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Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics and image processing the matrices are dense, but low-rank…
The radial velocity (RV) of a single star is easily obtained from cross-correlation of the spectrum with a template, but the treatment of double-lined spectroscopic binaries (SB2s) is more difficult. Two different approaches were applied to…
Matrix completion is a widely used technique for image inpainting and personalized recommender system, etc. In this work, we focus on accelerating the matrix completion using faster randomized singular value decomposition (rSVD). Firstly,…
The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng provides a hybrid approach to the t-product based third-order tensor singular value decomposition with the transform matrix being a factor matrix of the higher order…
At Diamond Light Source, the UK's national synchrotron facility, electron beam disturbances are attenuated by the fast orbit feedback (FOFB), which controls a cross-directional (CD) system with hundreds of inputs and outputs. Due to the…
In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently…
Efficiently computing a subset of a correlation matrix consisting of values above a specified threshold is important to many practical applications. Real-world problems in genomics, machine learning, finance other applications can produce…
Singular Value Decomposition (SVD) constitutes a bridge between the linear algebra concepts and multi-layer neural networks---it is their linear analogy. Besides of this insight, it can be used as a good initial guess for the network…
Unsupervised anomaly detection of multivariate time series is a challenging task, given the requirements of deriving a compact detection criterion without accessing the anomaly points. The existing methods are mainly based on reconstruction…
Traditional directed graph signal processing generally depends on fixed representation matrices, whose rigid structures limit the model's ability to adapt to complex graph topologies. To address this issue, this study employed the unified…
Hard X-ray spectra in solar flares provide knowledge of the electron spectrum that results from acceleration and propagation in the solar atmosphere. However, the inference of the electron spectra from solar X-ray spectra is an ill-posed…
We introduce a new method for reconstructing the primordial power spectrum, $P(k)$, directly from observations of the Cosmic Microwave Background (CMB). We employ Singular Value Decomposition (SVD) to invert the radiation perturbation…
In this paper, we propose a multi-user downlink system for two users based on the orthogonal time frequency space (OTFS) modulation scheme. The design leverages the generalized singular value decomposition (GSVD) of the channels between the…
With the advent of quantum technology, nitrogen vacancy ($NV$) centers in diamond turn out to be a frontier which provides an efficient platform for quantum computation, communication and sensing applications. Due to the coupled spin-charge…
Schmidt decomposition of a vector can be understood as writing the singular value decomposition (SVD) in vector form. A vector can be written as a linear combination of tensor product of two dimensional vectors by recursively applying…
Structural symmetries in the storage ring of synchrotrons are intentionally created during the design phase of the magnetic lattices, but they are not considered in the design of control algorithms that stabilize the beam of accelerated…
We present a cost-reduced approach for the distinguishable cluster approximation to coupled cluster with singles, doubles and iterative triples (DC-CCSDT) based on a tensor decomposition of the triples amplitudes. The triples amplitudes and…
This paper presents a portable, GPU-accelerated implementation of a QR-based singular value computation algorithm in Julia. The singular value ecomposition (SVD) is a fundamental numerical tool in scientific computing and machine learning,…
We propose a distributed design method for decentralized control by exploiting the underlying sparsity properties of the problem. Our method is based on chordal decomposition of sparse block matrices and the alternating direction method of…
Audio-Visual Dataset Distillation aims to compress large-scale datasets into compact subsets while preserving the performance of the original data. However, conventional Distribution Matching (DM) methods struggle to capture intrinsic…