Truncated Singular Value Decomposition

Truncated Singular Value Decomposition (SVD) is a dimensionality reduction technique used to approximate large matrices by retaining only the most significant singular values and vectors, thereby reducing computational complexity and noise. Current research focuses on applying truncated SVD within various machine learning contexts, including neural network compression, data-driven system modeling, and improving the efficiency of algorithms like Extended Dynamic Mode Decomposition. This technique finds applications across diverse fields, from enhancing autonomous driving systems and improving large language model performance to denoising time-series data and optimizing music recommendation systems, demonstrating its broad utility in data analysis and machine learning.

Papers

September 27, 2024

Analysis of Truncated Singular Value Decomposition for Koopman Operator-Based Lane Change Model
Chinnawut Nantabut
General Analysis Koopman Operator Singular Value Decomposition Dynamic Mode Decomposition Truncated Singular Value Decomposition

May 23, 2024

Minimum number of neurons in fully connected layers of a given neural network (the first approximation)
Oleg I. Berngardt
Neural Network Single Neuron Level Cross Validation Fully Connected Layer Minimum Number NN Hyperparameters Truncated Singular Value Decomposition

April 23, 2024

Uncertainty Quantification of Data-Driven Output Predictors in the Output Error Setting
Farzan Kaviani, Ivan Markovsky, Hamid R. Ossareh
Uncertainty Quantification Data Driven Structured Output Offline Data Truncated Singular Value Decomposition Hankel Matrix

March 12, 2024

SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression
Xin Wang, Yu Zheng, Zhongwei Wan, Mi Zhang
Large Language Model Singular Value Decomposition LLM Compression Truncated Singular Value Decomposition

February 6, 2024

Operator SVD with Neural Networks via Nested Low-Rank Approximation
J. Jon Ryu, Xiangxiang Xu, H. S. Melihcan Erol, Yuheng Bu, Lizhong Zheng, Gregory W. Wornell
Neural Network High Dimensional Average Approximation Low Rank Approximation Singular Value Decomposition Nested Entity Eigenfunction Decomposition Truncated Singular Value Decomposition

February 5, 2024

A Random Matrix Approach to Low-Multilinear-Rank Tensor Approximation
Hugo Lebeau, Florent Chatelain, Romain Couillet
Low Rank Low Rank Approximation Random Matrix High Dimensional Regime Tensor Approximation Truncated Singular Value Decomposition Spiked Tensor

August 27, 2023

Learning end-to-end inversion of circular Radon transforms in the partial radial setup
Deep Ray, Souvik Roy
LeArning Abstract Photoacoustic Imaging Eta Inversion Field Reconstruction Truncated Singular Value Decomposition Radon Sinogram Radial Azimuthal Configuration

June 30, 2023

Of Spiky SVDs and Music Recommendation
Darius Afchar, Romain Hennequin, Vincent Guigue
Singular Value Decomposition Music Recommendation Recommendation Datasets Truncated Singular Value Decomposition

September 21, 2022

Efficient Distribution Similarity Identification in Clustered Federated Learning via Principal Angles Between Client Data Subspaces
Saeed Vahidian, Mahdi Morafah, Weijia Wang, Vyacheslav Kungurtsev, Chen Chen, Mubarak Shah, Bill Lin
Clustered Federated Learning Truncated Singular Value Decomposition Similarity Distribution Client Data

March 15, 2022

Time-series image denoising of pressure-sensitive paint data by projected multivariate singular spectrum analysis
Yuya Ohmichi, Kohmi Takahashi, Kazuyuki Nakakita
Noise Reduction Truncated Singular Value Decomposition Pressure Data Singular Spectrum Analysis

Truncated Singular Value Decomposition

Papers

Analysis of Truncated Singular Value Decomposition for Koopman Operator-Based Lane Change Model

Minimum number of neurons in fully connected layers of a given neural network (the first approximation)

Uncertainty Quantification of Data-Driven Output Predictors in the Output Error Setting

SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression

Operator SVD with Neural Networks via Nested Low-Rank Approximation

A Random Matrix Approach to Low-Multilinear-Rank Tensor Approximation

Learning end-to-end inversion of circular Radon transforms in the partial radial setup

Of Spiky SVDs and Music Recommendation

Efficient Distribution Similarity Identification in Clustered Federated Learning via Principal Angles Between Client Data Subspaces

Time-series image denoising of pressure-sensitive paint data by projected multivariate singular spectrum analysis