Optimal Transport Research Articles

Variate Associated Domain Adaptation for Unsupervised Multivariate Time Series Anomaly Detection

Multivariate Time Series Anomaly Detection (MTS-AD) is crucial for the effective management and maintenance of devices in complex systems such as server clusters, spacecrafts and financial systems etc. However, upgrade or cross-platform deployment of these devices will introduce the issue of cross-domain distribution shift, which leads to the prototypical problem of Domain Adaptation for MTS-AD. Compared with general domain adaptation problems, MTS-AD domain adaptation presents two peculiar challenges: 1) The dimensions of data from the source domain and the target domain are usually different, so alignment without losing any information is necessary. 2) The association between different variates plays a vital role in the MTS-AD task, which is overlooked by traditional domain adaptation approaches. Aiming at addressing the above issues, we propose a V ariate A ssociated domai N a D aptation method combined with a Gr A ph Deviation Network (abbreviated as VANDA ) for MTS-AD, which includes two major contributions. First, we characterize the intra-domain variate associations of the source domain by a graph deviation network (GDN), which can share parameters across domains without dimension alignment. Second, we propose a sliding similarity to measure the inter-domain variate associations and perform joint training by minimizing the optimal transport distance between source and target data for transferring variate associations across domains. VANDA achieves domain adaptation by transferring both variate associations and GDN parameters from the source domain to the target domain. We construct two pairs of MTS-AD datasets from existing MTS-AD data and combine three domain adaptation strategies with six MTS-AD backbones as the benchmark methods for experimental evaluation and comparison. Extensive experiments demonstrate the effectiveness of our approach, which outperforms the benchmark methods, and significantly improves the AD performance of the target domain by effectively utilizing the source domain knowledge.

Efficient Preconditioners for Solving Dynamical Optimal Transport via Interior Point Methods

Efficient Preconditioners for Solving Dynamical Optimal Transport via Interior Point Methods

Nonparametric measure-transportation-based methods for directional data

Abstract This article proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile contours and regions and closed-form formulas under the classical assumption of rotational symmetry. The empirical versions of our distribution functions enjoy the expected Glivenko–Cantelli property of traditional distribution functions. They provide fully distribution-free concepts of ranks and signs and define data-driven systems of (curvilinear) parallels and (hyper)meridians. Based on this, we also construct a universally consistent test of uniformity and a class of fully distribution-free and universally consistent tests for directional MANOVA which, in simulations, outperform all their existing competitors. A real-data example involving the analysis of sunspots concludes the article.

Optimal Transport Approaches for Cloud Fusion in 3D Reconstruction

Cloud fusion plays a crucial role in achieving accurate 3D models. This paper introduces two optimal transport-based approaches, Gaussian Fusion and Cyclical Fusion, to showcase the effectiveness of optimal transport in establishing dense correspondence among incoming 3D point clouds. These approaches encompass several important components. Firstly, the fusion correspondences are derived from the optimal transport problem. The core principle of Gaussian Fusion and Cyclical Fusion involves manipulating points along geodesic curves to effectively leverage significant local geometric information. Secondly, this paper explores the fundamental concepts underlying Gaussian Fusion (displacement interpolation) and Cyclical Fusion (cyclical monotonicity), which greatly enhance the accuracy and completeness of the reconstruction process. And provides evidence for the uniqueness of displacement interpolation as geodesics on L2-Wasserstein space and the rationality of cyclical monotonicity in this context. Finally, the proposed approaches excel in capturing intricate surface details, particularly on small objects, when compared to the original fusion scheme which often introduces severe artifacts.

On the convergence of discrete dynamic unbalanced transport models

A generalized unbalanced optimal transport distance WBΛ on matrix-valued measures M(Ω, 𝕊n+) was defined in Li and Zou (arXiv:2011.05845) à la Benamou–Brenier, which extends the Kantorovich–Bures and the Wasserstein–Fisher–Rao distances. In this work, we investigate the convergence properties of the discrete transport problems associated with WBΛ. We first present a convergence framework for abstract discretization. Then, we propose a specific discretization scheme that aligns with this framework, whose convergence relies on the assumption that the initial and final distributions are absolutely continuous with respect to the Lebesgue measure. Further, in the case of the Wasserstein–Fisher–Rao distance, thanks to the static formulation, we show that such an assumption can be removed.

Empirical optimal transport between different measures adapts to lower complexity

Empirical optimal transport between different measures adapts to lower complexity

Improved object detection method for unmanned driving based on Transformers.

The object detection method serves as the core technology within the unmanned driving perception module, extensively employed for detecting vehicles, pedestrians, traffic signs, and various objects. However, existing object detection methods still encounter three challenges in intricate unmanned driving scenarios: unsatisfactory performance in multi-scale object detection, inadequate accuracy in detecting small objects, and occurrences of false positives and missed detections in densely occluded environments. Therefore, this study proposes an improved object detection method for unmanned driving, leveraging Transformer architecture to address these challenges. First, a multi-scale Transformer feature extraction method integrated with channel attention is used to enhance the network's capability in extracting features across different scales. Second, a training method incorporating Query Denoising with Gaussian decay was employed to enhance the network's proficiency in learning representations of small objects. Third, a hybrid matching method combining Optimal Transport and Hungarian algorithms was used to facilitate the matching process between predicted and actual values, thereby enriching the network with more informative positive sample features. Experimental evaluations conducted on datasets including KITTI demonstrate that the proposed method achieves 3% higher mean Average Precision (mAP) than that of the existing methodologies.

Disentangle Then Calibrate With Gradient Guidance: A Unified Framework for Common and Rare Disease Diagnosis.

The computer-aided diagnosis (CAD) for rare diseases using medical imaging poses a significant challenge due to the requirement of large volumes of labeled training data, which is particularly difficult to collect for rare diseases. Although Few-shot learning (FSL) methods have been developed for this task, these methods focus solely on rare disease diagnosis, failing to preserve the performance in common disease diagnosis. To address this issue, we propose the Disentangle then Calibrate with Gradient Guidance (DCGG) framework under the setting of generalized few-shot learning, i.e., using one model to diagnose both common and rare diseases. The DCGG framework consists of a network backbone, a gradient-guided network disentanglement (GND) module, and a gradient-induced feature calibration (GFC) module. The GND module disentangles the network into a disease-shared component and a disease-specific component based on gradient guidance, and devises independent optimization strategies for both components, respectively, when learning from rare diseases. The GFC module transfers only the disease-shared channels of common-disease features to rare diseases, and incorporates the optimal transport theory to identify the best transport scheme based on the semantic relationship among different diseases. Based on the best transport scheme, the GFC module calibrates the distribution of rare-disease features at the disease-shared channels, deriving more informative rare-disease features for better diagnosis. The proposed DCGG framework has been evaluated on three public medical image classification datasets. Our results suggest that the DCGG framework achieves state-of-the-art performance in diagnosing both common and rare diseases.

Optimal transport strategy-based meta-attention network for fault diagnosis of rotating machinery with zero sample

Optimal transport strategy-based meta-attention network for fault diagnosis of rotating machinery with zero sample

Non‐Euclidean Sliced Optimal Transport Sampling

AbstractIn machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well‐dispersed collection of samples. Providing a formal metric for measuring the distance between probability measures on general spaces, Optimal Transport (OT) emerges as a pivotal theoretical framework within this context. However, the associated computational burden is prohibitive in most real‐world scenarios. Leveraging the simple structure of OT in 1D, Sliced Optimal Transport (SOT) has appeared as an efficient alternative to generate samples in Euclidean spaces. This paper pushes the boundaries of SOT utilization in computational geometry problems by extending its application to sample densities residing on more diverse mathematical domains, including the spherical space 𝕊d, the hyperbolic plane ℍd, and the real projective plane ℙd. Moreover, it ensures the quality of these samples by achieving a blue noise characteristic, regardless of the dimensionality involved. The robustness of our approach is highlighted through its application to various geometry processing tasks, such as the intrinsic blue noise sampling of meshes, as well as the sampling of directions and rotations. These applications collectively underscore the efficacy of our methodology.

Learning quantum many-body systems from a few copies

Estimating physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. In this work, we identify conditions on states under which it is possible to infer the expectation values of all quasi-local observables of a state from a number of copies that scales polylogarithmically with the system's size and polynomially on the locality of the target observables. We show that this constitutes a provable exponential improvement in the number of copies over state-of-the-art tomography protocols. We achieve our results by combining the maximum entropy method with tools from the emerging fields of classical shadows and quantum optimal transport. The latter allows us to fine-tune the error made in estimating the expectation value of an observable in terms of how local it is and how well we approximate the expectation value of a fixed set of few-body observables. We conjecture that our condition holds for all states exhibiting some form of decay of correlations and establish it for several subsets thereof. These include widely studied classes of states such as one-dimensional thermal and high-temperature Gibbs states of local commuting Hamiltonians on arbitrary hypergraphs or outputs of shallow circuits. Moreover, we show improvements of the maximum entropy method beyond the sample complexity that are of independent interest. These include identifying regimes in which it is possible to perform the postprocessing efficiently as well as novel bounds on the condition number of covariance matrices of many-body states.

Confinement-induced drift in Marangoni-driven transport of surfactant: a Lagrangian perspective

Successive drops of coloured ink mixed with surfactant are deposited onto a thin film of water to create marbling patterns in the Japanese art technique of Suminagashi. To understand the physics behind this and other applications where surfactant transports adsorbed passive matter at gas–liquid interfaces, we investigate the Lagrangian trajectories of material particles on the surface of a thin film of a confined viscous liquid under Marangoni-driven spreading by an insoluble surfactant. We study a model problem in which several deposits of exogenous surfactant simultaneously spread on a bounded rectangular surface containing a pre-existing endogenous surfactant. We derive Eulerian and Lagrangian formulations of the equations governing the Marangoni-driven surface flow. Both descriptions show how confinement can induce drift and flow reversal during spreading. The Lagrangian formulation captures trajectories without the need to calculate surfactant concentrations; however, concentrations can still be inferred from the Jacobian of the map from initial to current particle position. We explore a link between thin-film surfactant dynamics and optimal transport theory to find the approximate equilibrium locations of material particles for any given initial condition by solving a Monge–Ampère equation. We find that as the endogenous surfactant concentration $\delta$ vanishes, the equilibrium shapes of deposits using the Monge–Ampère approximation approach polygons with corners curving in a self-similar manner over lengths scaling as $\delta ^{1/2}$ . We explore how Suminagashi patterns may be produced by using computationally efficient successive solutions of the Monge–Ampère equation.

The Inverse of Exact Renormalization Group Flows as Statistical Inference.

We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection-diffusion equation. We provide a new information-theoretic perspective for understanding the ERG through the intermediary of Bayesian Statistical Inference. This connection is facilitated by the Dynamical Bayesian Inference scheme, which encodes Bayesian inference in the form of a one-parameter family of probability distributions solving an integro-differential equation derived from Bayes' law. In this note, we demonstrate how the Dynamical Bayesian Inference equation is, itself, equivalent to a diffusion equation, which we dub Bayesian Diffusion. By identifying the features that define Bayesian Diffusion and mapping them onto the features that define the ERG, we obtain a dictionary outlining how renormalization can be understood as the inverse of statistical inference.

Development and Study of Novel Ultrafiltration Membranes Based on Cellulose Acetate.

Recently, increasing attention of researchers in the field of membrane technology has been paid to the development of membranes based on biopolymers. One of the well-proven polymers for the development of porous membranes is cellulose acetate (CA). This paper is devoted to the study of the influence of different parameters on ultrafiltration CA membrane formation and their transport properties, such as the variation in coagulation bath temperature, membrane shrinkage (post-treatment at 80 °C), introduction to casting CA solution of polymers (polyethylene glycol (PEG), polysulfone (PS), and Pluronic F127 (PL)) and carbon nanoparticles (SWCNTs, MWCNTs, GO, and C60). The structural and physicochemical properties of developed membranes were studied by scanning electron and atomic force microscopies, Fourier-transform infrared spectroscopy, X-ray photoelectron spectroscopy, and contact angle measurements. The transport properties of developed CA-based membranes were evaluated in ultrafiltration of bovine serum albumin (BSA), dextran 110 and PVP K-90. All developed membranes rejected 90% compounds with a molecular weight from ~270,000 g/mol. It was shown that the combination of modifications (addition of PEG, PS, PL, PS-PL, and 0.5 wt% C60) led to an increase in the fluxes and BSA rejection coefficients with slight decrease in the flux recovery ratio. These changes were due to an increased macrovoid number, formation of a more open porous structure and/or thinner top selective, and decreased surface roughness and hydrophobization during C60 modification of blend membranes. Optimal transport properties were found for CA-PEG+C60 (the highest water-394 L/(m2h) and BSA-212 L/(m2h) fluxes) and CA-PS+C60 (maximal rejection coefficient of BSA-59%) membranes.

Use of criteria for process optimization elevator complex routing

The goal of the work. The purpose of this work is to describe the optimality criteria for determining the direction of solving the problem of optimizing transport and technological routes of grain products at the elevator complex. Research methods. An analytical research method was applied to determine the technological characteristics of the elevator complex line and the dependence of the quality of transported products on the constructed transportation route. A mathematical method is applied to describe the constituent elements of the optimization criteria. Obtained results. One of the directions for increasing and improving the technological process at the elevator was determined, by improving the control algorithms in the direction of optimizing the technological processes of the elevator according to many criteria. According to optimization criteria, to ensure optimal transportation conditions, minimum losses, minimum transportation time, minimum energy consumption, and minimum length of the laid transportation path should be used, therefore, a description of the main criteria that can primarily affect the efficiency of the elevator complex was performed. Scientific news. The direction of solving the problem of optimization of transport and technological routes is determined. Analytical derivation of the minimum energy consumption criterion and the minimum grain fight criterion. Practical value. Optimization of the elevator complex to ensure variable transportation of grain masses, which will affect the productivity and quality of the technological process of the elevator complex.

Charging Station Site Selection Optimization for Electric Logistics Vehicles, Taking into Account Time-Window and Load Constraints

In order to improve the efficiency of the “last-mile” distribution in urban logistics and solve the problem of the difficult charging of electric logistics vehicles (ELVs), this paper proposes a charging station location optimization scheme for ELVs that takes into account time-window and load constraints (TW-LCs). Taking the optimal transportation path as the objective function and considering the time-window and vehicle load constraints, a charging station siting model was established. For the TW-LC problem, an improved genetic algorithm combining the farthest-insertion heuristic idea and local search operation was designed. Three different types of standardized arithmetic examples, C type, R type, and RC type, were used to test the proposed algorithm and compare it with the traditional genetic algorithm. The results indicate that, under the same conditions, compared to the traditional genetic algorithm, the improved genetic algorithm reduced the optimal path length by an average of 11.12%. It also decreased the number of charging stations selected, the number of vehicles in use, and the algorithm complexity by 22.97%, 13.71%, and 46.81%. Building on this, a case study was conducted on the TW-LC problem in a specific area of Chongqing, China. It resulted in a 50% reduction in the number of charging stations and a 25% reduction in the number of vehicles selected. In terms of economic indicators, the proposed algorithm improves unit electricity sales by 73.88% and reduces the total annualized cost of the logistics company by 18.81%, providing a theoretical basis for the subsequent promotion of ELVs.

Distributionally robust chance-constrained optimization with Gaussian mixture ambiguity set

Conventional chance-constrained programming methods suffer from the inexactness of the estimated probability distribution of the underlying uncertainty from data. To this end, a distributionally robust approach to the problem allows for a level of ambiguity considered around a reference distribution. In this work, we propose a novel formulation for the distributionally robust chance-constrained programming problem using an ambiguity set constructed from a variant of optimal transport distance that was developed for Gaussian Mixture Models. We show that for multimodal process uncertainty, our proposed method provides an effective way to incorporate statistical moment information into the ambiguity set construction step, thus leading to improved optimal solutions. We illustrate the performance of our method on a numerical example as well as a chemical process case study. We show that our proposed methodology leverages the multimodal characteristics from the uncertainty data to give superior performance over the traditional Wasserstein distance-based method.

Entropic transfer operators

We propose a new concept for the regularization and discretization of transfer and Koopman operators in dynamical systems. Our approach is based on the entropically regularized optimal transport between two probability measures. In particular, we use optimal transport plans in order to construct a finite-dimensional approximation of some transfer or Koopman operator which can be analyzed computationally. We prove that the spectrum of the discretized operator converges to the one of the regularized original operator, give a detailed analysis of the relation between the discretized and the original peripheral spectrum for a rotation map on the n-torus and provide code for three numerical experiments, including one based on the raw trajectory data of a small biomolecule from which its dominant conformations are recovered.

A System of IoT Devices to Prevent the Underloading And Overloading of Railway Wagons

Coal transportation poses substantial obstacles for corporations such as Coal India Limited (CIL), including concerns with route selection, rehandling, precise weighing, demurrage costs, and underloading fines. CIL's failure to adopt optimal transportation routes has resulted in needless costs. Coal rehandling at depots has proven expensive, and there are disparities in coal transportation rates. The lack of weighbridges makes accurate weighing difficult, resulting in probable pilferage. Demurrage costs have been a financial hardship, and railway carriages underloaded have resulted in fines. To address these challenges, the proposed IoT solution seeks to reduce financial losses, improve operational efficiency, increase accountability, ensure regulatory compliance, provide real-time monitoring, automate alerts and penalties, improve communication, improve data security, provide multilingual support, and, ultimately, increase revenue. This idea aims to change coal transportation by increasing efficiency, transparency, and cost-effectiveness for CIL and the government. However, it incurs initial expenses and complications associated with IoT deployment, maintenance, and regulatory compliance. Keywords: CIL, IOT, efficiency, pilferage.

ScPRAM accurately predicts single-cell gene expression perturbation response based on attention mechanism.

With the rapid advancement of single-cell sequencing technology, it becomes gradually possible to delve into the cellular responses to various external perturbations at the gene expression level. However, obtaining perturbed samples in certain scenarios may be considerably challenging, and the substantial costs associated with sequencing also curtail the feasibility of large-scale experimentation. A repertoire of methodologies has been employed for forecasting perturbative responses in single-cell gene expression. However, existing methods primarily focus on the average response of a specific cell type to perturbation, overlooking the single-cell specificity of perturbation responses and a more comprehensive prediction of the entire perturbation response distribution. Here, we present scPRAM, a method for predicting perturbation responses in single-cell gene expression based on attention mechanisms. Leveraging variational autoencoders and optimal transport, scPRAM aligns cell states before and after perturbation, followed by accurate prediction of gene expression responses to perturbations for unseen cell types through attention mechanisms. Experiments on multiple real perturbation datasets involving drug treatments and bacterial infections demonstrate that scPRAM attains heightened accuracy in perturbation prediction across cell types, species, and individuals, surpassing existing methodologies. Furthermore, scPRAM demonstrates outstanding capability in identifying differentially expressed genes under perturbation, capturing heterogeneity in perturbation responses across species, and maintaining stability in the presence of data noise and sample size variations. https://github.com/jiang-q19/scPRAM and https://doi.org/10.5281/zenodo.10935038.