# A Distributed Frank-Wolfe Framework for Learning Low-Rank Matrices with the Trace Norm

Source: [A Distributed Frank-Wolfe Framework for Learning Low-Rank Matrices with the Trace Norm](<https://www.sota2.com/research/paper/68fa64631e209131cea04409>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T21:02:11.964Z

Authors: Wenjie Zheng, Aur\\'elien Bellet, Patrick Gallinari

Published: 2017-12-20T14:28:21.000Z

## Abstract

We consider the problem of learning a high-dimensional but low-rank matrix from a large-scale dataset distributed over several machines, where low-rankness is enforced by a convex trace norm constraint. We propose DFW-Trace, a distributed Frank-Wolfe algorithm which leverages the low-rank structure of its updates to achieve efficiency in time, memory and communication usage. The step at the heart of DFW-Trace is solved approximately using a distributed version of the power method. We provide a theoretical analysis of the convergence of DFW-Trace, showing that we can ensure sublinear convergence in expectation to an optimal solution with few power iterations per epoch. We implement DFW-Trace in the Apache Spark distributed programming framework and validate the usefulness of our approach on synthetic and real data, including the ImageNet dataset with high-dimensional features extracted from a deep neural network.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1712.07495>)

[PDF](<https://arxiv.org/pdf/1712.07495.pdf>)