Premium
A theoretical guarantee for data completion via geometric separation
Author(s) -
King Emily J.,
Murphy James M.
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710384
Subject(s) - mathematical proof , missing data , computer science , separation (statistics) , superposition principle , data mining , algorithm , mathematics , machine learning , mathematical analysis , geometry
Scientific and commercial data is often incomplete. Recovery of the missing information is an important pre‐processing step in data analysis. Real‐world data can in many cases be represented as a superposition of two or more different types of structures. For example, images may often be decomposed into texture and cartoon‐like components. When incomplete data comes from a distribution well‐represented as a mixture of different structures, a sparsity‐based method combining concepts from data completion and data separation can successfully recover the missing data. This short note presents a theoretical guarantee for success of the combined separation and completion approach which generalizes proofs from the distinct problems. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)