Online low-rank tensor subspace tracking from incomplete data by CP decomposition using recursive least squares

Kasai, Hiroyuki

doi:10.1109/icassp.2016.7472131

Cited by 39 publications

(44 citation statements)

References 18 publications

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“…However, they do not deal with missing data presence. Online imputation algorithms based on the Candecomp/PARAFAC decomposition are proposed for the presence of missing data [38,39]. While [38] considers the RLS-based updates, it does not consider time-structured data and anomaly detection, [39] considers the stochastic gradient descent (SGD) for large-scale data, and is applied to analyze network anomalies.…”

Section: General Online-based Subspace Methods For High-dimensional Dmentioning

confidence: 99%

Network Volume Anomaly Detection and Identification in Large-Scale Networks Based on Online Time-Structured Traffic Tensor Tracking

Kasai

Kellerer

Kleinsteuber

2016

IEEE Trans. Netw. Serv. Manage.

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This paper addresses network anomography, that is, the problem of inferring network-level anomalies from indirect link measurements. This problem is cast as a low-rank subspace tracking problem for normal flows under incomplete observations, and an outlier detection problem for abnormal flows. Since traffic data is large-scale time-structured data accompanied with noise and outliers under partial observations, an efficient modeling method is essential. To this end, this paper proposes an online subspace tracking of a Hankelized time-structured traffic tensor for normal flows based on the Candecomp/PARAFAC decomposition exploiting the recursive least squares (RLS) algorithm. We estimate abnormal flows as outlier sparse flows via sparsity maximization in the underlying under-constrained linear-inverse problem. A major advantage is that our algorithm estimates normal flows by low-dimensional matrices with time-directional features as well as the spatial correlation of multiple links without using the past observed measurements and the past model parameters. Extensive numerical evaluations show that the proposed algorithm achieves faster convergence per iteration of model approximation, and better volume anomaly detection performance compared to state-of-the-art algorithms.

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Section: General Online-based Subspace Methods For High-dimensional Dmentioning

confidence: 99%

Network Volume Anomaly Detection and Identification in Large-Scale Networks Based on Online Time-Structured Traffic Tensor Tracking

Kasai

Kellerer

Kleinsteuber

2016

IEEE Trans. Netw. Serv. Manage.

Self Cite

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“…In some real-world situation, the processing speed could be faster than data acquiring speed. Kasai [92] proposes another online CP decomposition algorithm OLSTEC while conducting data imputation based on recursive least squares algorithm. ey consider the situations where the data processing speed is much faster than data acquiring speed and propose a more rapid convergence algorithm for tracking dramatically changed subspace.…”

Section: Streaming Tensor Completionmentioning

confidence: 99%

Tensor Completion Algorithms in Big Data Analytics

Song

Caverlee

et al. 2019

ACM Trans. Knowl. Discov. Data

167

118

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Tensor completion is a problem of lling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide a ention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data analytics characterized by diverse variety, large volume, and high velocity. We characterize these advances from four perspectives: general tensor completion algorithms, tensor completion with auxiliary information (variety), scalable tensor completion algorithms (volume), and dynamic tensor completion algorithms (velocity). Further, we identify several tensor completion applications on real-world data-driven problems and present some common experimental frameworks popularized in the literature. Our goal is to summarize these popular methods and introduce them to researchers and practitioners for promoting future research and applications. We conclude with a discussion of key challenges and promising research directions in this community for future exploration.

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“…OLSTEC. The Online Low-Rank Subspace Tracking by Tensor CP Decomposition (OLSTEC) method [12] is similar to one of the methods proposed in [19], but it can handle missing data and is the first paper to consider changes in the factor matrices in its experimental results. The experiment results show that they do better in this regime than OnlineSGD [17].…”

Section: Other Workmentioning

confidence: 99%

Streaming Generalized Canonical Polyadic Tensor Decompositions

Phipps¹,

Johnson²,

Kolda³

2021

Preprint

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In this paper, we develop a method which we call OnlineGCP for computing the Generalized Canonical Polyadic (GCP) tensor decomposition of streaming data. GCP differs from traditional canonical polyadic (CP) tensor decompositions as it allows for arbitrary objective functions which the CP model attempts to minimize. This approach can provide better fits and more interpretable models when the observed tensor data is strongly non-Gaussian. In the streaming case, tensor data is gradually observed over time and the algorithm must incrementally update a GCP factorization with limited access to prior data. In this work, we extend the GCP formalism to the streaming context by deriving a GCP optimization problem to be solved as new tensor data is observed, formulate a tunable history term to balance reconstruction of recently observed data with data observed in the past, develop a scalable solution strategy based on segregated solves using stochastic gradient descent methods, describe a software implementation that provides performance and portability to contemporary CPU and GPU architectures and integrates with Matlab for enhanced useability, and demonstrate the utility and performance of the approach and software on several synthetic and real tensor data sets.

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Online low-rank tensor subspace tracking from incomplete data by CP decomposition using recursive least squares

Cited by 39 publications

References 18 publications

Network Volume Anomaly Detection and Identification in Large-Scale Networks Based on Online Time-Structured Traffic Tensor Tracking

Network Volume Anomaly Detection and Identification in Large-Scale Networks Based on Online Time-Structured Traffic Tensor Tracking

Tensor Completion Algorithms in Big Data Analytics

Streaming Generalized Canonical Polyadic Tensor Decompositions

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