Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
97 tokens/sec
GPT-4o
53 tokens/sec
Gemini 2.5 Pro Pro
44 tokens/sec
o3 Pro
5 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Structured Low-Rank Matrix Factorization: Global Optimality, Algorithms, and Applications (1708.07850v1)

Published 25 Aug 2017 in cs.LG, cs.CV, and cs.NA

Abstract: Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it challenging to apply them to large scale datasets. Moreover, in many applications the data can display structures beyond simply being low-rank, e.g., images and videos present complex spatio-temporal structures that are largely ignored by standard low-rank methods. In this paper we study a matrix factorization technique that is suitable for large datasets and captures additional structure in the factors by using a particular form of regularization that includes well-known regularizers such as total variation and the nuclear norm as particular cases. Although the resulting optimization problem is non-convex, we show that if the size of the factors is large enough, under certain conditions, any local minimizer for the factors yields a global minimizer. A few practical algorithms are also provided to solve the matrix factorization problem, and bounds on the distance from a given approximate solution of the optimization problem to the global optimum are derived. Examples in neural calcium imaging video segmentation and hyperspectral compressed recovery show the advantages of our approach on high-dimensional datasets.

User Edit Pencil Streamline Icon: https://streamlinehq.com
Authors (2)
  1. Benjamin D. Haeffele (22 papers)
  2. Rene Vidal (47 papers)
Citations (64)

Summary

We haven't generated a summary for this paper yet.