2012 COLT COLT 2012

Exact Recovery of Sparsely-Used Dictionaries

Abstract

We consider the problem of learning sparsely used dictionaries with an arbitrary square dictionary and a random, sparse coefficient matrix. We prove that \emphO(n log \emphn) samples are sufficient to uniquely determine the coefficient matrix. Based on this proof, we design a polynomial-time algorithm, called Exact Recovery of Sparsely-Used Dictionaries (ER-SpUD), and prove that it probably recovers the dictionary and coefficient matrix when the coefficient matrix is sufficiently sparse. Simulation results show that ER-SpUD reveals the true dictionary as well as the coefficients with probability higher than many state-of-the-art algorithms.

🌉 Interdisciplinary Bridge — Machine Learning and Mathematics & Optimization
🐝 Cross-Pollinator — Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Interdisciplinary, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Speech & Audio
📈 Trend Setter — Feature Learning
🧭 Keyword Pioneer — sparse coefficient
🐣 Hot Topic Early Bird — dictionary learning