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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Low-rank representation (LRR) is an effective method for subspace clusteringand has found wide applications in computer vision and machine learning. Theexisting LRR solver is based on the alternating direction method (ADM). Itsuffers from $O(n^3)$ computation complexity due to the matrix-matrixmultiplications and matrix inversions, even if partial SVD is used. Moreover,introducing auxiliary variables also slows down the convergence. Such a heavycomputation load prevents LRR from large scale applications. In this paper, wegeneralize ADM by linearizing the quadratic penalty term and allowing thepenalty to change adaptively. We also propose a novel rule to update thepenalty such that the convergence is fast. With our linearized ADM withadaptive penalty (LADMAP) method, it is unnecessary to introduce auxiliaryvariables and invert matrices. The matrix-matrix multiplications are furtheralleviated by using the skinny SVD representation technique. As a result, wearrive at an algorithm for LRR with complexity $O(rn^2)$, where $r$ is the rankof the representation matrix. Numerical experiments verify that for LRR ourLADMAP method is much faster than state-of-the-art algorithms. Although we onlypresent the results on LRR, LADMAP actually can be applied to solving moregeneral convex programs.

Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation