Robust Generalized Low Rank Approximations of Matrices
- Release time:2024-08-09
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Affiliation of Author(s):
理学院
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Journal:
PloS one
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Key Words:
中文关键字：广义低秩逼近，英文关键字：Generalized Low Rank Approximations of Matrices
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Abstract:
In recent years, the intrinsic low rank structure of some datasets has been extensively
exploited to reduce dimensionality, remove noise and complete the missing entries. As a
well-known technique for dimensionality reduction and data compression, Generalized Low
Rank Approximations of Matrices (GLRAM) claims its superiority on computation time and
compression ratio over the SVD. However, GLRAM is very sensitive to sparse large noise
or outliers and its robust version does not have been explored or solved yet. To address
this problem, this paper proposes a robust method for GLRAM, named Robust GLRAM
(RGLRAM). We first formulate RGLRAM as an l 1 -norm optimization problem which mini-
mizes the l 1 -norm of the approximation errors. Secondly, we apply the technique of Aug-
mented Lagrange Multipliers (ALM) to solve this l 1 -norm minimization problem and derive a
corresponding iterative scheme. Then the weak convergence of the proposed algorithm is
discussed under mild conditions. Next, we investigate a special case of RGLRAM and
extend RGLRAM to a general tensor case. Finally, the extensive experiments on synthetic
data show that it is possible for RGLRAM to exactly recover both the low rank and the
sparse components while it may be difficult for previous state-of-the-art algorithms. We also
discuss three issues on RGLRAM: the sensitivity to initialization, the generalization ability
and the relationship between the running time and the size/number of matrices. Moreover,
the experimental results on images of faces with large corruptions illustrate that RGLRAM
obtains the best denoising and compression performance than other methods.
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Note:
SCI
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First Author:
zhengxiuyun,yangwei,shijiarong
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Indexed by:
Journal paper
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Volume:
卷：10
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Issue:
期：9
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Page Number:
页：
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Translation or Not:
no
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Date of Publication:
2015-09-01
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