Research
An Implementation of a Randomized Algorithm for Principal Component Analysis
June 22, 2015
Abstract
Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis (PCA) and the calculation of truncated singular value decompositions (SVD). The present paper presents an essentially black-box, fool-proof implementation for Mathworks’ MATLAB, a popular software platform for numerical computation. As illustrated via several tests, the randomized algorithms for low-rank approximation outperform or at least match the classical techniques (such as Lanczos iterations) in basically all respects: accuracy, computational efficiency (both speed and memory usage), ease-of-use, parallelizability, and reliability. However, the classical procedures remain the methods of choice for estimating spectral norms, and are far superior for calculating the least singular values and corresponding singular vectors (or singular subspaces).
Related Publications
May 26, 2026
Human & Machine Intelligence
Theory
Misalignment Between Backpropagation and the Hierarchy of Brain Responses to Images
Valentin Wyart, Huy V. Vo, Jean Remi King, Josephine Raugel, Jérémy Rapin, Marc Szafraniec, Max Seitzer, Patrick Labatut, Piotr Bojanowski
May 26, 2026
May 19, 2026
Human & Machine Intelligence
EgoBabyVLM: Benchmarking Cross-Modal Learning from Naturalistic Egocentric Video Data
Alvin W. M. Tan, Nicolas Hamilakis, Manel Khentout, Sho Tsuji, Balázs Kégl, Michael C. Frank, Angel Villar Corrales, Charles-Eric Saint-James, Dongyan Lin, Emmanuel Dupoux, Jiayi Shen, Juan Pino, Mahi Luthra, Martin Gleize, Phillip Rust, Rashel Moritz, Sheila Krogh-Jespersen, Surya Parimi, Tom Fizycki, Vanessa Stark, Yosuke Higuchi, Youssef Benchekroun
May 19, 2026
May 17, 2026
Conversational AI
GIM: Evaluating models via tasks that integrate multiple cognitive domains
Alexandre Rezende, Rohit Patel, Steven McClain
May 17, 2026
May 12, 2026
Human & Machine Intelligence
NeuralSet: A High-Performing Python Package for Neuro-AI
Corentin Bel, Linnea Evanson, Julien Gadonneix, Andrea Santos Revilla, Mingfang (Lucy) Zhang, Julie Bonnaire, Charlotte Caucheteux, Alexandre Défossez, Théo Desbordes, Pablo Diego-Simón, Shubh Khanna, Juliette Millet, Pierre Orhan, Saarang Panchavati, Antoine Ratouchniak, Alexis Thual, Hubert Jacob Banville, Jarod Levy, Jean Remi King, Josephine Raugel, Jérémy Rapin, Katelyn Begany, Marlene Careil, Simon Dahan, Sophia Houhamdi, Stéphane d'Ascoli, Teon Brooks, Yohann Benchetrit
May 12, 2026
October 31, 2019
NLP
Facebook AI's WAT19 Myanmar-English Translation Task Submission
Peng-Jen Chen, Jiajun Shen, Matt Le, Vishrav Chaudhary, Ahmed El-Kishky, Guillaume Wenzek, Myle Ott, Marc’Aurelio Ranzato
October 31, 2019
October 27, 2019
Order-Aware Generative Modeling Using the 3D-Craft Dataset | Facebook AI Research
Zhuoyuan Chen, Demi Guo, Tong Xiao, Saining Xie, Xinlei Chen, Haonan Yu, Jonathan Gray, Kavya Srinet, Haoqi Fan, Jerry Ma, Charles R. Qi, Shubham Tulsiani, Arthur Szlam, Larry Zitnick
October 27, 2019
April 25, 2020
Energy-Based Models for Atomic-Resolution Protein Conformations | Facebook AI Research
Yilun Du, Joshua Meier, Jerry Ma, Rob Fergus, Alexander Rives
April 25, 2020
June 11, 2019
Computer Vision
ELF OpenGo: An Analysis and Open Reimplementation of AlphaZero | Facebook AI Research
Yuandong Tian, Jerry Ma, Qucheng Gong, Shubho Sengupta, Zhuoyuan Chen, James Pinkerton, Larry Zitnick
June 11, 2019
Help Us Pioneer The Future of AI
We share our open source frameworks, tools, libraries, and models for everything from research exploration to large-scale production deployment.
Our approach
Latest news
Foundational models
Meta © 2026