Performance guarantees for Schatten-p quasi-norm minimization in recovery of low-rank matrices
نویسندگان
چکیده
منابع مشابه
Performance Guarantees for Schatten-$p$ Quasi-Norm Minimization in Recovery of Low-Rank Matrices
We address some theoretical guarantees for Schatten-p quasi-norm minimization (p ∈ (0, 1]) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measuring operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition guarantees unique recovery of matrices of ranks equal or larger than what is guaran...
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As an emerging machine learning and information retrieval technique, the matrix completion has been successfully applied to solve many scientific applications, such as collaborative prediction in information retrieval, video completion in computer vision, etc. The matrix completion is to recover a low-rank matrix with a fraction of its entries arbitrarily corrupted. Instead of solving the popul...
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The Schatten quasi-norm was introduced tobridge the gap between the trace norm andrank function. However, existing algorithmsare too slow or even impractical for large-scale problems. Motivated by the equivalencerelation between the trace norm and its bilin-ear spectral penalty, we define two tractableSchatten norms, i.e. the bi-trace and tri-tracenorms, and prov...
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متن کاملSupplementary Materials for “ Tractable and Scalable Schatten Quasi - Norm Approximations for Rank Minimization ”
In this supplementary material, we give the detailed proofs of some lemmas, properties and theorems, as well as some additional experimental results on synthetic data and four recommendation system data sets. A More Notations R n denotes the n-dimensional Euclidean space, and the set of all m×n matrices with real entries is denoted by R m×n. Given matrices X and Y ∈ R m×n , the inner product is...
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ژورنال
عنوان ژورنال: Signal Processing
سال: 2015
ISSN: 0165-1684
DOI: 10.1016/j.sigpro.2015.02.025