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Matrix Completion with Deterministic Sampling : Theories and Methods

In some significant applications such as data forecasting, the locations of missing entries cannot obey any non-degenerate distributions, questioning the validity of the prevalent assumption that the missing data is randomly chosen according to some probabilistic model. To break through the limits of random sampling, we explore in this paper the problem of real-valued matrix completion under the setup of deterministic sampling. We propose two conditions, isomeric condition and relative well-conditionedness, for guaranteeing an arbitrary matrix to be recoverable from a sampling of the matrix entries. It is provable that the proposed conditions are weaker than the assumption of uniform sampling and, most importantly, it is also provable that the isomeric condition is necessary for the completions of any partial matrices to be identifiable. Equipped with these new tools, we prove a collection of theorems for missing data recovery as well as convex/nonconvex matrix completion. Among other things, we study in detail a Schatten quasi-norm induced method termed isomeric dictionary pursuit (IsoDP), and we show that IsoDP exhibits some distinct behaviors absent in the traditional bilinear programs.

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Informasi Detail

Judul Seri

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE; Vol.43 No.2 February 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 549 - 566

Bahasa

English

ISBN/ISSN

-

Klasifikasi

-

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

IDENTIFIABILITY
MATRIX COMPLETION
DETERMINISTIC SAMPLING
ISOMERIC CONDITION
RELATIVE WELL-CONDITIONEDNESS
SCHATTEN QUASI-NORM
BILINEAR PROGRAMMING

Info Detail Spesifik

DOI: 10.1109/TPAMI.2019.2937869

Pernyataan Tanggungjawab

Guangcan Liu, Qingshan Liu, Xiao-Tong Yuan, Meng Wang

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