A robust online subspace estimation and tracking algorithm

Mansour, Hassan; Xin, Jiang

doi:10.1109/icassp.2015.7178735

Cited by 30 publications

(45 citation statements)

References 13 publications

(23 reference statements)

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“…8c and Fig. 8d The performance of the proposed RVBSF algorithm is compared with that of OP-RPCA [13] GRASTA [9] and ROSETA [10] in Table V. The RVBSF algorithm performs better than the subspace estimation and tracking algorithms.…”

Section: ) Robust Traffic Estimationmentioning

confidence: 99%

Online Variational Bayesian Subspace Filtering

Charul

Bhatt

Biyani

et al. 2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive approach of per-snapshot recovery is both expensive and sub-optimal. This paper develops generative Bayesian models that fit sequential multivariate measurements arising from a low-dimensional time-varying subspace. A variational Bayesian subspace filtering approach is proposed that learns the underlying subspace and its state-transition matrix. Different from the plethora of deterministic counterparts, the proposed approach utilizes automatic relevance determination priors that obviate the need to tune key parameters such as rank and noise power. We also propose a forward-backward algorithm that allows the updates to be carried out at low complexity. Extensive tests over traffic and electricity data demonstrate the superior imputation, outlier rejection, and temporal prediction prowess of the proposed algorithm over the state-of-the-art matrix/tensor completion algorithms.

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Section: ) Robust Traffic Estimationmentioning

confidence: 99%

Online Variational Bayesian Subspace Filtering

Charul

Bhatt

Biyani

et al. 2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…So, the idea of GLIMPS can easily be applied for other tasks if we can use subspace based model for the problems. Examples include robust PCA (principal component analysis), background separation, subspace tracking [18], [20], [27], [41], and matrix completion [42]- [51]. More details are discussed in Section IV.…”

Section: Contributions Of This Papermentioning

confidence: 99%

GLIMPS: A Greedy Mixed-Integer Approach for Super Robust Matched Subspace Detection

Rahman

Pimentel-Alarcón

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Due to diverse nature of data acquisition and modern applications, many contemporary problems involve high dimensional datum x ∈ R d whose entries often lie in a union of subspaces and the goal is to find out which entries of x match with a particular subspace U, classically called matched subspace detection. Consequently, entries that match with one subspace are considered as inliers w.r.t the subspace while all other entries are considered as outliers. Proportion of outliers relative to each subspace varies based on the degree of coordinates from subspaces. This problem is a combinatorial NP-hard in nature and has been immensely studied in recent years. Existing approaches can solve the problem when outliers are sparse. However, if outliers are abundant or in other words if x contains coordinates from a fair amount of subspaces, this problem can't be solved with acceptable accuracy or within a reasonable amount of time. This paper proposes a twostage approach called Greedy Linear Integer Mixed Programmed Selector (GLIMPS) for this abundant-outliers setting, which combines a greedy algorithm and mixed integer formulation and can tolerate over 80% outliers, outperforming the state-of-the-art.

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“…However, this method as well as the methods in [12,13,15] do not explore the correlations between the current frame and multiple previously separated frames.…”

Section: Related Workmentioning

confidence: 99%

“…A counterpart of batch RPCA that operates on compressive measurements known as Compressive PCP can be found in [16]. The studies in [12][13][14][15]17] aim at solving the problem of online estimation of low-dimensional subspaces from randomly subsampled data for modeling the background. An algorithm to recover the sparse component x t in (2) has been proposed in [18], however, the low-rank component v t in (2) is not recovered per time instance from a small number of measurements.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Compressive Online Video Background-Foreground Separation Using Multiple Prior Information and Optical Flow

Prativadibhayankaram¹,

Luong²,

Le³

et al. 2018

Preprint

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In the context of video background-foreground separation, we propose a compressive online Robust Principal Component Analysis (RPCA) with optical flow that separates recursively a sequence of video frames into foreground (sparse) and background (low-rank) components. This separation method can process per video frame from a small set of measurements, in contrast to conventional batch-based RPCA, which processes the full data. The proposed method also leverages multiple prior information by incorporating previously separated background and foreground frames in an n-1 minimization problem. Moreover, optical flow is utilized to estimate motions between the previous foreground frames and then compensate the motions to achieve higher quality prior foregrounds for improving the separation. Our method is tested on several video sequences in different scenarios for online background-foreground separation given compressive measurements. The visual and quantitative results show that the proposed method outperforms other existing methods.

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A robust online subspace estimation and tracking algorithm

Cited by 30 publications

References 13 publications

Online Variational Bayesian Subspace Filtering

Online Variational Bayesian Subspace Filtering

GLIMPS: A Greedy Mixed-Integer Approach for Super Robust Matched Subspace Detection

Compressive Online Video Background-Foreground Separation Using Multiple Prior Information and Optical Flow

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