Joint Tensor Factorization and Outlying Slab Suppression With Applications

Fu, Xiao; Huang, Kejun; Ma, Wing-Kin; Sidiropoulos, Nicholas D.; Bro, Rasmus

doi:10.1109/tsp.2015.2469642

Cited by 57 publications

(33 citation statements)

References 49 publications

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“…This is the main attraction of the AO-ADMM approach of [102], which can also deal with more general loss functions and missing elements, while maintaining the monotone decrease of the cost and conceptual simplicity of ALS. The AO-ADMM framework has been recently extended to handle robust tensor factorization problems where some slabs are grossly corrupted [106].…”

Section: G Constraintsmentioning

confidence: 99%

Tensor Decomposition for Signal Processing and Machine Learning

Sidiropoulos

Lathauwer

et al. 2017

IEEE Trans. Signal Process.

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1,299

989

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Tensors or {\em multi-way arrays} are functions of three or more indices $(i,j,k,\cdots)$ -- similar to matrices (two-way arrays), which are functions of two indices $(r,c)$ for (row,column). Tensors have a rich history, stretching over almost a century, and touching upon numerous disciplines; but they have only recently become ubiquitous in signal and data analytics at the confluence of signal processing, statistics, data mining and machine learning. This overview article aims to provide a good starting point for researchers and practitioners interested in learning about and working with tensors. As such, it focuses on fundamentals and motivation (using various application examples), aiming to strike an appropriate balance of breadth {\em and depth} that will enable someone having taken first graduate courses in matrix algebra and probability to get started doing research and/or developing tensor algorithms and software. Some background in applied optimization is useful but not strictly required. The material covered includes tensor rank and rank decomposition; basic tensor factorization models and their relationships and properties (including fairly good coverage of identifiability); broad coverage of algorithms ranging from alternating optimization to stochastic gradient; statistical performance analysis; and applications ranging from source separation to collaborative filtering, mixture and topic modeling, classification, and multilinear subspace learning.Comment: revised version, overview articl

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Section: G Constraintsmentioning

confidence: 99%

Tensor Decomposition for Signal Processing and Machine Learning

Sidiropoulos

Lathauwer

et al. 2017

IEEE Trans. Signal Process.

Self Cite

1,299

989

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“…This suggests that it can also be beneficial to perform simultaneous clustering and factorization. This idea is explored by the authors of Ref , where they demonstrate the effectiveness of such an approach.…”

Section: Tensor‐based Models In Rsmentioning

confidence: 99%

Tensor methods and recommender systems

Frolov

Oseledets

2017

WIREs Data Min & Knowl

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A substantial progress in development of new and efficient tensor factorization techniques has led to an extensive research of their applicability in recommender systems field. Tensor-based recommender models push the boundaries of traditional collaborative filtering techniques by taking into account a multifaceted nature of real environments, which allows to produce more accurate, situational (e.g. context-aware, criteria-driven) recommendations. Despite the promising results, tensor-based methods are poorly covered in existing recommender systems surveys. This survey aims to complement previous works and provide a comprehensive overview on the subject. To the best of our knowledge, this is the first attempt to consolidate studies from various application domains, which helps to get a notion of the current state of the field. We also provide a high level discussion of the future perspectives and directions for further improvement of tensor-based recommendation systems.

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“…within the processed tensor (also known as outliers), whether implemented by means of HOSVD, or HOOI [18]- [20]. The same sensitivity has also been documented in PCA, which is a special case of Tucker for 2-way tensors (matrices).…”

mentioning

confidence: 70%

“…Large datasets often contain heavily corrupted, outlying entries due to various causes, such as sensor malfunctions, errors in data storage/transfer, heavy-tail noise, intermittent variations of the sensing environment, and even intentional dataset "poisoning" [31]. Regretfully, such corruptions that lie far from the sought-after subspaces are known to significantly affect PCA and its multi-way generalization, Tucker, even when they appear as a small fraction of the processed data [18], [20], [21]. Accordingly, in such cases, the performance of any application that relies on PCA and Tucker can be compromised.…”

Section: Data Corruption and L1-norm Reformulation Of Pcamentioning

confidence: 99%

L1-Norm Tucker Tensor Decomposition

2019

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Tucker decomposition is a common method for the analysis of multi-way/tensor data. Standard Tucker has been shown to be sensitive against heavy corruptions, due to its L2-norm-based formulation which places squared emphasis to peripheral entries.In this work, we explore L1-Tucker, an L1-norm based reformulation of standard Tucker decomposition. After formulating the problem, we present two algorithms for its solution, namely L1-norm Higher-Order Singular Value Decomposition (L1-HOSVD) and L1-norm Higher-Order Orthogonal Iterations (L1-HOOI). The presented algorithms are accompanied by complexity and convergence analysis. Our numerical studies on tensor reconstruction and classification corroborate that L1-Tucker, implemented by means of the proposed methods, attains similar performance to standard Tucker when the processed data are corruption-free, while it exhibits sturdy resistance against heavily corrupted entries.

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Joint Tensor Factorization and Outlying Slab Suppression With Applications

Cited by 57 publications

References 49 publications

Tensor Decomposition for Signal Processing and Machine Learning

Tensor Decomposition for Signal Processing and Machine Learning

Tensor methods and recommender systems

L1-Norm Tucker Tensor Decomposition

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