High-dimensional Research Articles

Fitness noise in the Bak-Sneppen evolution model in high dimensions.

We study the Bak-Sneppen evolution model on a regular hypercubic lattice in high dimensions. Recent work [Phys. Rev. E 108, 044109 (2023)2470-004510.1103/PhysRevE.108.044109] showed the emergence of the 1/f^{α} noise for the fitness observable with α≈1.2 in one-dimension (1D) and α≈2 for the random neighbor (mean-field) version of the model. We examine the temporal correlation of fitness in 2, 3, 4, and 5 dimensions. As obtained by finite-size scaling, the spectral exponent tends to take the mean-field value at the upper critical dimension D_{u}=4, which is consistent with previous studies. Our approach provides an alternative way to understand the upper critical dimension of the model. We also show the local activity power spectra, which offer insight into the return time statistics and the avalanche dimension.

A comprehensive learning based swarm optimization approach for feature selection in gene expression data

Gene expression data analysis is challenging due to the high dimensionality and complexity of the data. Feature selection, which identifies relevant genes, is a common preprocessing step. We propose a Comprehensive Learning-Based Swarm Optimization (CLBSO) approach for feature selection in gene expression data. CLBSO leverages the strengths of ants and grasshoppers to efficiently explore the high-dimensional search space. Ants perform local search and leave pheromone trails to guide the swarm, while grasshoppers use their ability to jump long distances to explore new regions and avoid local optima. The proposed approach was evaluated on several publicly available gene expression datasets and compared with state-of-the-art feature selection methods. CLBSO achieved an average accuracy improvement of 15% over the original high-dimensional data and outperformed other feature selection methods by up to 10%. For instance, in the Pancreatic cancer dataset, CLBSO achieved 97.2% accuracy, significantly higher than XGBoost-MOGA's 84.0%. Convergence analysis showed CLBSO required fewer iterations to reach optimal solutions. Statistical analysis confirmed significant performance improvements, and stability analysis demonstrated consistent gene subset selection across different runs. These findings highlight the robustness and efficacy of CLBSO in handling complex gene expression datasets, making it a valuable tool for enhancing classification tasks in bioinformatics.

Convergence rates of Metropolis–Hastings algorithms

AbstractGiven a target probability density known up to a normalizing constant, the Metropolis–Hastings algorithm simulates realizations from a Markov chain which are eventual realizations from the target probability density. A key element for ensuring a reliable Metropolis–Hastings simulation experiment is understanding how quickly the simulation will generate a representative sample from target density. This corresponds to understanding the convergence properties of the Metropolis–Hastings Markov chain. State‐of‐the‐art methods for convergence analysis of Metropolis–Hastings algorithms are considered and reviewed. Practically important topics are discussed for an interdisciplinary audience. This includes convergence properties in high dimensions, proper tuning, initialization, and limitations of current convergence analyses.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

Task scheduling in cloud computing based on grey wolf optimization with a new encoding mechanism

Task scheduling in the cloud computing still remains challenging in terms of performance. Several evolutionary-derived algorithms have been proposed to solve or alleviate this problem. However, evolutionary algorithms have good exploration ability, but the performance drops significantly in high dimensions. To address this issue, considering the characteristic of task scheduling in cloud computing (i.e. all task-VM mappings are 1-dimensional and have the same search range), we propose a task scheduling algorithm based on grey wolf optimization using a new encoding mechanism (GWOEM) in this work. Through this new encoding mechanism, greedy and evolutionary algorithms are rationally integrated in GWOEM. Besides, based on the new mechanism, the dimension of search space is reduced to 1 and the key parameter (i.e., the population size) is eliminated. We apply the proposed GWOEM to the Google Cloud Jobs dataset (GoCJ) and demonstrate better performance than the prior state of the art in terms of makespan.

A study of one-factor copula models from a tail dependence perspective

AbstractModeling multivariate dependence in high dimensions is challenging, with popular solutions constructing multivariate copula as a composition of lower dimensional copulas. Pair-copula constructions do so by using bivariate linking copulas, but their parametrization, in size, being quadratic in the dimension, is not quite parsimonious. Besides, the number of regular vines grows super-exponentially with the dimension. One parsimonious solution is factor copulas, and in particular, the one-factor copula is touted for its simplicity – with the number of parameters linear in the dimension – while being able to cater to asymmetric non-linear dependence in the tails. In this paper, we add nuance to this claim from the point of view of a popular measure of multivariate tail dependence, the tail dependence matrix (TDM). We focus on the one-factor copula model with the linking copula belonging to the BB1 family, pointing out later the applicability of our results to a wider class of linking copulas. For this model, we derive tail dependence coefficients and study their basic properties as functions of the parameters of the linking copulas. Based on this, we study the representativeness of the class of TDMs supported by this model with respect to the class of all possible TDMs. We establish that since the parametrization is linear in the dimension, it is no surprise that the relative volume is zero for dimensions greater than three, and hence, by necessity, we present a novel manner of evaluating the representativeness that has a combinatorial flavor. We formulate the problem of finding the best representative one-factor BB1 model given a target TDM and suggest an implementation along with a simulation study of its performance across dimensions. Finally, we illustrate the results of the paper by modeling rainfall data, which is relevant in the context of weather-related insurance.

Symbolic Dynamics for Nonuniformly Hyperbolic Maps with Singularities in High Dimension

We construct Markov partitions for non-invertible and/or singular nonuniformly hyperbolic systems defined on higher dimensional Riemannian manifolds. The generality of the setup covers classical examples not treated so far, such as geodesic flows in closed manifolds, multidimensional billiard maps, and Viana maps, and includes all the recent results of the literature. We also provide a wealth of applications.

Fast clustering and cell-type annotation of scATAC data using pre-trained embeddings.

Data from the single-cell assay for transposase-accessible chromatin using sequencing (scATAC-seq) are now widely available. One major computational challenge is dealing with high dimensionality and inherent sparsity, which is typically addressed by producing lower dimensional representations of single cells for downstream clustering tasks. Current approaches produce such individual cell embeddings directly through a one-step learning process. Here, we propose an alternative approach by building embedding models pre-trained on reference data. We argue that this provides a more flexible analysis workflow that also has computational performance advantages through transfer learning. We implemented our approach in scEmbed, an unsupervised machine-learning framework that learns low-dimensional embeddings of genomic regulatory regions to represent and analyze scATAC-seq data. scEmbed performs well in terms of clustering ability and has the key advantage of learning patterns of region co-occurrence that can be transferred to other, unseen datasets. Moreover, models pre-trained on reference data can be exploited to build fast and accurate cell-type annotation systems without the need for other data modalities. scEmbed is implemented in Python and it is available to download from GitHub. We also make our pre-trained models available on huggingface for public use. scEmbed is open source and available at https://github.com/databio/geniml. Pre-trained models from this work can be obtained on huggingface: https://huggingface.co/databio.

A Novel Multiobjective Genetic Programming Approach to High-Dimensional Data Classification.

The development of data sensing technology has generated a vast amount of high-dimensional data, posing great challenges for machine learning models. Over the past decades, despite demonstrating its effectiveness in data classification, genetic programming (GP) has still encountered three major challenges when dealing with high-dimensional data: 1) solution diversity; 2) multiclass imbalance; and 3) large feature space. In this article, we have developed a problem-specific multiobjective GP framework (PS-MOGP) for handling classification tasks with high-dimensional data. To reduce the large solution space caused by high dimensionality, we incorporate the recursive feature elimination strategy based on mining the archive of evolved GP solutions. A progressive domination Pareto archive evolution strategy (PD-PAES), which optimizes the objectives in a specific order according to their objectives, is proposed to evaluate the GP individuals and maintain a better diversity of solutions. Besides, to address the seriously imbalanced class issue caused by traditional binary decomposition (BD) one versus rest (OVR) for multiclass classification problems, we design a method named BD with a similar positive and negative class size (BD-SPNCS) to generate a set of auxiliary classifiers. Experimental results on benchmark and real-world datasets demonstrate that our proposed PS-MOGP outperforms state-of-the-art traditional and evolutionary classification methods in the context of high-dimensional data classification.

Linear response theory for transport in non-Hermitian [formula omitted]-symmetric models

We analyzed the influence of dissipative non-Hermitian terms on electrical transport in one-dimensional non-Hermitian PT-symmetric models, which presents chiral symmetry. The combination of periodic modulation and non-Hermitian effects opens up exciting avenues for exploring new phases of matter and understanding of the role of non-Hermitian physics in topological systems. The effective Hermitian Hamiltonian has always a higher dimension than the corresponding non-Hermitian one. We analyzed the effect of periodic hopping modulation on Su-Schrieffer-Heeger chain, that exhibits the non-Hermiticity in the presence of an complex staggered potential, where this dissipative non-Hermitian extension modifies the features of the topological trivial phase and the topological nontrivial phase.

Rapid identification of moxa wool storage period based on hyperspectral imaging technology and machine learning

Moxa wool (MW), derived from the dried leaves of Artemisiaargyi, plays a significant role in traditional Chinese medicine. However, the quality of MW varies with its storage period, impacting its therapeutic efficacy. Traditional methods for quality detection are limited and destructive. To address this, we propose a non-destructive detection method using hyperspectral imaging technology and machine learning algorithms to accurately identify the storage period of MW. Nevertheless, hyperspectral data poses challenges due to its high dimensionality and redundancy, leading to increased computational complexity. To overcome this, we employed principal component analysis (PCA), competitive adaptive reweighted sampling (CARS), and successive projection algorithm (SPA) for data dimensionality reduction and wavelength selection. The results demonstrate that these techniques significantly enhance the accuracy of MW storage year identification. For Nanyang MW, the CARS+SVM model achieved the highest accuracy rates of 99.8% in the visible-near-infrared (VNIR) range and 99.55% in the shortwave infrared (SWIR) range. Similarly, for Qichun MW, the SPA+SVM model achieved identification accuracies of 99.78% and 99.47% in the VNIR and SWIR ranges, respectively. This research provides valuable insights into the rapid detection of MW quality by indication of storage years and presents a novel approach for quality control of MW in the field of traditional Chinese medicine. The combination of hyperspectral imaging and machine learning offers a promising solution for efficient and accurate MW identification, contributing to the advancement of traditional medicine practices.

Mini boson stars in higher dimensions are radially unstable

Boson stars are self-gravitating solutions made entirely of fundamental massive scalar fields. Here we investigate mini boson stars in D non-compact spacetime dimensions and we show that they are dynamically unstable for D>4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D>4$$\\end{document}.

Trajectory Planning Design for Parallel Parking of Autonomous Ground Vehicles with Improved Safe Travel Corridor

In this paper, the concept of symmetry is utilized to design the trajectory planning for parallel parking of autonomous ground vehicles—that is, the construction and the solution of the optimization-based trajectory planning approach are symmetrical. Parking is the main factor that troubles most drivers for their daily driving travel, and it can even lead to traffic congestion in severe cases. With the rise of new intelligent and autonomous vehicles, automatic parking seems to have become a trend. Traditional geometric planning methods are less adaptable to parking scenarios, while the parking paths planned by graph search methods may only achieve local optimality. Additionally, significant computational time is often required by numerical optimization methods to find a parking path when a good initial solution is not available. This paper presents a hierarchical trajectory planning approach for high-quality parallel parking of autonomous ground vehicles. The approach begins with a graph search layer to roughly generate an initial solution, which is refined by a numerical optimization layer to produce a high-quality parallel parking trajectory. Considering the high dimensionality and difficulty of finding an optimal solution for the path planning optimization problem, this paper proposes an improved safe travel corridor (I-STC) with the construction of collision constraints isolated from surrounding environmental obstacles. By constructing collision constraints of the I-STC based on the initial solution, the proposed method avoids the complexities and non-differentiability of traditional obstacle avoidance constraints, and simplifies the problem modeling the subsequent numerical optimization process. The simulation results demonstrate that the I-STC is capable of generating parallel parking trajectories with both comfort and safety.

Hierarchical homogeneity-based superpixel segmentation: application to hyperspectral image analysis

ABSTRACT Hyperspectral image (HI) analysis approaches have recently become increasingly complex and sophisticated. Recently, the combination of spectral-spatial information and superpixel techniques have addressed some hyperspectral data issues, such as the higher spatial variability of spectral signatures and dimensionality of the data. However, most existing superpixel approaches do not account for specific HI characteristics resulting from its high spectral dimension. In this work, we propose a multiscale superpixel method that is computationally efficient for processing hyperspectral data. The Simple Linear Iterative Clustering (SLIC) oversegmentation algorithm, on which the technique is based, has been extended hierarchically. Using a novel robust homogeneity testing, the proposed hierarchical approach leads to superpixels of variable sizes but with higher spectral homogeneity when compared to the classical SLIC segmentation. For validation, the proposed homogeneity-based hierarchical method was applied as a preprocessing step in the spectral unmixing and classification tasks carried out using, respectively, the Multiscale sparse Unmixing Algorithm (MUA) and the CNN-Enhanced Graph Convolutional Network (CEGCN) methods. Simulation results with both synthetic and real data show that the technique is competitive with state-of-the-art solutions.

Development of an Enhanced Human Face Recognition Model

Abstract Face recognition plays an important role in various areas of life and has attracted the interest of many scholars in the domain of computer vision, pattern recognition, and artificial intelligence. Most of the existing techniques adopted in the recognition of humans through facial images were found to be efficient but are computationally expensive due to the high dimension of facial images, which in turn increases processing speed and memory consumption. In this research, an enhanced model is proposed. Consequently, 6 facial images from 60 individuals were locally acquired using a Canon digital camera of default size 1200 × 1200. Thereafter, 240 images were used for training, while 120 images were used for testing. The enhanced model reduced the high dimension of images with improved feature extraction accuracy. Results showed significant improvement when compared to the existing ones.

Nonlinear model reduction from equations and data.

Modeling in applied science and engineering targets increasingly ambitious objectives, which typically yield increasingly complex models. Despite major advances in computations, simulating such models with exceedingly high dimensions remains a challenge. Even if technically feasible, numerical simulations on such high-dimensional problems do not necessarily give the simplified insight into these phenomena that motivated their initial models. Reduced-order models hold more promise for a quick assessment of changes under parameters and uncertainties, as well as for effective prediction and control. Such models are also highly desirable for systems that are only known in the form of data sets. This focus issue will survey the latest trends in nonlinear model reduction for equations and data sets across various fields of applications, ranging from computational to theoretical aspects.

RF‐GCN: Residual fused‐graph convolutional network using multimodalities for facial emotion recognition

AbstractBackgroundThe emotional state of individuals is difficult to identify and it is developing now a days because of vast interest in recognition. Many technologies have been developed to identify this emotional expression based on facial expressions, vocal expressions, physiological signals, and body expressions. Among these, facial emotion is very expressive for recognition using multimodalities. Understanding facial emotions has applications in mental well‐being, decision‐making, and even social change, as emotions play a crucial role in our lives. This recognition is complicated by the high dimensionality of data and non‐linear interactions across modalities. Moreover, the way emotion is expressed by people varies and these feature identification remains challenging, where these limitations are overcome by Deep learning models.MethodsThis research work aims at facial emotion recognition through the utilization of a deep learning model, named the proposed Residual Fused‐Graph Convolution Network (RF‐GCN). Here, multimodal data included is video as well as an Electroencephalogram (EEG) signal. Also, the Non‐Local Means (NLM) filter is used for pre‐processing input video frames. Here, the feature selection process is carried out using chi‐square, after feature extraction, which is done in both pre‐processed video frames and input EEG signals. Finally, facial emotion recognition and its types are determined by RF‐GCN, which is a combination of both the Deep Residual Network (DRN) and Graph Convolutional Network (GCN).ResultsFurther, RF‐GCN is evaluated for performance by metrics such as accuracy, recall, and precision, with superior values of 91.6%, 96.5%, and 94.7%.ConclusionsRF‐GCN captures the nuanced relationships between different emotional states and improves recognition accuracy. The model is trained and evaluated on the dataset and reflects real‐world conditions.

Clustering Hyperspectral Imagery via Sparse Representation Features of the Generalized Orthogonal Matching Pursuit

This study focused on improving the clustering performance of hyperspectral imaging (HSI) by employing the Generalized Orthogonal Matching Pursuit (GOMP) algorithm for feature extraction. Hyperspectral remote sensing imaging technology, which is crucial in various fields like environmental monitoring and agriculture, faces challenges due to its high dimensionality and complexity. Supervised learning methods require extensive data and computational resources, while clustering, an unsupervised method, offers a more efficient alternative. This research presents a novel approach using GOMP to enhance clustering performance in HSI. The GOMP algorithm iteratively selects multiple dictionary elements for sparse representation, which makes it well-suited for handling complex HSI data. The proposed method was tested on two publicly available HSI datasets and evaluated in comparison with other methods to demonstrate its effectiveness in enhancing clustering performance.

Bayesian L 1/2 Regression

It is well known that Bridge regression enjoys superior theoretical properties when compared to traditional LASSO. However, the current latent variable representation of its Bayesian counterpart, based on the exponential power prior, is computationally expensive in higher dimensions. In this article, we show that the exponential power prior has a closed form scale mixture of normal decomposition for α = ( 1 2 ) γ , γ ∈ { 1 , 2 , … } . We call these types of priors L 1 2 prior for short. We develop an efficient partially collapsed Gibbs sampling scheme for computation using the L 1 2 prior and study theoretical properties when p > n . In addition, we introduce a non-separable Bridge penalty function inspired by the fully Bayesian formulation and a novel, efficient coordinate descent algorithm. We prove the algorithm’s convergence and show that the local minimizer from our optimization algorithm has an oracle property. Finally, simulation studies were carried out to illustrate the performance of the new algorithms. Supplementary materials for this article are available online.

The resultant method in higher dimensions

Stability results play an important role in Galois geometries. The famous resultant method, developed by Szőnyi and Weiner [12], [11], became very fruitful and resulted in many stability theorems in the last two decades. This method is based on some bivariate polynomials associated to point sets. In this paper we generalize the method for the multidimensional case and show some new applications. We build up the multivariate polynomial machinery and apply it for Rédei polynomials. We can prove a high dimensional analogue of the result of Szőnyi-Weiner [9], concerning the number of hyperplanes being skew to a point set of the space. We prove general results on “partial blocking sets”, using the tools we have developed.

A Quantitative Computational Framework for Allopolyploid Single-Cell Data Integration and Core Gene Ranking in Development.

Polyploidization drives regulatory and phenotypic innovation. How the merger of different genomes contributes to polyploid development is a fundamental issue in evolutionary developmental biology and breeding research. Clarifying this issue is challenging because of genome complexity and the difficulty in tracking stochastic subgenome divergence during development. Recent single-cell sequencing techniques enabled probing subgenome-divergent regulation in the context of cellular differentiation. However, analyzing single-cell data suffers from high error rates due to high dimensionality, noise, and sparsity, and the errors stack up in polyploid analysis due to the increased dimensionality of comparisons between subgenomes of each cell, hindering deeper mechanistic understandings. In this study, we develop a quantitative computational framework, called "pseudo-genome divergence quantification" (pgDQ), for quantifying and tracking subgenome divergence directly at the cellular level. Further comparing with cellular differentiation trajectories derived from single-cell RNA sequencing data allows for an examination of the relationship between subgenome divergence and the progression of development. pgDQ produces robust results and is insensitive to data dropout and noise, avoiding high error rates due to multiple comparisons of genes, cells, and subgenomes. A statistical diagnostic approach is proposed to identify genes that are central to subgenome divergence during development, which facilitates the integration of different data modalities, enabling the identification of factors and pathways that mediate subgenome-divergent activity during development. Case studies have demonstrated that applying pgDQ to single-cell and bulk tissue transcriptomic data promotes a systematic and deeper understanding of how dynamic subgenome divergence contributes to developmental trajectories in polyploid evolution.