Open AccessMatrix completion with side information using manifold optimisation
Author(s) -
Mahdi Mohades Mohamad,
Hossein Kahaei Mohammad
Publication year - 2020
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
ISSN - 1751-9683
DOI - 10.1049/iet-spr.2019.0377
Subject(s) - manifold (fluid mechanics) , matrix completion , matrix (chemical analysis) , linear subspace , rank (graph theory) , computer science , manifold alignment , algorithm , construct (python library) , constant (computer programming) , mathematics , nonlinear dimensionality reduction , mathematical optimization , artificial intelligence , pure mathematics , combinatorics , dimensionality reduction , mechanical engineering , physics , materials science , quantum mechanics , engineering , composite material , gaussian , programming language
The authors solve the matrix completion (MC) problem based on manifold optimisation by incorporating the side information under which the columns of the intended matrix are drawn from a union of low‐dimensional subspaces. It is proved that this side information leads us to construct new manifolds, as an embedded sub‐manifold of the manifold of constant rank matrices, using which the MC problem is solved more accurately. The required geometrical properties of the aforementioned manifold are then presented for MC. Simulation results over both synthetic and real‐world data show that the proposed method outperforms some recent techniques either based on side information or not.