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This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

Consider a sparse polynomial in several variables given explicitly as a sum of non-zero terms with coefficients in an effective field. In this paper, we present several algorithms for factoring such polynomials and related tasks (such as…

Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…

To solve the problem of poor performance of deep neural network models due to insufficient data, a simple yet effective interpolation-based data augmentation method is proposed: MSMix (Manifold Swap Mixup). This method feeds two different…

We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many…

Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…

Spectral-based subspace clustering methods have proved successful in many challenging applications such as gene sequencing, image recognition, and motion segmentation. In this work, we first propose a novel spectral-based subspace…

In this paper we develop a data-driven smoothing technique for high-dimensional and non-linear panel data models. We allow for individual specific (non-linear) functions and estimation with econometric or machine learning methods by using…

We address the problem of converting large-scale high-dimensional image data into binary codes so that approximate nearest-neighbor search over them can be efficiently performed. Different from most of the existing unsupervised approaches…

In complex visual recognition tasks it is typical to adopt multiple descriptors, that describe different aspects of the images, for obtaining an improved recognition performance. Descriptors that have diverse forms can be fused into a…

We propose a novel image sampling method for differentiable image transformation in deep neural networks. The sampling schemes currently used in deep learning, such as Spatial Transformer Networks, rely on bilinear interpolation, which…

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

Compression is a crucial solution for data reduction in modern scientific applications due to the exponential growth of data from simulations, experiments, and observations. Compression with progressive retrieval capability allows users to…

This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there…

Greedy methods have recently been successfully applied to generalized kernel interpolation, or the recovery of a function from data stemming from the evaluation of linear functionals, including the approximation of solutions of linear PDEs…

Inverse medium scattering problems arise in many applications, but in practice, the measurement data are often restricted to a limited aperture by physical or experimental constraints. Classical sampling methods, such as MUSIC and the…