arXiv subjects

Zhongming Chen

Publications and source records attributed to Zhongming Chen.

At least 19 recordsLinked to original sources

arXiv2026

Maximum-distance nonnegative matrix factorization for unmixing highly mixed grain-size distribution data: A generalization of AnalySize

Nonnegative matrix factorization (NMF) decomposes a nonnegative matrix into the product of two nonnegative matrices. This property makes NMF well suited for unmixing grain-size distribution data, which are inherently nonnegative and have row sums equal to one. Previous studies have shown that AnalySize, an NMF-based method, performs well on poorly mixed grain-size distribution data but struggles when the data is highly mixed, where no observed samples are close to the true end members. To overcome this limitation, we introduce a maximum-distance NMF that encourages the estimated end members to be as distinct as possible and develop a hierarchical alternating least squares algorithm for optimization. The proposed formulation can be regarded as a generalization of AnalySize, where AnalySize minimizes the distance among end members while the proposed method maximizes it. Experimental results demonstrate that the method effectively decomposes highly mixed grain-size distribution data.

cs.LG↗

arXiv2026

Life 2.0: A Scalable Distributed Space-Telescope Array for Biosignature Spectroscopy

Answering the question "Are we alone?" requires atmospheric spectroscopy of nearby terrestrial planets. For an Earth--Sun analog, even the strongest transmission signals are expected to be of order 1 part per million (ppm). Unlike short-period planets, Earth 2.0 planets transit only about once per year, so single-transit sensitivity, rather than stacking repeated observations, is the fundamental design driver. Life 2.0 is a scalable space-mission concept linking Earth 2.0 candidates discovered by PLATO and the Earth 2.0 (ET) mission with atmospheric characterization and biosignature assessment. The baseline architecture comprises 900 one-meter space telescopes, each equipped with a high-throughput Waveguide Integrated Miniature Spectrograph and an ultra-low-read-noise CMOS detector. After independent calibration, spectra acquired simultaneously during a transit are combined, providing the photon-collecting capability of an approximately 30-m aperture at the selected spectral resolution while retaining a modular architecture. The baseline 0.2--1.05 $μ$m range covers O$_3$, O$_2$, H$_2$O, Rayleigh scattering, and other diagnostics, with extension into the infrared as detector technologies mature. Prototype Waveguide Spectral Lens devices have demonstrated 40--66\% throughput at resolving powers from $R \sim 200$ to $R \sim 20{,}000$. Lightweight silicon-carbide mirrors and sub-electron-noise CMOS detectors support replicated production. Life 2.0 must address detector systematics, instrument stability, and stellar variability; rather than assuming these limitations disappear, it builds on calibration, detector-characterization, and data-analysis techniques advanced during the JWST era. The concept offers a scalable alternative to a monolithic 30-m-class space telescope and a staged pathway toward biosignature spectroscopy of nearby Earth-like planets.

astro-ph.IM↗

arXiv2026

Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry

Owing to the effectiveness of Tensor Train (TT) decomposition in managing high-order tensors, low-rank tensor completion within the TT-format has emerged as a prominent research focus. In this paper, we leverage the left-orthogonal property of the TT-decomposition to construct a novel quotient manifold and introduce a family of admissible Riemannian metrics. Within this geometric framework, we propose a new approach to constructing retractions compatible with the quotient structure, realized via two novel retractions based on recursive polar and QR decompositions that respect the recursive orthogonalization structure of the TT format. We then derive Riemannian gradient descent and conjugate gradient methods to solve the tensor completion problem. Theoretically, our approach streamlines the horizontal projection by reducing the number of unknowns per block from a quadratic dependence on the TT-ranks to a near-half scaling, thereby enhancing computational efficiency over conventional quotient-based methods. Numerical experiments demonstrate that the proposed algorithms achieve reconstruction accuracy comparable to state-of-the-art TT-based geometric methods.

math.NA↗

arXiv2026

Identification of NMF by choosing maximum-volume basis vectors

In nonnegative matrix factorization (NMF), minimum-volume-constrained NMF is a widely used framework for identifying the solution of NMF by making basis vectors as similar as possible. This typically induces sparsity in the coefficient matrix, with each row containing zero entries. Consequently, minimum-volume-constrained NMF may fail for highly mixed data, where such sparsity does not hold. Moreover, the estimated basis vectors in minimum-volume-constrained NMF may be difficult to interpret as they may be mixtures of the ground truth basis vectors. To address these limitations, in this paper we propose a new NMF framework, called maximum-volume-constrained NMF, which makes the basis vectors as distinct as possible. We further establish an identifiability theorem for maximum-volume-constrained NMF and provide an algorithm to estimate it. Experimental results demonstrate the effectiveness of the proposed method.

cs.LG↗

arXiv2026

Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimization

Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical interpretability. This paper systematically studies matrix product states (MPS) for generative modeling and shows that unitary MPS, which is a tensor-network architecture that is both simple and expressive, offers clear benefits for unsupervised learning by reducing ambiguity in parameter updates and improving efficiency. To overcome the inefficiency of standard gradient-based MPS training, we develop a Riemannian optimization approach that casts probabilistic modeling as an optimization problem with manifold constraints, and further derive an efficient space-decoupling algorithm. Experiments on Bars-and-Stripes and EMNIST datasets demonstrate fast adaptation to data structure, stable updates, and strong performance while maintaining the efficiency and expressive power of MPS.

cs.LG↗

arXiv2026

Unmixing highly mixed grain size distribution data via maximum volume constrained end member analysis

End member analysis (EMA) unmixes grain size distribution (GSD) data into a mixture of end members (EMs), thus helping understand sediment provenance and depositional regimes and processes. In highly mixed data sets, however, many EMA algorithms find EMs which are still a mixture of true EMs. To overcome this, we propose maximum volume constrained EMA (MVC-EMA), which finds EMs as different as possible. We provide a uniqueness theorem and a quadratic programming algorithm for MVC-EMA. Experimental results show that MVC-EMA can effectively find true EMs in highly mixed data sets.

stat.ME↗

arXiv2025

The 1st International Workshop on Disentangled Representation Learning for Controllable Generation (DRL4Real): Methods and Results

This paper reviews the 1st International Workshop on Disentangled Representation Learning for Controllable Generation (DRL4Real), held in conjunction with ICCV 2025. The workshop aimed to bridge the gap between the theoretical promise of Disentangled Representation Learning (DRL) and its application in realistic scenarios, moving beyond synthetic benchmarks. DRL4Real focused on evaluating DRL methods in practical applications such as controllable generation, exploring advancements in model robustness, interpretability, and generalization. The workshop accepted 9 papers covering a broad range of topics, including the integration of novel inductive biases (e.g., language), the application of diffusion models to DRL, 3D-aware disentanglement, and the expansion of DRL into specialized domains like autonomous driving and EEG analysis. This summary details the workshop's objectives, the themes of the accepted papers, and provides an overview of the methodologies proposed by the authors.

cs.LG↗

arXiv2024

Two-stream joint matching method based on contrastive learning for few-shot action recognition

Although few-shot action recognition based on metric learning paradigm has achieved significant success, it fails to address the following issues: (1) inadequate action relation modeling and underutilization of multi-modal information; (2) challenges in handling video matching problems with different lengths and speeds, and video matching problems with misalignment of video sub-actions. To address these issues, we propose a Two-Stream Joint Matching method based on contrastive learning (TSJM), which consists of two modules: Multi-modal Contrastive Learning Module (MCL) and Joint Matching Module (JMM). The objective of the MCL is to extensively investigate the inter-modal mutual information relationships, thereby thoroughly extracting modal information to enhance the modeling of action relationships. The JMM aims to simultaneously address the aforementioned video matching problems. The effectiveness of the proposed method is evaluated on two widely used few shot action recognition datasets, namely, SSv2 and Kinetics. Comprehensive ablation experiments are also conducted to substantiate the efficacy of our proposed approach.

cs.CV↗

arXiv2023

Low-rank Tensor Train Decomposition Using TensorSketch

Tensor train decomposition is one of the most powerful approaches for processing high-dimensional data. For low-rank tensor train decomposition of large tensors, the alternating least squares (ALS) algorithm is widely used by updating each core tensor alternatively. However, it may suffer from the curse of dimensionality due to the large scale of subproblems. In this paper, a novel randomized proximal ALS algorithm is proposed for low-rank tensor train decomposition by using TensorSketch, which allows for efficient implementation via fast Fourier transform. The theoretical lower bounds of sketch size are estimated for approximating the optimal value of subproblems. Numerical experiments on synthetic and real-world data also demonstrate the effectiveness and efficiency of the proposed algorithm.

math.NA↗

arXiv2023

A Randomized Block Krylov Method for Tensor Train Approximation

Tensor train decomposition is a powerful tool for dealing with high-dimensional, large-scale tensor data, which is not suffering from the curse of dimensionality. To accelerate the calculation of the auxiliary unfolding matrix, some randomized algorithms have been proposed; however, they are not suitable for noisy data. The randomized block Krylov method is capable of dealing with heavy-tailed noisy data in the low-rank approximation of matrices. In this paper, we present a randomized algorithm for low-rank tensor train approximation of large-scale tensors based on randomized block Krylov subspace iteration and provide theoretical guarantees. Numerical experiments on synthetic and real-world tensor data demonstrate the effectiveness of the proposed algorithm.

math.NA↗

arXiv2022

A regularization-patching dual quaternion optimization method for solving the hand-eye calibration problem

The hand-eye calibration problem is an important application problem in robot research. Based on the 2-norm of dual quaternion vectors, we propose a new dual quaternion optimization method for the hand-eye calibration problem. The dual quaternion optimization problem is decomposed to two quaternion optimization subproblems. The first quaternion optimization subproblem governs the rotation of the robot hand. It can be solved efficiently by the eigenvalue decomposition or singular value decomposition. If the optimal value of the first quaternion optimization subproblem is zero, then the system is rotationwise noiseless, i.e., there exists a ``perfect'' robot hand motion which meets all the testing poses rotationwise exactly. In this case, we apply the regularization technique for solving the second subproblem to minimize the distance of the translation. Otherwise we apply the patching technique to solve the second quaternion optimization subproblem. Then solving the second quaternion optimization subproblem turns out to be solving a quadratically constrained quadratic program. In this way, we give a complete description for the solution set of hand-eye calibration problems. This is new in the hand-eye calibration literature. The numerical results are also presented to show the efficiency of the proposed method.

cs.RO↗

arXiv2022

Forcing the Whole Video as Background: An Adversarial Learning Strategy for Weakly Temporal Action Localization

With video-level labels, weakly supervised temporal action localization (WTAL) applies a localization-by-classification paradigm to detect and classify the action in untrimmed videos. Due to the characteristic of classification, class-specific background snippets are inevitably mis-activated to improve the discriminability of the classifier in WTAL. To alleviate the disturbance of background, existing methods try to enlarge the discrepancy between action and background through modeling background snippets with pseudo-snippet-level annotations, which largely rely on artificial hypotheticals. Distinct from the previous works, we present an adversarial learning strategy to break the limitation of mining pseudo background snippets. Concretely, the background classification loss forces the whole video to be regarded as the background by a background gradient reinforcement strategy, confusing the recognition model. Reversely, the foreground(action) loss guides the model to focus on action snippets under such conditions. As a result, competition between the two classification losses drives the model to boost its ability for action modeling. Simultaneously, a novel temporal enhancement network is designed to facilitate the model to construct temporal relation of affinity snippets based on the proposed strategy, for further improving the performance of action localization. Finally, extensive experiments conducted on THUMOS14 and ActivityNet1.2 demonstrate the effectiveness of the proposed method.

cs.CV↗

arXiv2022

Low Rank Approximation of Dual Complex Matrices

Dual complex numbers can represent rigid body motion in 2D spaces. Dual complex matrices are linked with screw theory, and have potential applications in various areas. In this paper, we study low rank approximation of dual complex matrices. We define $2$-norm for dual complex vectors, and Frobenius norm for dual complex matrices. These norms are nonnegative dual numbers. We establish the unitary invariance property of dual complex matrices. We study eigenvalues of square dual complex matrices, and show that an $n \times n$ dual complex Hermitian matrix has exactly $n$ eigenvalues, which are dual numbers. We present a singular value decomposition (SVD) theorem for dual complex matrices, define ranks and appreciable ranks for dual complex matrices, and study their properties. We establish an Eckart-Young like theorem for dual complex matrices, and present an algorithm framework for low rank approximation of dual complex matrices via truncated SVD. The SVD of dual complex matrices also provides a basic tool for Principal Component Analysis (PCA) via these matrices. Numerical experiments are reported.

math.NA↗

arXiv2018

Two Irreducible Functional Bases of Isotropic Invariants of A Fourth Order Three-Dimensional Symmetric and Traceless Tensor

The elasticity tensor is one of the most important fourth order tensors in mechanics. Fourth order three-dimensional symmetric and traceless tensors play a crucial role in the study of the elasticity tensors. In this paper, we present two isotropic irreducible functional bases of a fourth order three-dimensional symmetric and traceless tensor. One of them is the minimal integrity basis introduced by Smith and Bao in 1997. It has nine homogeneous polynomial invariants of degrees two, three, four, five, six, seven, eight, nine and ten, respectively. We prove that it is also an irreducible functional basis. The second irreducible functional basis also has nine homogeneous polynomial invariants. It has no quartic invariant but has two sextic invariants. The other seven invariants are the same as those of the Smith-Bao basis. Hence, the second irreducible functional basis is not contained in any minimal integrity basis.

math-ph↗

arXiv2018

An Irreducible Function Basis of Isotropic Invariants of A Third Order Three-Dimensional Symmetric Tensor

In this paper, we present an eleven invariant isotropic irreducible function basis of a third order three-dimensional symmetric tensor. This irreducible function basis is a proper subset of the Olive-Auffray minimal isotropic integrity basis of that tensor. The octic invariant and a sextic invariant in the Olive-Auffray integrity basis are dropped out. This result is of significance to the further research of irreducible function bases of higher order tensors.

math-ph↗

arXiv2017

Parallelized Tensor Train Learning of Polynomial Classifiers

In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support vector machines, because polynomials quickly become impractical for high-dimensional problems. In this paper, we effectively overcome the curse of dimensionality by employing the tensor train format to represent a polynomial classifier. Based on the structure of tensor trains, two learning algorithms are proposed which involve solving different optimization problems of low computational complexity. Furthermore, we show how both regularization to prevent overfitting and parallelization, which enables the use of large training sets, are incorporated into these methods. Both the efficiency and efficacy of our tensor-based polynomial classifier are then demonstrated on the two popular datasets USPS and MNIST.

cs.LG↗

arXiv2016

Tensor Network alternating linear scheme for MIMO Volterra system identification

This article introduces two Tensor Network-based iterative algorithms for the identification of high-order discrete-time nonlinear multiple-input multiple-output (MIMO) Volterra systems. The system identification problem is rewritten in terms of a Volterra tensor, which is never explicitly constructed, thus avoiding the curse of dimensionality. It is shown how each iteration of the two identification algorithms involves solving a linear system of low computational complexity. The proposed algorithms are guaranteed to monotonically converge and numerical stability is ensured through the use of orthogonal matrix factorizations. The performance and accuracy of the two identification algorithms are illustrated by numerical experiments, where accurate degree-10 MIMO Volterra models are identified in about 1 second in Matlab on a standard desktop pc.

math.NA↗

arXiv2016

A Tensor Network Kalman filter with an application in recursive MIMO Volterra system identification

This article introduces a Tensor Network Kalman filter, which can estimate state vectors that are exponentially large without ever having to explicitly construct them. The Tensor Network Kalman filter also easily accommodates the case where several different state vectors need to be estimated simultaneously. The key lies in rewriting the standard Kalman equations as tensor equations and then implementing them using Tensor Networks, which effectively transforms the exponential storage cost and computational complexity into a linear one. We showcase the power of the proposed framework through an application in recursive nonlinear system identification of high-order discrete-time multiple-input multiple-output (MIMO) Volterra systems. The identification problem is transformed into a linear state estimation problem wherein the state vector contains all Volterra kernel coefficients and is estimated using the Tensor Network Kalman filter. The accuracy and robustness of the scheme are demonstrated via numerical experiments, which show that updating the Kalman filter estimate of a state vector of length $10^9$ and its covariance matrix takes about 0.007s on a standard desktop computer in Matlab.

eess.SY↗