Search Results (79)

This paper presents a novel four-dimensional autonomous conservative model characterized by an infinite set of equilibrium points and an unusual algebraic structure in which all eigenvalues of the Jacobian matrix are zero. The linearization of the proposed model implies that classical stability analysis is inadequate, as only the center manifolds are obtained. Consequently, the stability of the system is investigated through both analytical and numerical methods using Lyapunov functions and numerical simulations. The proposed model exhibits rich dynamics, including hyperchaotic behavior, which is characterized using the Lyapunov exponents, bifurcation diagrams, sensitivity analysis, attractor projections, and Poincaré map. Moreover, in this paper, we explore the model with fractional-order derivatives, demonstrating that the fractional dynamics fundamentally change the geometrical structure of the attractors and significantly change the system stability. The Grünwald–Letnikov formulation is used for modeling, while numerical integration is performed using the Caputo operator to capture the memory effects inherent in fractional models. Finally, an analog electronic circuit realization is provided to experimentally validate the theoretical and numerical findings. Full article

Seismic waveform feature extraction is a critical task in seismic exploration, as it directly impacts reservoir prediction and geological interpretation. However, large-scale seismic data and nonlinear relationships between seismic signals and reservoir properties are challenging for traditional machine learning methods. To address these limitations, this paper proposes a novel framework combining Convolutional Neural Network (CNN) and Uniform Manifold Approximation and Projection (UMAP) for seismic waveform feature extraction and analysis. The UMAP-CNN framework leverages the strengths of manifold learning and deep learning, enabling multi-scale feature extraction and dimensionality reduction while preserving both local and global data structures. The evaluation experiments, which considered runtime, receiver operating characteristic (ROC) curves, embedding distribution maps, and other quantitative assessments, illustrated that the UMAP-CNN outperformed t-distributed stochastic neighbor embedding (t-SNE), locally linear embedding (LLE) and isometric feature mapping (Isomap). A case study in the Ordos Basin further demonstrated that UMAP-CNN offers a high degree of accuracy in predicting coal seam thickness. Furthermore, our framework exhibited superior computational efficiency and robustness in handling large-scale datasets. Full article

Thestability of a control system is essential for its effective operation. Stability implies that small changes in input, initial conditions, or parameters do not lead to significant fluctuations in output. Various stability properties, such as inner stability, asymptotic stability, and BIBO (Bounded Input, Bounded Output) stability, are well understood for classical linear control systems in Euclidean spaces. This paper aims to thoroughly address the stability problem for a class of linear control systems defined on matrix Lie groups. This approach generalizes classical models corresponding to the latter when the group is Abelian and non-compact. It is important to note that this generalization leads to a very difficult control system, due to the complexity of the state space and the special dynamics resulting from the drift and control vectors. Several mathematical concepts help us understand and characterize stability in the classical case. We first show how to extend these algebraic, topological, and dynamical concepts from Euclidean space to a connected Lie group of matrices. Building on classical results, we identify a pathway that enables us to formulate conjectures about stability in this broader context. This problem is closely linked to the controllability and observability properties of the system. Fortunately, these properties are well established for both classes of linear systems, whether in Euclidean spaces or on Lie groups. We are confident that these conjectures can be proved in future work, initially for the class of nilpotent and solvable groups, and later for semi-simple groups. This will provide valuable insights that will facilitate, through Jouan’s Equivalence Theorem, the analysis of an important class of nonlinear control systems on manifolds beyond Lie groups. We provide an example involving a three-dimensional solvable Lie group of rigid motions in a plane to illustrate these conjectures. Full article

Wind energy has emerged as a cornerstone in global efforts to transition to renewable energy, driven by its low environmental impact and significant generation potential. However, the inherent intermittency of wind, influenced by complex and dynamic atmospheric patterns, poses significant challenges for accurate wind speed prediction. Existing approaches, including statistical methods, machine learning, and deep learning, often struggle with limitations such as non-linearity, non-stationarity, computational demands, and the requirement for extensive, high-quality datasets. In response to these challenges, we propose a novel neighborhood preserving cross-dataset data augmentation framework for high-horizon wind speed prediction. The proposed method addresses data variability and dynamic behaviors through three key components: (i) the uniform manifold approximation and projection (UMAP) is employed as a non-linear dimensionality reduction technique to encode local relationships in wind speed time-series data while preserving neighborhood structures, (ii) a localized cross-dataset data augmentation (DA) approach is introduced using UMAP-reduced spaces to enhance data diversity and mitigate variability across datasets, and (iii) recurrent neural networks (RNNs) are trained on the augmented datasets to model temporal dependencies and non-linear patterns effectively. Our framework was evaluated using datasets from diverse geographical locations, including the Argonne Weather Observatory (USA), Chengdu Airport (China), and Beijing Capital International Airport (China). Comparative tests using regression-based measures on RNN, GRU, and LSTM architectures showed that the proposed method was better at improving the accuracy and generalizability of predictions, leading to an average reduction in prediction error. Consequently, our study highlights the potential of integrating advanced dimensionality reduction, data augmentation, and deep learning techniques to address critical challenges in renewable energy forecasting. Full article

This study presents an innovative approach for marine diesel engine fault detection, integrating unsupervised learning through Uniform Manifold Approximation and Projection (UMAP) dimensionality reduction with time series prediction, offering significant improvements over existing methods. Unlike traditional model-based or expert-driven approaches, which struggle with complex nonlinear systems, or supervised data-driven methods limited by scarce labeled fault data, our unsupervised method establishes a normal operational baseline without requiring fault labels, enhancing applicability across diverse conditions. Leveraging UMAP’s nonlinear dimensionality reduction, the proposed method outperforms conventional linear techniques (e.g., PCA) by amplifying subtle system anomalies, enabling earlier detection of state transitions—up to two batches before deviations appear in traditional performance indicators (Ps)—thus improving fault detection sensitivity. To address nonlinear relationships in UMAP-reduced dimensions, the proposed TimeMixer-FI model enhances the TimeMixer architecture with MLP-Mixer layers. The TimeMixer-FI model demonstrates consistent improvements over the original TimeMixer across various sequence lengths, achieving an MSE reduction of 69.1% (from 0.0544 to 0.0168) and an MAE reduction of 46.3% (from 0.1023 to 0.0549) at an input sequence length of 60 time steps, thereby enhancing the reliability of the time series prediction baseline. Experimental results validate that this approach significantly enhances both the sensitivity and accuracy of early fault detection, providing a more robust and efficient solution for predictive maintenance in marine diesel engines. Full article

The significant computational cost incurred due to the iterative nature of Computational Fluid Dynamics (CFD) in traditional aerodynamic shape design frameworks poses a major challenge, especially in the context of modern integrated design requirements and increasingly complex design conditions. To address the demands of modern design, we developed an efficient aerodynamic shape design framework based on our previous work involving the locally linear embedding plus constrained optimization genetic algorithm (LLE+COGA) high-fidelity reduced-order model (ROM). An active manifold (AM) auto-en/decoder was employed to address the dimensionality curse arising from an excessively large design space. The fast mesh deformation method was utilized for high-precision, rapid mesh deformation, significantly reducing the computational cost associated with transferring geometric deformations to CFD fine mesh. This work addressed the transonic optimization problem of the undeflected Common Research Model (uCRM) three-dimensional wing (with an aspect ratio of 9), involving 241 design variables. The results demonstrate that the optimized design achieved a significant reduction in the drag coefficient by 38.9% and 54.5% compared to the baseline in Case 1 and Case 2, respectively. Additionally, the total optimization time was shortened by 62.6% and 57.7% in the two cases. Moreover, the optimization outcomes aligned well with those obtained from the FOM-based framework, further validating the effectiveness and practical applicability of the proposed approach. Full article

In the field of video image processing, high definition is one of the main directions for future development. Faced with the curse of dimensionality caused by the increasingly large amount of ultra-high-definition video data, effective dimensionality reduction techniques have become increasingly important. Linear discriminant analysis (LDA) is a supervised learning dimensionality reduction technique that has been widely used in data preprocessing for dimensionality reduction and video image processing tasks. However, traditional LDA methods are not suitable for the dimensionality reduction and processing of small high-dimensional samples. In order to improve the accuracy and robustness of linear discriminant analysis, this paper proposes a new distributed sparse manifold constraint (DSC) optimization LDA method, called DSCLDA, which introduces $L_{2,0}$-norm regularization for local sparse feature representation and manifold regularization for global feature constraints. By iterating the hard threshold operator and transforming the original problem into an approximate non-convex sparse optimization problem, the manifold proximal gradient (ManPG) method is used as a distributed iterative solution. Each step of the algorithm has an explicit solution. Simulation experiments have verified the correctness and effectiveness of this method. Compared with several advanced sparse linear discriminant analysis methods, this method effectively improves the average classification accuracy by at least $0.90\%$. Full article

The underwater electric field signal can be excited by underwater vehicles, such as the shaft-rate electric field and the corrosion electric field. The electric field signature of each vehicle exhibits significant differences in time and frequency domain, which can be exploited to determine target positions. In this paper, a novel passive localization method for underwater targets is presented, leveraging a uniform linear electrode array (ULEA). The ULEA manifold along the axial direction is derived from the electric field propagation in an infinite lossy medium, which provides the nonlinear mapping relationship between the target position and the voltage data acquired by the ULEA. In order to locate the targets, the multiple signal classification (MUSIC) algorithm is applied. Then, capitalizing on the rotational invariance of matrix operations and exploiting the symmetry inherent in the ULEA, we streamline the six-dimensional spatial spectral scanning onto a two-dimensional plane, providing azimuth and distance information for the targets. This method significantly reduces computational overhead. To validate the efficacy of our proposed method, we devise a localization system and conduct a simulation environment to estimate targets. Results show that our method achieves satisfactory direction and reliable distance estimations, even in scenarios with low signal-to-noise ratios. Full article

We explore a new approach for the parsimonious, generalizable, efficient, and potentially automatable characterization of spectral diversity of sparse targets in spectroscopic imagery. The approach focuses on pixels which are not well modeled by linear subpixel mixing of the Substrate, Vegetation and Dark (S, V, and D) endmember spectra which dominate spectral variance for most of Earth’s land surface. We illustrate the approach using AVIRIS-3 imagery of anthropogenic surfaces (primarily hydrocarbon extraction infrastructure) embedded in a background of Arctic tundra near Prudhoe Bay, Alaska. Computational experiments further explore sensitivity to spatial and spectral resolution. Analysis involves two stages: first, computing the mixture residual of a generalized linear spectral mixture model; and second, nonlinear dimensionality reduction via manifold learning. Anthropogenic targets and lakeshore sediments are successfully isolated from the Arctic tundra background. Dependence on spatial resolution is observed, with substantial degradation of manifold topology as images are blurred from 5 m native ground sampling distance to simulated 30 m ground projected instantaneous field of view of a hypothetical spaceborne sensor. Degrading spectral resolution to mimicking the Sentinel-2A MultiSpectral Imager (MSI) also results in loss of information but is less severe than spatial blurring. These results inform spectroscopic characterization of sparse targets using spectroscopic images of varying spatial and spectral resolution. Full article

Spaceborne spectroscopic imaging offers the potential to improve our understanding of biodiversity and ecosystem services, particularly for challenging and rich environments like mangroves. Understanding the signals present in large volumes of high-dimensional spectroscopic observations of vegetation communities requires the characterization of seasonal phenology and response to environmental conditions. This analysis leverages both spectroscopic and phenological information to characterize vegetation communities in the Sundarban riverine mangrove forest of the Ganges–Brahmaputra delta. Parallel analyses of surface reflectance spectra from NASA’s EMIT imaging spectrometer and MODIS vegetation abundance time series (2000–2022) reveal the spectroscopic and phenological diversity of the Sundarban mangrove communities. A comparison of spectral and temporal feature spaces rendered with low-order principal components and 3D embeddings from Uniform Manifold Approximation and Projection (UMAP) reveals similar structures with multiple spectral and temporal endmembers and multiple internal amplitude continua for both EMIT reflectance and MODIS Enhanced Vegetation Index (EVI) phenology. The spectral and temporal feature spaces of the Sundarban represent independent observations sharing a common structure that is driven by the physical processes controlling tree canopy spectral properties and their temporal evolution. Spectral and phenological endmembers reside at the peripheries of the mangrove forest with multiple outward gradients in amplitude of reflectance and phenology within the forest. Longitudinal gradients of both phenology and reflectance amplitude coincide with LiDAR-derived gradients in tree canopy height and sub-canopy ground elevation, suggesting the influence of surface hydrology and sediment deposition. RGB composite maps of both linear (PC) and nonlinear (UMAP) 3D feature spaces reveal a strong contrast between the phenological and spectroscopic diversity of the eastern Sundarban and the less diverse western Sundarban. Full article

With the rapid advancements in data analysis and the increasing complexity of high-dimensional datasets, traditional dimensionality reduction techniques like Local Linear Embedding (LLE) often face challenges in maintaining accuracy and efficiency. This research aims to overcome the limitations of LLE, specifically its reliance on the nearest neighbor concept, its inability to distinguish differences among manifold points, and its underutilization of data discrimination information. To address these issues, we propose an advanced LLE algorithm that integrates decision tree-based neighbor recognition with Gaussian kernel density estimation. Decision trees accurately determine neighboring relationships, which are then optimized using Gaussian kernel density estimation to better reflect the distribution of sample points on the manifold. The algorithm also incorporates data discrimination information to enhance classification accuracy and efficiency. Evaluations in facial recognition tasks using SVM classifiers demonstrate significant improvements. Integrating decision trees (LLE-DT) yielded accuracy gains, with LFW at 98.75%, CFP 96.10%, and Olivetti 92.18%. Gaussian density estimation (LLE-GDE) achieved further enhancements, especially in LFW (99.13%), with CFP at 96.85%, and Olivetti at 91.82%. Combining both methods (LLE-DT-GDE) led to substantial improvements: LFW 99.61%, CFP 97.23%, and Olivetti 93.56%, highlighting the synergy between decision trees and Gaussian estimation. This advanced LLE algorithm effectively addresses the limitations of traditional approaches, showing promising results in complex data processing tasks such as facial recognition. These findings suggest its potential for broader applications in fields requiring robust data analysis and classification. Full article

In recent years, the frequency and intensity of global extreme weather events have gradually increased, leading to significant changes in urban rainfall patterns. The uneven distribution of rainfall has caused varying degrees of water security issues in different regions. Accurately grasping the spatiotemporal distribution patterns of rainfall is crucial for understanding the hydrological cycle and predicting the availability of water resources. This study collected rainfall data every five minutes from 62 rain gauge stations in the main urban area of Kunming City from 2019 to 2021, constructing an unsupervised hybrid dimensionality reduction-clustering (HDRC) model. The model employs the Locally Linear Embedding (LLE) algorithm from manifold learning for dimensionality reduction of the data samples and uses the dynamic clustering K-Means algorithm for cluster analysis. The results show that the model categorizes the rainfall in the Kunming area into three types: The first type has its rainfall center distributed on the north shore of Dian Lake and the southern part of Kunming’s main urban area, with spatial dynamics showing the rainfall distribution gradually developing from the Dian Lake water body towards the land. The second type’s rainfall center is located in the northern mountainous area of Kunming, with a smaller spatial dynamic change trend. The water vapor has a relatively fixed and concentrated rainfall center due to the orographic uplift effect of the mountains. The third type’s rainfall center is located in the main urban area of Kunming, with this type of rainfall showing smaller variations in all indicators, mainly occurring in May and September when the temperature is lower, related to the urban heat island effect. This research provides a general workflow for spatial rainfall classification, capable of mining the spatiotemporal distribution patterns of regional rainfall based on extensive data and generating typical samples of rainfall types. Full article

With the rapid advancement of remote-sensing technology, the spectral information obtained from hyperspectral remote-sensing imagery has become increasingly rich, facilitating detailed spectral analysis of Earth’s surface objects. However, the abundance of spectral information presents certain challenges for data processing, such as the “curse of dimensionality” leading to the “Hughes phenomenon”, “strong correlation” due to high resolution, and “nonlinear characteristics” caused by varying surface reflectances. Consequently, dimensionality reduction of hyperspectral data emerges as a critical task. This paper begins by elucidating the principles and processes of hyperspectral image dimensionality reduction based on manifold theory and learning methods, in light of the nonlinear structures and features present in hyperspectral remote-sensing data, and formulates a dimensionality reduction process based on manifold learning. Subsequently, this study explores the capabilities of feature extraction and low-dimensional embedding for hyperspectral imagery using manifold learning approaches, including principal components analysis (PCA), multidimensional scaling (MDS), and linear discriminant analysis (LDA) for linear methods; and isometric mapping (Isomap), locally linear embedding (LLE), Laplacian eigenmaps (LE), Hessian locally linear embedding (HLLE), local tangent space alignment (LTSA), and maximum variance unfolding (MVU) for nonlinear methods, based on the Indian Pines hyperspectral dataset and Pavia University dataset. Furthermore, the paper investigates the optimal neighborhood computation time and overall algorithm runtime for feature extraction in hyperspectral imagery, varying by the choice of neighborhood k and intrinsic dimensionality d values across different manifold learning methods. Based on the outcomes of feature extraction, the study examines the classification experiments of various manifold learning methods, comparing and analyzing the variations in classification accuracy and Kappa coefficient with different selections of neighborhood k and intrinsic dimensionality d values. Building on this, the impact of selecting different bandwidths t for the Gaussian kernel in the LE method and different Lagrange multipliers λ for the MVU method on classification accuracy, given varying choices of neighborhood k and intrinsic dimensionality d, is explored. Through these experiments, the paper investigates the capability and effectiveness of different manifold learning methods in feature extraction and dimensionality reduction within hyperspectral imagery, as influenced by the selection of neighborhood k and intrinsic dimensionality d values, identifying the optimal neighborhood k and intrinsic dimensionality d value for each method. A comparison of classification accuracies reveals that the LTSA method yields superior classification results compared to other manifold learning approaches. The study demonstrates the advantages of manifold learning methods in processing hyperspectral image data, providing an experimental reference for subsequent research on hyperspectral image dimensionality reduction using manifold learning methods. Full article

The principal component analysis is a well-known and widely used technique to determine the essential dimension of a data set. Broadly speaking, it aims to find a low-dimensional linear manifold that retains a large part of the information contained in the original data set. It may be the case that one cannot approximate the entirety of the original data set using a single low-dimensional linear manifold even though large subsets of it are amenable to such approximations. For these cases we raise the related but different challenge (problem) of locating subsets of a high dimensional data set that are approximately 1-dimensional. Naturally, we are interested in the largest of such subsets. We propose a method for finding these 1-dimensional manifolds by finding cliques in a purpose-built auxiliary graph. Full article

The goal of Feature Extraction Algorithms (FEAs) is to combat the dimensionality curse, which renders machine learning algorithms ineffective. The most representative FEAs are investigated conceptually and experimentally in our work. First, we discuss the theoretical foundation of a variety of FEAs from various categories like supervised vs. unsupervised, linear vs. nonlinear and random-projection-based vs. manifold-based, show their algorithms and compare these methods conceptually. Second, we determine the finest sets of new features for various datasets, as well as in terms of statistical significance, evaluate the eminence of the different types of transformed feature spaces and power analysis, and also determine the FEA efficacy in terms of speed and classification accuracy. Full article