Related papers: Reduced Basis Decomposition: a Certified and Fast …
The monitoring and management of high-volume feature-rich traffic in large networks offers significant challenges in storage, transmission and computational costs. The predominant approach to reducing these costs is based on performing a…
This paper presents a method for the numerical treatment of reaction-convection-diffusion problems with parameter-dependent coefficients that are arbitrary rough and possibly varying at a very fine scale. The presented technique combines…
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…
The deployment of Large Language Models is constrained by the memory and bandwidth demands of static weights and dynamic Key-Value cache. SVD-based compression provides a hardware-friendly solution to reduce these costs. However, existing…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
Matrix decomposition is one of the fundamental tools to discover knowledge from big data generated by modern applications. However, it is still inefficient or infeasible to process very big data using such a method in a single machine.…
Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…
The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for…
Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some…
We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is…
A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current…
This work introduces Structured 3D-SVD as a practical framework for the reconstruction, compression, and analysis of biological volumetric data. Inspired by the logic of matrix singular value decomposition (SVD), the proposed approach…
These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…
In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm…
We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…
Existing distribution compression methods reduce the number of observations in a dataset by minimising the Maximum Mean Discrepancy (MMD) between original and compressed sets, but modern datasets are often large in both sample size and…
The Randomized Singular Value Decomposition (RSVD) is a widely used algorithm for efficiently computing low-rank approximations of large matrices, without the need to construct a full-blown SVD. Of interest, of course, is the approximation…
Over the past few decades, we have witnessed a large family of algorithms that have been designed to provide different solutions to the problem of dimensionality reduction (DR). The DR is an essential tool to excavate the important…
The state-of-the-art dimensionality reduction approaches largely rely on complicated optimization procedures. On the other hand, closed-form approaches requiring merely eigen-decomposition do not have enough sophistication and nonlinearity.…
Signal decomposition (SD) approaches aim to decompose non-stationary signals into their constituent amplitude- and frequency-modulated components. This represents an important preprocessing step in many practical signal processing…