Low Rank Regularization: A review

Hu, Zhanxuan; Nie, Feiping; Wang, Rong; Li, Xuelong

doi:10.1016/j.neunet.2020.09.021

Cited by 95 publications

(82 citation statements)

References 136 publications

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“…Due to the incomplete or corrupted observation of the low-rank matrix, many of previous attempts focus on the low-rank matrix recovery problem [10]. Hu et al [13] provides a comprehensive survey for Low Rank Regularization (LRR), mainly analysing the effect of using LRR as loss function by nuclear norm or other tools. Cui et al [8] and Xiong et al [37] apply nuclear norm and weighted nuclear norm as loss functions to minimize rank of matrix for image classification task respectively, and both of them achieve superior results.…”

Section: Related Workmentioning

confidence: 99%

“…As each column of the matrix Z represents an encoded state, the rank(Z) can be used to represent the diversity within the matrix, due to the fact that higher rank(Z) denotes larger linear irrelevance among the encoded states. Unlike previous studies and applications based on the rank of matrix [11,8,13,37] employing the lowrank modeling, on the contrary, we creatively use the rank by maximizing rank(Z) to enlarge the exploration diversity, which encourages the agent to visit more different states of high diversity. Thus, the intuition of our intrinsic reward can be achieved by: max Z rank(Z).…”

Section: Nuclear-norm Maximization-based Intrinsic Rewardsmentioning

confidence: 99%

See 1 more Smart Citation

Nuclear Norm Maximization Based Curiosity-Driven Learning

Chen¹,

Gao²,

Xu³

et al. 2022

Preprint

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To handle the sparsity of the extrinsic rewards in reinforcement learning, researchers have proposed intrinsic reward which enables the agent to learn the skills that might come in handy for pursuing the rewards in the future, such as encouraging the agent to visit novel states. However, the intrinsic reward can be noisy due to the undesirable environment's stochasticity and directly applying the noisy value predictions to supervise the policy is detrimental to improve the learning performance and efficiency. Moreover, many previous studies employ ℓ 2 norm or variance to measure the exploration novelty, which will amplify the noise due to the square operation. In this paper, we address aforementioned challenges by proposing a novel curiosity leveraging the nuclear norm maximization (NNM), which can quantify the novelty of exploring the environment more accurately while providing high-tolerance to the noise and outliers. We conduct extensive experiments across a variety of benchmark environments and the results suggest that NNM can provide state-of-the-art performance compared with previous curiosity methods. On 26 Atari games subset, NNM achieves a human-normalized score of 1.09, which doubles that of competitive intrinsic rewards-based approaches. Our code will be released publicly to enhance the reproducibility.

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Section: Related Workmentioning

confidence: 99%

Section: Nuclear-norm Maximization-based Intrinsic Rewardsmentioning

confidence: 99%

Nuclear Norm Maximization Based Curiosity-Driven Learning

Chen¹,

Gao²,

Xu³

et al. 2022

Preprint

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show abstract

“…It is well-known that matrix rank minimization is an NP-hard problem. Nuclear norm minimization, as a relaxation to the low-rank regularizer, is a common alternative to directly calculating the rank of the matrix [41], [42]. The rank of X is replaced by its nuclear norm, the problem (5) is represented as follows:…”

Section: B the Proposed Sslrsu Modelmentioning

confidence: 99%

Hyperspectral Sparse Unmixing With Spectral-Spatial Low-Rank Constraint

Zhang

Liang

et al. 2021

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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Spectral unmixing is a consequential preprocessing task in hyperspectral image interpretation. With the help of large spectral libraries, unmixing is equivalent to finding the optimal subset of the library entries that can best model the image. Sparse regression techniques have been widely used to solve this optimization problem, since the number of materials present in a scene is usually small. However, the high mutual coherence of library signatures negatively affects the sparse unmixing performance. To cope with this challenge, a new algorithm called spectral-spatial low-rank sparse unmixing (SSLRSU) is established. In this work, the double weighting factors under the ℓ1 framework aim to improve the row sparsity of the abundance matrix and the sparsity of each abundance map. Meanwhile, the low-rank regularization term exploits the low-dimensional structure of the image, which makes for accurate endmember identification from the spectral library. The underlying optimization problem can be solved by the alternating direction method of multipliers efficiently. The experimental results, conducted by using both synthetic and real hyperspectral data, uncover that the proposed SSLRSU strategy can get accurate unmixing results over those gave by other advanced sparse unmixing strategies.

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“…Another approach that we consider is the greedy heuristic of atomic decomposition for minimum rank approximation (admira) proposed by Lee and Bresler [14], which aims to find k rank-one matrices representing the original matrix. Finally, in addition to nuclear, we consider schatten approach proposed by Mohan and Fazel [17] to solve the Schatten p-norm minimization problem with p = 1/2, one of the non-convex relaxation methods for which k is a priori unknown (see, e.g., Hu et al [11]). The tolerance is again set at = 10 −6 for X s+1 − X s F and the maximum number of iterations is set higher atN max = 10000 for these methods given that their (least-squares) subproblems require less computational efforts.…”

Section: Recoverabilitymentioning

confidence: 99%

Low-rank matrix recovery with Ky Fan 2-k-norm

Doan

Vavasis

2021

J Glob Optim

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Low-rank matrix recovery problem is difficult due to its non-convex properties and it is usually solved using convex relaxation approaches. In this paper, we formulate the non-convex low-rank matrix recovery problem exactly using novel Ky Fan 2-k-norm-based models. A general difference of convex functions algorithm (DCA) is developed to solve these models. A proximal point algorithm (PPA) framework is proposed to solve sub-problems within the DCA, which allows us to handle large instances. Numerical results show that the proposed models achieve high recoverability rates as compared to the truncated nuclear norm method and the alternating bilinear optimization approach. The results also demonstrate that the proposed DCA with the PPA framework is efficient in handling larger instances.

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Low Rank Regularization: A review

Cited by 95 publications

References 136 publications

Nuclear Norm Maximization Based Curiosity-Driven Learning

Nuclear Norm Maximization Based Curiosity-Driven Learning

Hyperspectral Sparse Unmixing With Spectral-Spatial Low-Rank Constraint

Low-rank matrix recovery with Ky Fan 2-k-norm

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