforated plate made of stiff material with holes filled by a soft matrix material. The structure is clamped on a cylindrical part. Two cases of asymptotic analysis are considered: one without pre-strain and the other with matrix pre-strain. In both cases, the total elastic energy is in the von-Kármán (vK) regime ( ε 5 ). A new splitting of the displacements is introduced to analyze the asymptotic behavior. The displacements are decomposed using the Kirchhoff–Love (KL) plate displacement decomposition. The use of a re-scaling unfolding operator allows for deriving the asymptotic behavior of the Green St. Venant's strain tensor in terms of displacements. The limit homogenized energy is shown to be of vK type with linear elastic cell problems, established using the Γ-convergence. Additionally, it is shown that for isotropic homogenized material, our limit vK plate is orthotropic. The derived results have practical applications in the design and analysis of composite structures. [ABSTRACT FROM AUTHOR]

This article presents a novel approach to introducing principal component analysis (PCA), using summary tables and descriptive statistics. Given its applicability across a variety of academic disciplines, this topic offers abundant opportunity for class discussion and activities. However, teaching PCA in an introductory class can be challenging due to the potential abstraction of multivariate datasets, and especially when students have a minimal background in statistics or data science. This method aims to help teachers bridge the gap between basic descriptive statistics and the more advanced concepts of PCA; this is done by disregarding mathematical optimization, while emphasizing the use of summary tables and the programming language R. The focus is on implementing this method in an introductory tertiary data science course; however, it may potentially be used in higher level courses, and across a variety of disciplines. [ABSTRACT FROM AUTHOR]

Dimension reduction techniques have long been an important topic in statistics, and active subspaces (AS) have received much attention this past decade in the computer experiments literature. The most common approach toward estimating the AS is to use Monte Carlo with numerical gradient evaluation. While sensible in some settings, this approach has obvious drawbacks. Recent research has demonstrated that active subspace calculations can be obtained in closed form, conditional on a Gaussian process (GP) surrogate, which can be limiting in high-dimensional settings for computational reasons. In this article, we produce the relevant calculations for a more general case when the model of interest is a linear combination of tensor products. These general equations can be applied to the GP, recovering previous results as a special case, or applied to the models constructed by other regression techniques including multivariate adaptive regression splines (MARS). Using a MARS surrogate has many advantages including improved scaling, better estimation of active subspaces in high dimensions and the ability to handle a large number of prior distributions in closed form. In one real-world example, we obtain the active subspace of a radiation-transport code with 240 inputs and 9372 model runs in under half an hour. for this article are available online. [ABSTRACT FROM AUTHOR]

Dimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible. This approach is crucial in many disciplines like engineering, biology, astronomy, and economics. In this paper, we consider the following dimensionality reduction instance: Given an n-dimensional probability distribution p and an integer m < n , we aim to find the m-dimensional probability distribution q that is the closest to p, using the Kullback–Leibler divergence as the measure of closeness. We prove that the problem is strongly NP-hard, and we present an approximation algorithm for it. [ABSTRACT FROM AUTHOR]

• The FPK equation of ABH energy harvester is established. • The dimension reduction method is used to converted the high dimension FPK equation. • The Lax-Friedrichs scheme is used and its stability condition is also given. The ABH effect shows potential application in vibration energy harvesting due to its wave localization property. In this study, the stochastic response of output voltage of ABH energy harvester has been investigated under Gaussian white noise excitation. The high dimensional Fokker–Planck–Kolmogorov equation of this piezoelectric coupling systems is given by using Gaussian Expansion method and dimension reduction method is used to convert it to one-dimensional first-order partial differential equation. Finally, the Lax-Friedrichs scheme is developed to solve the partial differential equation to obtain the probability density of output voltage. The results between calculated probability distribution and that of Monte Carlo simulation shows good accuracy of propose method. Finally, a comprehensive parametric analysis has been performed on this stochastic system and some conclusions are given. [ABSTRACT FROM AUTHOR]

Three-way clustering uses core region and fringe region to describe a cluster, which divide the dataset into three parts. The division helps identify the central core and outer sparse regions of a cluster. One of the main challenges in three-way clustering is the meaningful construction of the two sets. Aimed at handling high-dimensional data and improving the stability of clustering, this paper proposes a novel three-way clustering method. The proposed method uses dimensionality reduction techniques to reduce data dimensions and eliminate noise. Based on the reduced dataset, random sampling and feature extraction are performed multiple times to introduce randomness and diversity, enhancing the algorithm's robustness. Ensemble strategies are applied on these subsets, and the k-means algorithm is utilized to obtain multiple clustering results. Based on these results, we obtain co-association frequency between different samples and fused clustering result using the single-linkage method of hierarchical clustering. In order to describe the core region and fringe region of each cluster, the similar class of each sample is defined by co-association frequency. The lower and upper approximations of each cluster are obtained based on similar class. The samples in the lower approximation of each cluster belong to the core region of the cluster. The differences between lower and upper approximations of each cluster are defined as fringe region. Therefore, a three-way explanation of each cluster is naturally formed. By employing various UC Irvine Machine Learning Repository (UCI) datasets and comparing different clustering metrics such as Normalized Mutual Information (NMI), Adjusted Rand Index (ARI), and Accuracy (ACC), the experimental results show that the proposed strategy is effective in improving the structure of clustering results. [ABSTRACT FROM AUTHOR]

In this paper, 3D–2D-dimensional reduction for hyperelastic thin films modeled through energies with point-dependent growth, assuming that the sample is clamped on the lateral boundary, is performed in the framework of Γ -convergence. Integral representation results, with a more regular Lagrangian related to the original energy density, are provided for the lower dimensional limiting energy, in different contexts. [ABSTRACT FROM AUTHOR]

Microbiome scientists critically need modern tools to explore and analyze microbial evolution. Often this involves studying the evolution of microbial genomes as a whole. However, different genes in a single genome can be subject to different evolutionary pressures, which can result in distinct gene-level evolutionary histories. To address this challenge, we propose to treat estimated gene-level phylogenies as data objects, and present an interactive method for the analysis of a collection of gene phylogenies. We use a local linear approximation of phylogenetic tree space to visualize estimated gene trees as points in low-dimensional Euclidean space, and address important practical limitations of existing related approaches, allowing an intuitive visualization of complex data objects. We demonstrate the utility of our proposed approach through microbial data analyses, including by identifying outlying gene histories in strains of Prevotella , and by contrasting Streptococcus phylogenies estimated using different gene sets. Our method is available as an open-source R package, and assists with estimating, visualizing, and interacting with a collection of bacterial gene phylogenies. [ABSTRACT FROM AUTHOR]

In this work we propose a low rank approximation of areal, particularly three dimensional, data utilizing additional weights. This way we enable effective compression if additional information indicates that parts of the data are of higher interest than others. The guiding example are high fidelity finite element simulations of an abdominal aortic aneurysm, i.e. a deformed blood vessel. The additional weights encapsulate the areas of high stress, which we assume indicates the rupture risk of the aorta. The stress values on the grid are modeled as a Gaussian Markov random field and we define our approximation as a basis of vectors that solve a series of optimization problems. Each of these problems describes the minimization of an expected weighted quadratic loss. We provide an effective numerical heuristic to compute the basis under general conditions, which relies on the sparsity of the precision matrix to ensure acceptable computing time even for large grids. We explicitly explore two such bases on the surface of a high fidelity finite element grid and show their efficiency for compression. Finally, we utilize the approach as part of a larger model to predict the van Mises stress in areas of interest using low and high fidelity simulations. [ABSTRACT FROM AUTHOR]

Dimension reduction is an effective method for system's resilience analysis. In this paper, we investigate the effect of network structure on the accuracy of resilience dimension reduction. First, we introduce the resilience dimension reduction method and define the evaluation indicator of the resilience dimension reduction method. Then, by adjusting node connections, preferential connection mechanisms, and connection probabilities, we generate artificial networks, small-world networks and social networks with tunable assortativity coefficients, average clustering coefficients, and modularities, respectively. Experimental results for the gene regulatory dynamics show that the network structures with positive assortativity, large clustering coefficient, and significant community can enhance the accuracy of resilience dimension reduction. The result of this paper indicates that optimizing network structure can enhance the accuracy of resilience dimension reduction, which is of great significance for system resilience analysis and provides a new perspective and theoretical basis for selecting dimension reduction methods in system resilience analysis. [ABSTRACT FROM AUTHOR]

Hyperspectral imaging is a crucial technology of remote sensing that captures hundreds of continuous spectral bands. In hyperspectral image (HSI) classification, pixels of HSI are classified into a particular class. HSI classification methods face challenges due to high dimensional data and the small number of labeled samples available. Recent years have witnessed impressive advancements in HSI classification using deep learning models. This research proposes an innovative method that uses a pretrained convolutional neural network (CNN) to extract robust spatial features from the HSI to assist in classification. Our strategy begins with the principal component analysis for spectral dimensionality reduction, then moves on to the pretrained CNN model for spatial feature extraction, and finally, utilizes a support vector machine (SVM) as the classifier. We conducted tests using three widely-used pretrained CNNs, namely AlexNet, VGG-16, and GoogLeNet, on three different HSI datasets (Indian Pines, University of Pavia, and Salinas) to assess the effectiveness of our approach. The results reveal that the proposed model achieves better performance. Specifically, when utilizing the VGG-16 model for feature extraction on the Salinas dataset, our model achieves an overall accuracy of 99.12%, an average accuracy of 99.40%, and a Kappa coefficient of 0.9901. Furthermore, we compare our results with other commonly used HSI classification methods, highlighting the superior performance of our proposed model. [ABSTRACT FROM AUTHOR]

This article explores the application of Variational AutoEncoders (VAEs) to insurance data. Previous research has demonstrated the successful implementation of generative models, especially VAEs, across various domains, such as image recognition, text classification, and recommender systems. However, their application to insurance data, particularly to heterogeneous insurance portfolios with mixed continuous and discrete attributes, remains unexplored. This study introduces novel insights into utilising VAEs for unsupervised learning tasks in actuarial science, including dimension reduction and synthetic data generation. We propose a VAE model with a quantile transformation for continuous (latent) variables, a reconstruction loss that combines categorical cross-entropy and mean squared error, and a KL divergence-based regularisation term. Our VAE model’s architecture circumvents the need to pre-train and fine-tune a neural network to encode categorical variables into n-dimensional representative vectors within a continuous vector space of dimension Rn. We assess our VAE’s ability to reconstruct complex insurance data and generate synthetic insurance policies using a motor portfolio. Our experimental results and analysis highlight the potential of VAEs in addressing challenges related to data availability in the insurance industry.

Sparse canonical correlation analysis (sCCA) has been a useful approach for integrating different high-dimensional datasets by finding a subset of correlated features that explain the most correlation in the data. In the context of microbiome studies, investigators are always interested in knowing how the microbiome interacts with the host at different molecular levels such as genome, methylol, transcriptome, metabolome and proteome. sCCA provides a simple approach for exploiting the correlation structure among multiple omics data and finding a set of correlated omics features, which could contribute to understanding the host-microbiome interaction. However, existing sCCA methods do not address compositionality, and its application to microbiome data is thus not optimal. This paper proposes a new sCCA framework for integrating microbiome data with other high-dimensional omics data, accounting for the compositional nature of microbiome sequencing data. It also allows integrating prior structure information such as the grouping structure among bacterial taxa by imposing a “soft” constraint on the coefficients through varying penalization strength. As a result, the method provides significant improvement when the structure is informative while maintaining robustness against a misspecified structure. Through extensive simulation studies and real data analysis, we demonstrate the superiority of the proposed framework over the state-of-the-art approaches.

A signal decomposition is presented that disentangles the deterministic and stochastic components of a multivariate time series. The dynamical component analysis (DyCA) algorithm is based on the assumption that an unknown set of ordinary differential equations (ODEs) describes the dynamics of the deterministic part of the signal. The algorithm is thoroughly derived and accompanied by a link to the GitHub repository containing the algorithm. The method was applied to both simulated and real-world data sets and compared to the results of principal component analysis (PCA), independent component analysis (ICA), and dynamic mode decomposition (DMD). The results demonstrate that DyCA is capable of separating the deterministic and stochastic components of the signal. Furthermore, the algorithm is able to estimate the number of linear and non-linear differential equations and to extract the corresponding amplitudes. The results demonstrate that DyCA is an effective tool for signal decomposition and dimension reduction of multivariate time series. In this regard, DyCA outperforms PCA and ICA and is on par or slightly superior to the DMD algorithm in terms of performance.