期刊
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
卷 29, 期 1, 页码 218-224出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2016.2608834
关键词
l(2)-minimization; equivalence; least square regression; low rank representation (LRR); rank minimization
类别
资金
- A*STAR Industrial Robotics Programme-Distributed Sensing and Perception under SERC Grant [1225100002]
- National Natural Science Foundation of China [61432012, 61673283]
A lot of works have shown that frobenius-norm-based representation (FNR) is competitive to sparse representation and nuclear-norm-based representation (NNR) in numerous tasks such as subspace clustering. Despite the success of FNR in experimental studies, less theoretical analysis is provided to understand its working mechanism. In this brief, we fill this gap by building the theoretical connections between FNR and NNR. More specially, we prove that: 1) when the dictionary can provide enough representative capacity, FNR is exactly NNR even though the data set contains the Gaussian noise, Laplacian noise, or sample-specified corruption and 2) otherwise, FNR and NNR are two solutions on the column space of the dictionary.
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