Related papers: SVD Based Image Processing Applications: State of …

This paper provides an advanced mathematical theory of the Generalized Singular Value Decomposition (GSVD) and its applications. We explore the geometry of the GSVD which provides a long sought for ellipse picture which includes a…

Large language models (LLMs) have achieved remarkable success in natural language processing (NLP) tasks, yet their substantial memory requirements present significant challenges for deployment on resource-constrained devices. Singular…

Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many…

This work considers noise removal from images, focusing on the well known K-SVD denoising algorithm. This sparsity-based method was proposed in 2006, and for a short while it was considered as state-of-the-art. However, over the years it…

This paper proposes a neural network approach based on Error Back Propagation (EBP) for classification of different eye images. To reduce the complexity of layered neural network the dimensions of input vectors are optimized using Singular…

Low-rank decomposition, particularly Singular Value Decomposition (SVD), is a pivotal technique for mitigating the storage and computational demands of Large Language Models (LLMs). However, prevalent SVD-based approaches overlook the…

In this work we propose a photorealistic style transfer method for image and video that is based on vision science principles and on a recent mathematical formulation for the deterministic decoupling of sample statistics. The novel aspects…

Image Classification is a fundamental task in the field of computer vision that frequently serves as a benchmark for gauging advancements in Computer Vision. Over the past few years, significant progress has been made in image…

Semantic image parsing, which refers to the process of decomposing images into semantic regions and constructing the structure representation of the input, has recently aroused widespread interest in the field of computer vision. The recent…

Singular Value Decomposition can be considered as an effective method for Signal Processing/especially data compression. In this short paper we investigate the application of SVD to predict data equation from data. The method is similar to…

We present an alternative method for carrying out a principal-component analysis of Wilson coefficients in standard model effective field theory (SMEFT). The method is based on singular-value decomposition (SVD). The SVD method provides…

The Shapley value (SV) has emerged as a promising method for data valuation. However, computing or estimating the SV is often computationally expensive. To overcome this challenge, Jia et al. (2019) propose an advanced SV estimation…

With the recent advancements in the field of information industry, critical data in the form of digital images is best understood by the human brain. Therefore, digital images play a significant part and backbone role in many areas such as…

As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…

This paper aims to develop a simple procedure to reduce and control the condition number of random matrices, and investigate the effect on the persistent homology (PH) of point clouds of well- and ill-conditioned matrices. For a square…

In spherical surface wave tomography, one measures the integrals of a function defined on the sphere along great circle arcs. This forms a generalization of the Funk--Radon transform, which assigns to a function its integrals along full…

To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…

Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Previous work allows using the SVD in Neural Networks…

Transformers have achieved great success in natural language processing. Due to the powerful capability of self-attention mechanism in transformers, researchers develop the vision transformers for a variety of computer vision tasks, such as…

We propose an efficient, distributed, out-of-memory implementation of the truncated singular value decomposition (t-SVD) for heterogeneous (CPU+GPU) high performance computing (HPC) systems. Various implementations of SVD have been…