Adaptive Low Rank Matrix Completion

Tripathi, Ruchi; Mohan, B.R.; Rajawat, Ketan

doi:10.1109/tsp.2017.2695450

Cited by 21 publications

(10 citation statements)

References 48 publications

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“…where A(k) ∈ R (2m−2)×(2m+2) and 0 is the all zero matrix of appropriate size. At time k, robots estimate the position of the leader p 1 (k + 1) and follow it while maintaining the shape described by (33). The further details about the constraint in (33) can be found in [28] and discussed in Appendix D of the supplementary material.…”

Section: ) Problem Formulationmentioning

confidence: 99%

“…At time k, robots estimate the position of the leader p 1 (k + 1) and follow it while maintaining the shape described by (33). The further details about the constraint in (33) can be found in [28] and discussed in Appendix D of the supplementary material. To this end, the leader broadcasts a signal that is subsequently used by the robots in order to estimate p 1 (k + 1).…”

Section: ) Problem Formulationmentioning

confidence: 99%

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Online Learning With Inexact Proximal Online Gradient Descent Algorithms

Dixit

Bedi

Tripathi

et al. 2019

IEEE Trans. Signal Process.

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We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is desirable, while the accuracy of the solution may only increase slowly over time. We put forth the proximal online gradient descent (OGD) algorithm for tracking the optimum of a composite objective function comprising of a differentiable loss function and a non-differentiable regularizer. An online learning framework is considered and the gradient of the loss function is allowed to be erroneous. Both, the gradient error as well as the dynamics of the function optimum or target are adversarial and the performance of the inexact proximal OGD is characterized in terms of its dynamic regret, expressed in terms of the cumulative error and path length of the target. The proposed inexact proximal OGD is generalized for application to large-scale problems where the loss function has a finite sum structure. In such cases, evaluation of the full gradient may not be viable and a variance reduced version is proposed that allows the component functions to be sub-sampled. The efficacy of the proposed algorithms is tested on the problem of formation control in robotics and on the dynamic foreground-background separation problem in video.

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Section: ) Problem Formulationmentioning

confidence: 99%

Section: ) Problem Formulationmentioning

confidence: 99%

Online Learning With Inexact Proximal Online Gradient Descent Algorithms

Dixit

Bedi

Tripathi

et al. 2019

IEEE Trans. Signal Process.

Self Cite

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show abstract

“…Compared with other approximate matrix methods such as Incomplete Cholesky (ICD), Nystron method is faster in solving problems. The main idea of the Nystrom method is to obtain the approximate matrixK of the original matrix K by reducing the rank, which is equivalent to taking m rows and m columns randomly from K. This approximationK can be written asK = K n,m K −1 m,m K m,n , where K n,m is the n×m block matrix in the original matrix K, but m n. The low-rank approximation of the matrix is usually used to approximate kernel matrix [20], which has been used in combination with the kernel SVM algorithm. However, the optimization algorithm for solving LR usually requires iteration, so the kernel trick used in this algorithm is very inefficient.…”

Section: Introductionmentioning

confidence: 99%

Using Low-Rank Approximations to Speed Up Kernel Logistic Regression Algorithm

Lei

Tang

et al. 2019

IEEE Access

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Logistic regression as a classic classification algorithm has limitations that can only be applied to linearly separable data. For linearly indivisible data, we use a kernel trick to map it to a higher dimensional space, making it easier to separate and structure in this space. However, with the increasing scale of data, the use of kernel trick is becoming more and more restricted. When the data reaches a certain scale, the cost of storage and computing kernel matrix is very expensive. To mitigate the problem of kernel matrix overload, we employ the low-rank approximate kernel matrix to speed up the solution of kernel logistic regression (KLR) and propose a framework for quickly solving the KLR algorithm. We use a fast iterative algorithm similar to the sequential minimal optimization (SMO) algorithm to solve the dual problem in the KLR. In addition, in this framework, the low-rank approximation is combined with gradient descent and Newton iteration algorithm, respectively. The low-rank approximation is used to reduce the redundant information in the data, which not only speeds up the solution of the KLR but also improves the accuracy of classification. Finally, the extensive experiments show that the KLR optimization algorithms based on our proposed framework outperform the state-of-the-art algorithms. INDEX TERMS Kernel logistic regression, sequential minimal optimization, dual problem, low-rank approximation.

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“…In this paper, a method based on matrix completion and compressed sensing [17,18] is presented and referred to as sparse low-rank matrix completion (SLR-MC). Different from the method proposed in [16], the low-rank part and sparse part of corrupted matrix were recovered by matrix completion and compressed sensing individually.…”

Section: Introductionmentioning

confidence: 99%

Temperature Field Data Reconstruction Using the Sparse Low-Rank Matrix Completion Method

Wang

Shan

et al. 2019

Advances in Meteorology

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Due to limited number of weather stations and interruption of data collection, the temperature field data may be incomplete. In the past, spatial interpolation is usually used for filling the data gap. However, the interpolation method does not work well for the case of the large-scale data loss. Matrix completion has emerged very recently and provides a global optimization for temperature field data reconstruction. A recovery method is proposed for improving the accuracy of temperature field data by using sparse low-rank matrix completion (SLR-MC). The method is tested using continuous gridded data provided by ERA Interim and the station temperature data provided by Jiangxi Meteorological Bureau. Experimental results show that the average signal-to-noise ratio can be increased by 12.5%, and the average reconstruction error is reduced by 29.3% compared with the matrix completion (MC) method.

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Adaptive Low Rank Matrix Completion

Cited by 21 publications

References 48 publications

Online Learning With Inexact Proximal Online Gradient Descent Algorithms

Online Learning With Inexact Proximal Online Gradient Descent Algorithms

Using Low-Rank Approximations to Speed Up Kernel Logistic Regression Algorithm

Temperature Field Data Reconstruction Using the Sparse Low-Rank Matrix Completion Method

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