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Communication efficiency is a widely recognised research problem in Federated Learning (FL), with recent work focused on developing techniques for efficient compression, distribution and aggregation of model parameters between clients and…
We propose a new topological tool for computer vision - Scalar Function Topology Divergence (SFTD), which measures the dissimilarity of multi-scale topology between sublevel sets of two functions having a common domain. Functions can be…
Learning an encoding of feature vectors in terms of an over-complete dictionary or a information geometric (Fisher vectors) construct is wide-spread in statistical signal processing and computer vision. In content based information…
The structure tensor method is often used for 2D and 3D analysis of imaged structures, but its results are in many cases very dependent on the user's choice of method parameters. We simplify this parameter choice in first order structure…
While many works focus on 3D reconstruction from images, in this paper, we focus on 3D shape reconstruction and completion from a variety of 3D inputs, which are deficient in some respect: low and high resolution voxels, sparse and dense…
Coupled tensor decomposition (CTD) can extract joint features from multimodal data in various applications. It can be employed for federated learning networks with data confidentiality. Federated CTD achieves data privacy protection by…
This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the…
Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the…
In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…
Homogeneous polynomial dynamical systems (HPDSs), which can be equivalently represented by tensors, are essential for modeling higher-order networked systems, including ecological networks, chemical reactions, and multi-agent robotic…
Nonnegative Tucker Factorization (NTF) minimizes the euclidean distance or Kullback-Leibler divergence between the original data and its low-rank approximation which often suffers from grossly corruptions or outliers and the neglect of…
The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way…
A common pipeline in functional data analysis is to first convert the discretely observed data to smooth functions, and then represent the functions by a finite-dimensional vector of coefficients summarizing the information. Existing…
We derive a Kronecker product approximation for the micromagnetic long range interactions in a collocation framework by means of separable sinc quadrature. Evaluation of this operator for structured tensors (Canonical format, Tucker format,…
The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT…
Tensor completion is crucial in many scientific domains with missing data problems. Traditional low-rank tensor models, including CP, Tucker, and Tensor-Train, exploit low-dimensional structures to recover missing data. However, these…
The rigorous solution to the grating diffraction problem is a cornerstone step in many scientific fields and industrial applications ranging from the study of the fundamental properties of metasurfaces to the simulation of photolithography…
Tensor factorization models offer an effective approach to convert massive electronic health records into meaningful clinical concepts (phenotypes) for data analysis. These models need a large amount of diverse samples to avoid population…
The discrete fracture model (DFM) has been widely used in the simulation of fluid flow in fractured porous media. Traditional DFM uses the so-called hybrid-dimensional approach to treat fractures explicitly as low-dimensional entries (e.g.…
Generative modeling for tabular data has recently gained significant attention in the Deep Learning domain. Its objective is to estimate the underlying distribution of the data. However, estimating the underlying distribution of tabular…