相关论文: Snapshot-driven Rational Interpolation of Parametr…

It is often of interest to infer lower-dimensional structure underlying complex data. As a flexible class of non-linear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the…

Classically, data interpolation with a parametrized model class is possible as long as the number of parameters is larger than the number of equations to be satisfied. A puzzling phenomenon in deep learning is that models are trained with…

Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…

Random graph models are widely used to understand network properties and graph algorithms. Key to such analyses are the different parameters of each model, which affect various network features, such as its size, clustering, or degree…

Fitting a data set with a parametrized model can be seen geometrically as finding the global minimum of the chi^2 hypersurface, depending on a set of parameters {P_i}. This is usually done using the Levenberg-Marquardt algorithm. The main…

We develop a unifying framework for interpolatory $\mathcal{L}_2$-optimal reduced-order modeling for a wide classes of problems ranging from stationary models to parametric dynamical systems. We first show that the framework naturally…

The overdraw problem of scatterplots seriously interferes with the visual tasks. Existing methods, such as data sampling, node dispersion, subspace mapping, and visual abstraction, cannot guarantee the correspondence and consistency between…

High-dimensional multivariate time series are common in many scientific and industrial applications, where the interest lies in identifying key dependence structure within the data for subsequent analysis tasks, such as forecasting. An…

We investigate the problem of localizing multiple targets using a single set of measurements from a network of radar sensors. Such "single snapshot imaging" provides timely situational awareness, but can utilize neither platform motion, as…

Optical flow estimation is a fundamental task in computer vision. Recent direct-regression methods using deep neural networks achieve remarkable performance improvement. However, they do not explicitly capture long-term motion…

We introduce a new spectral method for image segmentation that incorporates long range relationships for global appearance modeling. The approach combines two different graphs, one is a sparse graph that captures spatial relationships…

Adapting neural networks to new tasks typically requires task-specific fine-tuning, which is time-consuming and reliant on labeled data. We explore a generative alternative that produces task-specific parameters directly from task identity,…

We deal with the minimization of the ${\mathcal H}_\infty$-norm of the transfer function of a parameter-dependent descriptor system over the set of admissible parameter values. Subspace frameworks are proposed for such minimization problems…

In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are…

Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are…

Non-uniform fast Fourier Transform (NUFFT) and inverse NUFFT (INUFFT) algorithms, based on the Fast Multipole Method (FMM) are developed and tested. Our algorithms are based on a novel factorization of the FFT kernel, and are implemented…

Presented is a novel way to combine snapshot compressive imaging and lateral shearing interferometry in order to capture the spatio-spectral phase of an ultrashort laser pulse in a single shot. A deep unrolling algorithm is utilised for the…

We discuss the nonlinear phenomena of irreversible tipping for non-autonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We express tipping in terms of pullback…

We introduce a method for deterministic decoupling of global features and show its applicability to improve data analysis performance, as well as to open new venues for feature transfer. We propose a new formalism that is based on defining…

Snapshot matrices built from solutions to hyperbolic partial differential equations exhibit slow decay in singular values, whereas fast decay is crucial for the success of projection- based model reduction methods. To overcome this problem,…