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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
Abstract 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)