English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Recent work has demonstrated the effectiveness of gradient descent fordirectly recovering the factors of low-rank matrices from random linearmeasurements in a globally convergent manner when initialized properly.However, the performance of existing algorithms is highly sensitive in thepresence of outliers that may take arbitrary values. In this paper, we proposea truncated gradient descent algorithm to improve the robustness againstoutliers, where the truncation is performed to rule out the contributions ofsamples that deviate significantly from the {\em sample median} of measurementresiduals adaptively in each iteration. We demonstrate that, when initializedin a basin of attraction close to the ground truth, the proposed algorithmconverges to the ground truth at a linear rate for the Gaussian measurementmodel with a near-optimal number of measurements, even when a constant fractionof the measurements are arbitrarily corrupted. In addition, we propose a newtruncated spectral method that ensures an initialization in the basin ofattraction at slightly higher requirements. We finally provide numericalexperiments to validate the superior performance of the proposed approach.

Nonconvex Low-Rank Matrix Recovery with Arbitrary Outliers via Median-Truncated Gradient Descent