arXiv subjects

Yimin Wei

Publications and source records attributed to Yimin Wei.

At least 19 recordsLinked to original sources

arXiv2026

Intrinsic Low-Tucker-Rank Theory and Unified Tensor CUR Decomposition for High-Dimensional Hyperinterpolation

High-dimensional hyperinterpolation is severely hampered by the curse of dimensionality, as its coefficient tensors grow exponentially with the ambient dimension. Existing research predominantly focuses on heuristic algorithmic optimizations, often overlooking the inherent structural properties of these tensors. This paper establishes a rigorous theory of intrinsic low-$\epsilon$-Tucker-rank for hyperinterpolation coefficient tensors, delivering near-optimal low-rank approximations with error bounds that are nearly independent of the dimension. We further construct a unified, Tucker-compatible theoretical framework that integrates both Chidori-type and Fiber-type tensor CUR (TCUR) decompositions, deriving tight and stable Frobenius-norm error estimates that depend exclusively on tensor spectral properties and index set geometry. We mathematically verify the convergence and numerical stability of greedy adaptive index selection schemes and prove their near-optimality, enabling a fully tensor-free hyperinterpolation workflow that avoids constructing the full coefficient array. Three practical greedy TCUR algorithms and a lightweight TCUR-to-Tucker recompression pipeline are proposed as direct corollaries of our structural theory. Numerical experiments across three distinct families of high-dimensional test functions validate all theoretical predictions and confirm the intrinsic low-rank compressibility of hyperinterpolation coefficients. In contrast to prior algorithm-centric studies, this work prioritizes rigorous theoretical characterization over implementation tricks, establishing a unified structural and mathematical foundation for high-dimensional hyperinterpolation.

math.NA↗

arXiv2026

MM-OVSeg:Multimodal Optical-SAR Fusion for Open-Vocabulary Segmentation in Remote Sensing

Open-vocabulary segmentation enables pixel-level recognition from an open set of textual categories, allowing generalization beyond fixed classes. Despite great potential in remote sensing, progress in this area remains largely limited to clear-sky optical data and struggles under cloudy or haze-contaminated conditions. We present MM-OVSeg, a multimodal Optical-SAR fusion framework for resilient open-vocabulary segmentation under adverse weather conditions. MM-OVSeg leverages the complementary strengths of the two modalities--optical imagery provides rich spectral semantics, while synthetic aperture radar (SAR) offers cloud-penetrating structural cues. To address the cross-modal domain gap and the limited dense prediction capability of current vision-language models, we propose two key designs: a cross-modal unification process for multi-sensor representation alignment, and a dual-encoder fusion module that integrates hierarchical features from multiple vision foundation models for text-aligned multimodal segmentation. Extensive experiments demonstrate that MM-OVSeg achieves superior robustness and generalization across diverse cloud conditions. The source dataset and code are available at https://github.com/Jimmyxichen/MM-OVSeg.

cs.CV↗

arXiv2026

Low T-Phase Rank Approximation of Third Order Tensors

We study low T-phase-rank approximation of sectorial third-order tensors $\mathscr{A}\in\mathbb{C}^{n\times n\times p}$ under the tensor T-product. We introduce canonical T-phases and T-phase rank, and formulate the approximation task as minimizing a symmetric gauge of the canonical phase vector under a T-phase-rank constraint. Our main tool is a tensor phase-majorization inequality for the geometric mean, obtained by lifting the matrix inequality through the block-circulant representation. In the positive-imaginary regime, this yields an exact optimal-value formula and an explicit optimal half-phase truncation family. We further establish tensor counterparts of classical matrix phase inequalities and derive a tensor small phase theorem for MIMO linear time-invariant systems.

math.NA↗

arXiv2025

A tensor phase theory with applications in multilinear control

The purpose of this paper is to initiate a phase theory for tensors under the Einstein product, and explore its applications in multilinear control systems. Firstly, the sectorial tensor decomposition for sectorial tensors is derived, which allows us to define phases for sectorial tensors. A numerical procedure for computing phases of a sectorial tensor is also proposed. Secondly, the maximin and minimax expressions for tensor phases are given, which are used to quantify how close the phases of a sectorial tensor are to those of its compressions. Thirdly, the compound spectrum, compound numerical ranges and compound angular numerical ranges of two sectorial tensors $A,B$ are defined and characterized in terms of the compound numerical ranges and compound angular numerical ranges of the sectorial tensors $A,B$. Fourthly, it is shown that the angles of eigenvalues of the product of two sectorial tensors are upper bounded by the sum of their individual phases. Finally, based on the tensor phase theory developed above, a tensor version of the small phase theorem is presented, which can be regarded as a natural generalization of the matrix case, recently proposed in Ref. [10]. The results offer powerful new tools for the stability and robustness analysis of multilinear feedback control systems.

math.OC↗

arXiv2025

How many integrals should be evaluated at least in two-dimensional hyperinterpolation?

This paper introduces a novel approach to approximating continuous functions over high-dimensional hypercubes by integrating matrix CUR decomposition with hyperinterpolation techniques. Traditional Fourier-based hyperinterpolation methods suffer from the curse of dimensionality, as the number of coefficients grows exponentially with the dimension. To address this challenge, we propose two efficient strategies for constructing low-rank matrix CUR decompositions of the coefficient matrix, significantly reducing computational complexity while preserving accuracy. The first method employs structured index selection to form a compressed representation of the tensor, while the second utilizes adaptive sampling to further optimize storage and computation. Theoretical error bounds are derived for both approaches, ensuring rigorous control over approximation quality. Additionally, practical algorithms -- including randomized and adaptive decomposition techniques -- are developed to efficiently compute the CUR decomposition. Numerical experiments demonstrate the effectiveness of our methods in drastically reducing the number of required coefficients without compromising precision. Our results bridge matrix/tensor decomposition and function approximation, offering a scalable solution for high-dimensional problems. This work advances the field of numerical analysis by providing a computationally efficient framework for hyperinterpolation, with potential applications in scientific computing, machine learning, and data-driven modeling.

math.NA↗

arXiv2025

Quantification of Electrolyte Degradation in Lithium-ion Batteries with Neutron Imaging Techniques

Non-destructive characterization of lithium-ion batteries provides critical insights for optimizing performance and lifespan while preserving structural integrity. Optimizing electrolyte design in commercial LIBs requires consideration of composition, electrolyte-to-capacity ratio, spatial distribution, and associated degradation pathways. However, existing non-destructive methods for studying electrolyte infiltration, distribution, and degradation in LIBs lack the spatiotemporal resolution required for precise observation and quantification of the electrolyte. In this study, we employ neutron imaging with sufficient spatial resolution ~150 um and large field of view 20x20 cm2 to quantitatively resolve the electrolyte inventory and distribution within LiFePO4/graphite pouch cells under high-temperature accelerated aging. Quantitative standard curves based on neutron transmission attenuation reveal a clear electrolyte dry-out threshold at 3.18 g Ah-1 and the two stages evolutions of EI during cell aging were quantified. By integrating non-destructive electrochemical diagnostics, accelerated graphite material loss and liquid phase Li+ diffusion degradation is observed during pore-drying. Further analysis, including operando cyclic aging, reveals that the neutron transmission below the saturation reference is due to the enrichment of hydrogen nuclei within the solid-electrolyte interphase. Assumed pore-drying does not occur, the SEI signal of the electrodes can be quantitatively decoupled during ageing. Combined analyses with NI, TOF-SIMS, and SEM reveal that high EI cells exhibit uniform SEI growth and reduced degradation, while low EI cells show uneven SEI formation, accelerating capacity loss. This study unveils a dynamic electrolyte infiltration-consumption-dry-out process in LIBs, offering non-destructive and quantitative insights to guide sustainable and durable battery development.

physics.app-ph↗

arXiv2025

BRIGHT: A globally distributed multimodal building damage assessment dataset with very-high-resolution for all-weather disaster response

Disaster events occur around the world and cause significant damage to human life and property. Earth observation (EO) data enables rapid and comprehensive building damage assessment (BDA), an essential capability in the aftermath of a disaster to reduce human casualties and to inform disaster relief efforts. Recent research focuses on the development of AI models to achieve accurate mapping of unseen disaster events, mostly using optical EO data. However, solutions based on optical data are limited to clear skies and daylight hours, preventing a prompt response to disasters. Integrating multimodal (MM) EO data, particularly the combination of optical and SAR imagery, makes it possible to provide all-weather, day-and-night disaster responses. Despite this potential, the development of robust multimodal AI models has been constrained by the lack of suitable benchmark datasets. In this paper, we present a BDA dataset using veRy-hIGH-resoluTion optical and SAR imagery (BRIGHT) to support AI-based all-weather disaster response. To the best of our knowledge, BRIGHT is the first open-access, globally distributed, event-diverse MM dataset specifically curated to support AI-based disaster response. It covers five types of natural disasters and two types of man-made disasters across 14 regions worldwide, with a particular focus on developing countries where external assistance is most needed. The optical and SAR imagery in BRIGHT, with a spatial resolution between 0.3-1 meters, provides detailed representations of individual buildings, making it ideal for precise BDA. In our experiments, we have tested seven advanced AI models trained with our BRIGHT to validate the transferability and robustness. The dataset and code are available at https://github.com/ChenHongruixuan/BRIGHT. BRIGHT also serves as the official dataset for the 2025 IEEE GRSS Data Fusion Contest.

cs.CV↗

arXiv2025

$M$-QR decomposition and hyperpower iterative methods for computing outer inverses of tensors

The outer inverse of tensors plays increasingly significant roles in computational mathematics, numerical analysis, and other generalized inverses of tensors. In this paper, we compute outer inverses with prescribed ranges and kernels of a given tensor through tensor QR decomposition and hyperpower iterative method under the M-product structure, which is a family of tensor-tensor products, generalization of the t-product and c-product, allows us to suit the physical interpretations across those different modes. We discuss a theoretical analysis of the nineteen-order convergence of the proposed tensor-based iterative method. Further, we design effective tensor-based algorithms for computing outer inverses using M-QR decomposition and hyperpower iterative method. The theoretical results are validated with numerical examples demonstrating the appropriateness of the proposed methods.

math.NA↗

arXiv2025

Algebraic Riccati Tensor Equations with Applications in Multilinear Control Systems

In a recent paper by Chen et al. [8], the authors initiated the control-theoretic study of a class of discrete-time multilinear time-invariant (MLTI) control systems, where system states, inputs, and outputs are all tensors endowed with the Einstein product. They established criteria for fundamental system-theoretic notions such as stability, reachability, and observability through tensor decomposition. Building on this new research direction, the purpose of our paper is to extend the study to continuous-time MLTI control systems. Specifically, we define Hamiltonian tensors and symplectic tensors, and we establish the Schur-Hamiltonian tensor decomposition and the symplectic tensor singular value decomposition (SVD). Based on these concepts, we propose the algebraic Riccati tensor equation (ARTE) and demonstrate that it has a unique positive semidefinite solution if the system is stabilizable and detectable. To find numerical solutions to the ARTE, we introduce a tensor-based Newton method. Additionally, we establish the tensor versions of the bounded real lemma and the small gain theorem. A first-order robustness analysis of the ARTE is also conducted. Finally, we provide a numerical example to illustrate the proposed theory and algorithms.

math.OC↗

arXiv2025

sparseGeoHOPCA: A Geometric Solution to Sparse Higher-Order PCA Without Covariance Estimation

We propose sparseGeoHOPCA, a novel framework for sparse higher-order principal component analysis (SHOPCA) that introduces a geometric perspective to high-dimensional tensor decomposition. By unfolding the input tensor along each mode and reformulating the resulting subproblems as structured binary linear optimization problems, our method transforms the original nonconvex sparse objective into a tractable geometric form. This eliminates the need for explicit covariance estimation and iterative deflation, enabling significant gains in both computational efficiency and interpretability, particularly in high-dimensional and unbalanced data scenarios. We theoretically establish the equivalence between the geometric subproblems and the original SHOPCA formulation, and derive worst-case approximation error bounds based on classical PCA residuals, providing data-dependent performance guarantees. The proposed algorithm achieves a total computational complexity of $O\left(\sum_{n=1}^{N} (k_n^3 + J_n k_n^2)\right)$, which scales linearly with tensor size. Extensive experiments demonstrate that sparseGeoHOPCA accurately recovers sparse supports in synthetic settings, preserves classification performance under 10$\times$ compression, and achieves high-quality image reconstruction on ImageNet, highlighting its robustness and versatility.

math.NA↗

arXiv2025

Efficient randomized algorithms for the fixed Tucker-rank problem of Tucker decomposition with adaptive shifts

Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem of Tucker decomposition, through the integration of adaptive shifted power iterations. The proposed algorithms enhance randomized variants of truncated high-order singular value decomposition (T-HOSVD) and sequentially T-HOSVD (ST-HOSVD) by incorporating dynamic shift strategies, which accelerate convergence by refining the singular value gap and reduce the number of required power iterations while maintaining accuracy. Theoretical analyses provide probabilistic error bounds, demonstrating that the proposed methods achieve comparable or superior accuracy compared to deterministic approaches. Numerical experiments on synthetic and real-world datasets validate the efficiency and robustness of the proposed algorithms, showing a significant decline in runtime and approximation error over state-of-the-art techniques.

math.NA↗

arXiv2025

SARLANG-1M: A Benchmark for Vision-Language Modeling in SAR Image Understanding

Synthetic Aperture Radar (SAR) is a crucial remote sensing technology, enabling all-weather, day-and-night observation with strong surface penetration for precise and continuous environmental monitoring and analysis. However, SAR image interpretation remains challenging due to its complex physical imaging mechanisms and significant visual disparities from human perception. Recently, Vision-Language Models (VLMs) have demonstrated remarkable success in RGB image understanding, offering powerful open-vocabulary interpretation and flexible language interaction. However, their application to SAR images is severely constrained by the absence of SAR-specific knowledge in their training distributions, leading to suboptimal performance. To address this limitation, we introduce SARLANG-1M, a large-scale benchmark tailored for multimodal SAR image understanding, with a primary focus on integrating SAR with textual modality. SARLANG-1M comprises more than 1 million high-quality SAR image-text pairs collected from over 59 cities worldwide. It features hierarchical resolutions (ranging from 0.1 to 25 meters), fine-grained semantic descriptions (including both concise and detailed captions), diverse remote sensing categories (1,696 object types and 16 land cover classes), and multi-task question-answering pairs spanning seven applications and 1,012 question types. Extensive experiments on mainstream VLMs demonstrate that fine-tuning with SARLANG-1M significantly enhances their performance in SAR image interpretation, reaching performance comparable to human experts. The dataset and code will be made publicly available at https://github.com/Jimmyxichen/SARLANG-1M.

cs.CV↗

arXiv2025

Tensor-based Model Reduction and Identification for Generalized Memory Polynomial

Power amplifiers (PAs) are essential components in wireless communication systems, and the design of their behavioral models has been an important research topic for many years. The widely used generalized memory polynomial (GMP) model suffers from rapid growth in the number of parameters with increasing memory depths and nonlinearity order, which leads to a significant increase in model complexity and the risk of overfitting. In this study, we introduce tensor networks to compress the unknown coefficient tensor of the GMP model, resulting in three novel tensor-based GMP models. These models can achieve comparable performance to the GMP model, but with far fewer parameters and lower complexity. For the identification of these models, we derive the alternating least-squares (ALS) method to ensure the rapid updates and convergence of model parameters in an iterative manner. In addition, we notice that the horizontal slices of the third-order data tensor constructed from the input signals are Vandermonde matrices, which have a numerically low-rank structure. Hence, we further propose the RP-ALS algorithm, which first performs a truncated higher-order singular value decomposition on the data tensor to generate random projections, then conducts the ALS algorithm for the identification of projected models with downscaled dimensions, thus reducing the computational effort of the iterative process. The experimental results show that the proposed models outperform the full GMP model and sparse GMP model via LASSO regression in terms of the reduction in the number of parameters and running complexity.

eess.SP↗

arXiv2025

Randomized algorithms for computing the tensor train approximation and their applications

In this paper, we focus on the fixed TT-rank and precision problems of finding an approximation of the tensor train (TT) decomposition of a tensor. Note that the TT-SVD and TT-cross are two well-known algorithms for these two problems. Firstly, by combining the random projection technique with the power scheme, we obtain two types of randomized algorithms for the fixed TT-rank problem. Secondly, by using the non-asymptotic theory of sub-random Gaussian matrices, we derive the upper bounds of the proposed randomized algorithms. Thirdly, we deduce a new deterministic strategy to estimate the desired TT-rank with a given tolerance and another adaptive randomized algorithm that finds a low TT-rank representation satisfying a given tolerance, and is beneficial when the target TT-rank is not known in advance. We finally illustrate the accuracy of the proposed algorithms via some test tensors from synthetic and real databases. In particular, for the fixed TT-rank problem, the proposed algorithms can be several times faster than the TT-SVD, and the accuracy of the proposed algorithms and the TT-SVD are comparable for several test tensors.

math.NA↗

arXiv2025

Coseparable Nonnegative Tensor Factorization With T-CUR Decomposition

Nonnegative Matrix Factorization (NMF) is an important unsupervised learning method to extract meaningful features from data. To address the NMF problem within a polynomial time framework, researchers have introduced a separability assumption, which has recently evolved into the concept of coseparability. This advancement offers a more efficient core representation for the original data. However, in the real world, the data is more natural to be represented as a multi-dimensional array, such as images or videos. The NMF's application to high-dimensional data involves vectorization, which risks losing essential multi-dimensional correlations. To retain these inherent correlations in the data, we turn to tensors (multidimensional arrays) and leverage the tensor t-product. This approach extends the coseparable NMF to the tensor setting, creating what we term coseparable Nonnegative Tensor Factorization (NTF). In this work, we provide an alternating index selection method to select the coseparable core. Furthermore, we validate the t-CUR sampling theory and integrate it with the tensor Discrete Empirical Interpolation Method (t-DEIM) to introduce an alternative, randomized index selection process. These methods have been tested on both synthetic and facial analysis datasets. The results demonstrate the efficiency of coseparable NTF when compared to coseparable NMF.

cs.LG↗

arXiv2025

OpenEarthMap-SAR: A Benchmark Synthetic Aperture Radar Dataset for Global High-Resolution Land Cover Mapping

High-resolution land cover mapping plays a crucial role in addressing a wide range of global challenges, including urban planning, environmental monitoring, disaster response, and sustainable development. However, creating accurate, large-scale land cover datasets remains a significant challenge due to the inherent complexities of geospatial data, such as diverse terrain, varying sensor modalities, and atmospheric conditions. Synthetic Aperture Radar (SAR) imagery, with its ability to penetrate clouds and capture data in all-weather, day-and-night conditions, offers unique advantages for land cover mapping. Despite these strengths, the lack of benchmark datasets tailored for SAR imagery has limited the development of robust models specifically designed for this data modality. To bridge this gap and facilitate advancements in SAR-based geospatial analysis, we introduce OpenEarthMap-SAR, a benchmark SAR dataset, for global high-resolution land cover mapping. OpenEarthMap-SAR consists of 1.5 million segments of 5033 aerial and satellite images with the size of 1024$\times$1024 pixels, covering 35 regions from Japan, France, and the USA, with partially manually annotated and fully pseudo 8-class land cover labels at a ground sampling distance of 0.15--0.5 m. We evaluated the performance of state-of-the-art methods for semantic segmentation and present challenging problem settings suitable for further technical development. The dataset also serves the official dataset for IEEE GRSS Data Fusion Contest Track I. The dataset has been made publicly available at https://zenodo.org/records/14622048.

eess.IV↗

arXiv2025

Effective algorithms for tensor train decomposition via the UTV framework

The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for constructing the TT format is the well-known TT-SVD method, which performs singular value decompositions (SVDs) on the successive matrices sequentially. But in practical applications, it is often unnecessary to compute full SVDs. In this article, we propose a new method called the TT-UTV. It utilizes the virtues of rank-revealing UTV decomposition to compute the TT format for a large-scale tensor, resulting in lower computational cost. We analyze the error bounds on the accuracy of these algorithms in both the URV and ULV cases and then recommend different sweep patterns for these two cases. Based on the theoretical analysis, we also formulate the rank-adaptive algorithms with prescribed accuracy. Numerical experiments on various applications, including magnetic resonance imaging data completion, are performed to illustrate their good performance in practice.

math.NA↗

arXiv2025

LU Decomposition and Generalized Autoone-Takagi Decomposition of Dual Matrices and their Applications

This paper uses matrix transformations to provide the Autoone-Takagi decomposition of dual complex symmetric matrices and extends it to dual quaternion $η$-Hermitian matrices. The LU decomposition of dual matrices is given using the general solution of the Sylvester equation, and its equivalence to the existence of rank-k decomposition and dual Moore-Penrose generalized inverse (DMPGI) is proved. Similar methods are then used to provide the Cholesky decomposition of dual real symmetric positive definite matrices. Both of our decompositions are driven by applications in numerical linear algebra.

math.NA↗