Coupled Graph and Tensor Factorization for Recommender Systems and Community Detection

Ioannidis, Vassilis N.; Zamzam, Ahmed S.; Giannakis, Georgios B.; Sidiropoulos, Nicholas D.

doi:10.1109/tkde.2019.2941716

Cited by 38 publications

(25 citation statements)

References 26 publications

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“…Then, we update A ðnÞ . The distance function kX ðnÞ in;: À a ðnÞ in;: E ðnÞ k 2 2 is an euclidean distance with L 2 norm regularization A ka ðnÞ in;: k 2 2 , i n 2 I n [52]. Thus, the optimization objective ( 9) is a u-convex and L-smooth function obviously [49], [50], [53].…”

Section: Optimization Process For Factor Matricesmentioning

confidence: 99%

“…The CPU server is equipped with 8 Intel(R) Xeon(R) E5-2620 v4 CPUs and each core has 2 hyperthreads, running on 2.10 GHz, for the state of the art algorithms for STD, e.g., PÀTucker [46], CD [47] and HOOI [41]. The experiments are conducted 3 public datasets : Netflix, 1 Movielens, 2 and Yahoo-music. 3 The datasets which be used in our experiments can be downloaded in this link.…”

Section: Experimental Settingsmentioning

confidence: 99%

“…T ENSORS are a widely used data representation style for interaction data in the Machine Learning (ML) application community [1], e.g, in Recommendation Systems [2], Quality of Service (QoS) [3], Network Flow [4], Cyber-Physical-Social (CPS) [5], or Social Networks [6]. In addition to applications in which the data is naturally represented in the form of tensors, another common used case is the fusion in multi-view or multi-modality problems [7].…”

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confidence: 99%

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SGD_Tucker: A Novel Stochastic Optimization Strategy for Scalable Parallel Sparse Tucker Decomposition

Rellermeyer

et al. 2021

IEEE Trans. Parallel Distrib. Syst.

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Sparse Tucker Decomposition (STD) algorithms learn a core tensor and a group of factor matrices to obtain an optimal low-rank representation feature for the High-Order, High-Dimension, and Sparse Tensor (HOHDST). However, existing STD algorithms face the problem of intermediate variables explosion which results from the fact that the formation of those variables, i.e., matrices Khatri-Rao product, Kronecker product, and matrix-matrix multiplication, follows the whole elements in sparse tensor. The above problems prevent deep fusion of efficient computation and big data platforms. To overcome the bottleneck, a novel stochastic optimization strategy (SGD Tucker) is proposed for STD which can automatically divide the high-dimension intermediate variables into small batches of intermediate matrices. Specifically, SGD Tucker only follows the randomly selected small samples rather than the whole elements, while maintaining the overall accuracy and convergence rate. In practice, SGD Tucker features the two distinct advancements over the state of the art. First, SGD Tucker can prune the communication overhead for the core tensor in distributed settings. Second, the low data-dependence of SGD Tucker enables fine-grained parallelization, which makes SGD Tucker obtaining lower computational overheads with the same accuracy. Experimental results show that SGD Tucker runs at least 2X faster than the state of the art.

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Section: Optimization Process For Factor Matricesmentioning

confidence: 99%

Section: Experimental Settingsmentioning

confidence: 99%

mentioning

confidence: 99%

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SGD_Tucker: A Novel Stochastic Optimization Strategy for Scalable Parallel Sparse Tucker Decomposition

Rellermeyer

et al. 2021

IEEE Trans. Parallel Distrib. Syst.

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“…I N the past decades, tensor completion has aroused increasing attention due to its wide applications in a variety of fields, such as computer vision [1]- [11], multi-relational link prediction [12]- [14], and recommendation system [15]- [18]. The goal of tensor completion is to recover an incomplete tensor from partially observed entries, and the most existing methods try to achieve it via the low-rank structure assumption.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Tensor Completion Method Via New Latent Nuclear Norm

Sun

Qiu

et al. 2020

IEEE Access

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In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding schemes. To overcome this drawback, a new latent nuclear norm equipped with a more balanced unfolding scheme is defined for low-rank regularizer. Moreover, the new latent nuclear norm together with the Frank-Wolfe (FW) algorithm is developed as an efficient completion method by utilizing the sparsity structure of observed tensor. Specifically, both FW linear subproblem and line search only need to access the observed entries, by which we can instead maintain the sparse tensors and a set of small basis matrices during iteration. Most operations are based on sparse tensors, and the closed-form solution of FW linear subproblem can be obtained from rank-one SVD. We theoretically analyze the space-complexity and time-complexity of the proposed method, and show that it is much more efficient over other norm-based completion methods for higher-order tensors. Extensive experimental results of visual-data inpainting demonstrate that the proposed method is able to achieve state-of-the-art performance at smaller costs of time and space, which is very meaningful for the memory-limited equipment in practical applications. INDEX TERMS Tensor completion, tensor ring decomposition, tensor ring rank, latent nuclear norm, image/video inpainting.

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“…The different types of data are exposed to noise that requires sophisticated robust algorithms to have an acceptable level of performance. The heterogeneous data sets are present, nowadays, in multiple fields such as the bio-medical [2], or recommendation systems and social networks [3], to mention a few. These data sets may be structured in matrices or tensors of low and highorder.…”

Section: Introductionmentioning

confidence: 99%

Breaking the Curse of Dimensionality for Coupled Matrix-Tensor Factorization

Boudehane

Zniyed

Tenenhaus

et al. 2019

2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

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In different application fields, heterogeneous data sets are structured into either matrices or higher-order tensors. In some cases, these structures present the property of having common underlying factors, which is used to improve the efficiency of factor-matrices estimation in the process of the so-called coupled matrix-tensor factorization (CMTF). Many methods target the CMTF problem relying on alternating algorithms or gradient approaches. However, computational complexity remains a challenge when the data sets are tensors of high-order, which is linked to the well-known "curse of dimensionality". In this paper, we present a methodological approach, using the Joint dImensionality Reduction And Factors rEtrieval (JIRAFE) algorithm for joint factorization of high-order tensor and matrix. This approach reduces the high-order CMTF problem into a set of 3-order CMTF and canonical polyadic decomposition (CPD) problems. The proposed algorithm is evaluated on simulation and compared with a gradient-based method.

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Coupled Graph and Tensor Factorization for Recommender Systems and Community Detection

Cited by 38 publications

References 26 publications

SGD_Tucker: A Novel Stochastic Optimization Strategy for Scalable Parallel Sparse Tucker Decomposition

SGD_Tucker: A Novel Stochastic Optimization Strategy for Scalable Parallel Sparse Tucker Decomposition

An Efficient Tensor Completion Method Via New Latent Nuclear Norm

Breaking the Curse of Dimensionality for Coupled Matrix-Tensor Factorization

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