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36
Dynamic anomalography: Tracking network anomalies via sparsity and low rank
, 2013
"... In the backbone of largescale networks, origintodestination (OD) traffic flows experience abrupt unusual changes known as traffic volume anomalies, which can result in congestion and limit the extent to which enduser quality of service requirements are met. As a means of maintaining seamless en ..."
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Cited by 24 (10 self)
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In the backbone of largescale networks, origintodestination (OD) traffic flows experience abrupt unusual changes known as traffic volume anomalies, which can result in congestion and limit the extent to which enduser quality of service requirements are met. As a means of maintaining seamless enduser experience in dynamic environments, as well as for ensuring network security, this paper deals with a crucial network monitoring task termed dynamic anomalography. Given link traffic measurements (noisy superpositions of unobserved OD flows) periodically acquired by backbone routers, the goal is to construct an estimated map of anomalies in real time, and thus summarize the network ‘health state ’ along both the flow and time dimensions. Leveraging the low intrinsicdimensionality of OD flows and the sparse nature of anomalies, a novel online estimator is proposed based on an exponentiallyweighted leastsquares criterion regularized with the sparsitypromotingnorm of the anomalies, and the nuclear norm of the nominal traffic matrix. After recasting the nonseparable nuclear norm into a form amenable to online optimization, a realtime algorithm for dynamic anomalography is developed and its convergence established under simplifying technical assumptions. For operational conditions where computational complexity reductions are at a premium, a lightweight stochastic gradient algorithm based on Nesterov’s acceleration technique is developed as well. Comprehensive numerical tests with both synthetic and real network data corroborate the effectiveness of the proposed online algorithms and their tracking capabilities, and demonstrate that they outperform stateoftheart approaches developed to diagnose traffic anomalies.
Recursive robust pca or recursive sparse recovery in large but structured noise
 in IEEE Intl. Symp. on Information Theory (ISIT
, 2013
"... This Dissertation is brought to you for free and open access by the Graduate College at Digital Repository @ Iowa State University. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Digital Repository @ Iowa State University. For more informati ..."
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Cited by 22 (17 self)
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This Dissertation is brought to you for free and open access by the Graduate College at Digital Repository @ Iowa State University. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Digital Repository @ Iowa State University. For more information, please contact
An online algorithm for separating sparse and lowdimensional signal sequences from their sum
 IEEE Trans. Signal Process
"... Abstract—This paper designs and extensively evaluates an online algorithm, called practical recursive projected compressive sensing (PracReProCS), for recovering a time sequence of sparse vectors and a time sequence of dense vectors from their sum, , when the ’s lie in a slowly changing lowdimens ..."
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Cited by 10 (8 self)
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Abstract—This paper designs and extensively evaluates an online algorithm, called practical recursive projected compressive sensing (PracReProCS), for recovering a time sequence of sparse vectors and a time sequence of dense vectors from their sum, , when the ’s lie in a slowly changing lowdimensional subspace of the full space. A key application where this problem occurs is in realtime video layering where the goal is to separate a video sequence into a slowly changing background sequence and a sparse foreground sequence that consists of one or more moving regions/objects onthefly. PracReProCS is a practical modification of its theoretical counterpart which was analyzed in our recent work. Extension to the undersampled case is also developed. Extensive experimental comparisons demonstrating the advantage of the approach for both simulated and real videos, over existing batch and recursive methods, are shown. Index Terms—Online robust PCA, recursive sparse recovery, large but structured noise, compressed sensing. I.
A Probabilistic Approach to Robust Matrix Factorization
"... Abstract. Matrix factorization underlies a large variety of computer vision applications. It is a particularly challenging problem for largescale applications and when there exist outliers and missing data. In this paper, we propose a novel probabilistic model called Probabilistic Robust Matrix Fac ..."
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Cited by 9 (1 self)
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Abstract. Matrix factorization underlies a large variety of computer vision applications. It is a particularly challenging problem for largescale applications and when there exist outliers and missing data. In this paper, we propose a novel probabilistic model called Probabilistic Robust Matrix Factorization (PRMF) to solve this problem. In particular, PRMF is formulated with a Laplace error and a Gaussian prior which correspond to an ℓ1 loss and an ℓ2 regularizer, respectively. For model learning, we devise a parallelizable expectationmaximization (EM) algorithm which can potentially be applied to largescale applications. We also propose an online extension of the algorithm for sequential data to offer further scalability. Experiments conducted on both synthetic data and some practical computer vision applications show that PRMF is comparable to other stateoftheart robust matrix factorization methods in terms of accuracy and outperforms them particularly for large data matrices. 1
Background subtraction with Dirichlet processes
 In ECCV
, 2012
"... Abstract. Background subtraction is an important first step for video analysis, where it is used to discover the objects of interest for further processing. Such an algorithm often consists of a background model and a regularisation scheme. The background model determines a perpixel measure of if ..."
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Abstract. Background subtraction is an important first step for video analysis, where it is used to discover the objects of interest for further processing. Such an algorithm often consists of a background model and a regularisation scheme. The background model determines a perpixel measure of if a pixel belongs to the background or the foreground, whilst the regularisation brings in information from adjacent pixels. A new method is presented that uses a Dirichlet process Gaussian mixture model to estimate a perpixel background distribution, which is followed by probabilistic regularisation. Key advantages include inferring the perpixel mode count, such that it accurately models dynamic backgrounds, and that it updates its model continuously in a principled way. 1
Robust pca with partial subspace knowledge,”
 in IEEE Intl. Symp. on Information Theory (ISIT),
, 2014
"... AbstractIn recent work, robust Principal Components Analysis (PCA) has been posed as a problem of recovering a lowrank matrix L and a sparse matrix S from their sum, M := L + S and a provably exact convex optimization solution called PCP has been proposed. This work studies the following problem. ..."
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AbstractIn recent work, robust Principal Components Analysis (PCA) has been posed as a problem of recovering a lowrank matrix L and a sparse matrix S from their sum, M := L + S and a provably exact convex optimization solution called PCP has been proposed. This work studies the following problem. Suppose that we have partial knowledge about the column space of the low rank matrix L. Can we use this information to improve the PCP solution, i.e. allow recovery under weaker assumptions? We propose here a simple but useful modification of the PCP idea, called modifiedPCP, that allows us to use this knowledge. We derive its correctness result which shows that, when the available subspace knowledge is accurate, modifiedPCP indeed requires significantly weaker incoherence assumptions than PCP. Extensive simulations are also used to illustrate this. Comparisons with PCP and other existing work are shown for a stylized real application as well. Finally, we explain how this problem naturally occurs in many applications involving time series data, i.e. in what is called the online or recursive robust PCA problem. A corollary for this case is also given.
Efficient higherorder clustering on the grassmann manifold
 In ICCV
, 2013
"... The higherorder clustering problem arises when data is drawn from multiple subspaces or when observations fit a higherorder parametric model. Most solutions to this problem either decompose higherorder similarity measures for use in spectral clustering or explicitly use lowrank matrix represent ..."
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The higherorder clustering problem arises when data is drawn from multiple subspaces or when observations fit a higherorder parametric model. Most solutions to this problem either decompose higherorder similarity measures for use in spectral clustering or explicitly use lowrank matrix representations. In this paper we present our approach of Sparse Grassmann Clustering (SGC) that combines attributes of both categories. While we decompose the higherorder similarity tensor, we cluster data by directly finding a low dimensional representation without explicitly building a similarity matrix. By exploiting recent advances in online estimation on the Grassmann manifold (GROUSE) we develop an efficient and accurate algorithm that works with individual columns of similarities or partial observations thereof. Since it avoids the storage and decomposition of large similarity matrices, our method is efficient, scalable and has low memory requirements even for largescale data. We demonstrate the performance of our SGC method on a variety of segmentation problems including planar segmentation of Kinect depth maps and motion segmentation of the Hopkins 155 dataset for which we achieve performance comparable to the stateoftheart. 1.
GOSUS: Grassmannian Online Subspace Updates with Structuredsparsity
"... We study the problem of online subspace learning in the context of sequential observations involving structured perturbations. In online subspace learning, the observations are an unknown mixture of two components presented to the model sequentially — the main effect which pertains to the subspace a ..."
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Cited by 3 (1 self)
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We study the problem of online subspace learning in the context of sequential observations involving structured perturbations. In online subspace learning, the observations are an unknown mixture of two components presented to the model sequentially — the main effect which pertains to the subspace and a residual/error term. If no additional requirement is imposed on the residual, it often corresponds to noise terms in the signal which were unaccounted for by the main effect. To remedy this, one may impose ‘structural’ contiguity, which has the intended effect of leveraging the secondary terms as a covariate that helps the estimation of the subspace itself, instead of merely serving as a noise residual. We show that the corresponding online estimation procedure can be written as an approximate optimization process on a Grassmannian. We propose an efficient numerical solution, GOSUS, Grassmannian Online Subspace Updates with Structuredsparsity, for this problem. GOSUS is expressive enough in modeling both homogeneous perturbations of the subspace and structural contiguities of outliers, and after certain manipulations, solvable via an alternating direction method of multipliers (ADMM). We evaluate the empirical performance of this algorithm on two problems of interest: online background subtraction and online multiple face tracking, and demonstrate that it achieves competitive performance with the stateoftheart in near real time. 1.
Hyperspectral compressive sensing
 Proc. SPIE 7810, 781003
, 2010
"... Deformable models with sparsity constraints for cardiac motion analysis ..."
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Deformable models with sparsity constraints for cardiac motion analysis
PRACTICAL REPROCS FOR SEPARATING SPARSE AND LOWDIMENSIONAL SIGNAL SEQUENCES FROM THEIR SUM – PART 1
"... This paper designs and evaluates a practical algorithm, called PracReProCS, for recovering a time sequence of sparse vectors St and a time sequence of dense vectors Lt from their sum, Mt: = St + Lt, when any subsequence of the Lt’s lies in a slowly changing lowdimensional subspace. A key applica ..."
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Cited by 3 (3 self)
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This paper designs and evaluates a practical algorithm, called PracReProCS, for recovering a time sequence of sparse vectors St and a time sequence of dense vectors Lt from their sum, Mt: = St + Lt, when any subsequence of the Lt’s lies in a slowly changing lowdimensional subspace. A key application where this problem occurs is in video layering where the goal is to separate a video sequence into a slowly changing background sequence and a sparse foreground sequence that consists of one or more moving regions/objects. PracReProCS is the practical analog of its theoretical counterpart that was studied in our recent work. Index Terms — robust PCA, robust matrix completion, sparse recovery, compressed sensing 1.