| Autor: |
Fanhua Shang, Yuanyuan Liu, Fanjie Shang, Hongying Liu, Lin Kong, Licheng Jiao |
| Jazyk: |
angličtina |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Mathematics, Vol 8, Iss 8, p 1325 (2020) |
| Druh dokumentu: |
article |
| ISSN: |
2227-7390 |
| DOI: |
10.3390/math8081325 |
| Popis: |
The Schatten quasi-norm is an approximation of the rank, which is tighter than the nuclear norm. However, most Schatten quasi-norm minimization (SQNM) algorithms suffer from high computational cost to compute the singular value decomposition (SVD) of large matrices at each iteration. In this paper, we prove that for any p, p1, p2>0 satisfying 1/p=1/p1+1/p2, the Schatten p-(quasi-)norm of any matrix is equivalent to minimizing the product of the Schatten p1-(quasi-)norm and Schatten p2-(quasi-)norm of its two much smaller factor matrices. Then, we present and prove the equivalence between the product and its weighted sum formulations for two cases: p1=p2 and p1≠p2. In particular, when p>1/2, there is an equivalence between the Schatten p-quasi-norm of any matrix and the Schatten 2p-norms of its two factor matrices. We further extend the theoretical results of two factor matrices to the cases of three and more factor matrices, from which we can see that for any 0
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| Databáze: |
Directory of Open Access Journals |
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