Supplementary Materials for “ Tractable and Scalable Schatten Quasi - Norm Approximations for Rank Minimization ”
نویسندگان
چکیده
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 defined by ⟨X, Y ⟩ := Tr(X T Y), where Tr(·) denotes the trace of a matrix. ∥X∥ 2 is the spectral norm and is equal to the maximum singular value of X. I denotes an identity matrix. For any vector x ∈ R n , its ℓ p quasi-norm for 0 < p < 1 is defined as ∥x∥ p =
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