Partitioned Alternating Least Squares Technique for Canonical Polyadic Tensor Decomposition

Tichavský, Petr; Phan, Anh-Huy; Cichocki, Andrzej

doi:10.1109/lsp.2016.2577383

Cited by 16 publications

(14 citation statements)

References 12 publications

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“….Using the optimization problem of the MKLMF algorithm (15) in this paper, we study the linear combination of 3 base kernels. At the same time, we use 3 base cores to test the KMF algorithm proposed in this paper.…”

Section: Results Analysismentioning

confidence: 99%

“… Representing Frobenius 2 -norm;  a normalization term that can avoid overfitting. These problems are non-convex and can be solved by gradient descent algorithm and alternative Least Square (ALS) [15]:Assuming that U is fixed, V is obtained by solving equation (2).At this point, the problem can be decomposed into N separate ridge regression problems [16]. For the j column of V , the ridge regression problem can be expressed as follows:…”

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confidence: 99%

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Research on Matrix Factorization Algorithm based on Multiple Kernel Learning in Collaborative Filtering

Liu¹,

Zhang²

2018

Proceedings of the 2018 International Conference on Transportation &Amp; Logistics, Information &Amp; Communication, Smart City

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The matrix factorization (MF) algorithm plays an important role in collaborative filtering (CF). The traditional MF algorithms usually assume that the correlated data is distributed on a linear hyperplane, which is not always the case. Therefore, it is a hot topic to combine the kernel algorithm with the matrix factorization algorithm for collaborative filtering. Aiming at the shortcomings of the existing CF algorithm, an single matrix factorization method based on dictionary is firstly proposed for collaborative filtering. On this basis, considering that data can be efficiently embedded into high dimensional space, only one kernel function can not achieve the limitation of optimality energy, a matrix factorization algorithm based on multi kernel learning (MKLMF) is proposed for collaborative filtering. The MKLMF algorithm assumes that there are a set of p positive defined base kernels, and then the two potential factor matrices are embedded into the high dimensional Hilbert space by the best linear group of the learned p kernels. Finally, the product of the two potential factor matrices is used to realize the nonlinear reconstruction of the scoring matrix in the original space. A full simulation experiment is carried out with real data sets. The simulation results show that the proposed algorithm can accurately grasp the nonlinear correlation between data, and the prediction accuracy is better than the latest CF algorithm.

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Section: Results Analysismentioning

confidence: 99%

mentioning

confidence: 99%

Research on Matrix Factorization Algorithm based on Multiple Kernel Learning in Collaborative Filtering

Liu¹,

Zhang²

2018

Proceedings of the 2018 International Conference on Transportation &Amp; Logistics, Information &Amp; Communication, Smart City

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“…Felten, et al, [35] The goal of Alternating least squares (ALS) algorithm is to update each matrix factor alternately in each iteration by solving quadratic problems. Tichavský, et al, [36] Alternating least squares (ALS) algorithm worked as multiple matrices A, B, C which resolved to find a quadratic matrix A, B and C in balanced way. Similarly, when looking for the quadratic form of B, then C and A are equal, and when looking for the quadratic form of C, then A and B are equal.…”

Section: Where Representmentioning

confidence: 99%

“…Tensor data is conventionally still needed to estimate the filtering about the data mismatch and estimation error. In this study, they are implemented together with other algorithms [36].Therefore, we added Alternating Least Squares (ALS) as an embedded algorithm capable of calculating customer and menu matrices that are considered not sequential and have many negative values that must be converted to quadratic form without eliminating back and forth mode. Previous studies [40] [36] [35] reported that ALS is useful for overcoming convexity or bulging coordinates towards the middle or to the edge of void values.…”

Section: C5 Calculations By Tensor Alternating Least Squares (Als)mentioning

confidence: 99%

Recommender System Based Tensor Candecomp Parafact Algorithm-ALS to Handle Sparse Data in Food Commerce Information Services

Hanafi

Suryana

Basari³

2019

International Journal of Simulation: Systems, Science &Amp; Technology

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Recommender systems have been widely researched in many applications especially in e-commerce services with the aim to make clear and easy communication between consumer and provider. Simple examples of Recommender systems would include personal and commercial recommendation for the purchase of everyday goods. However, previous studies have not included high order matrix calculation to estimate consumer parameters, e.g., customer behavior, location and their purchase preferences such as those in the field of business online commerce. This study extends the use of Candecomp Parafact algorithm when applied to recommender system to understand consumer preferences. In addition, it is also aimed to produce bilinear models which are constant and stable so that localization can be done to provide more accurate results. As an example the research provides a model based on tensor theory for restaurant and menu selection by analyzing the customer and restaurant parameters.

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“…To obtain the CPD, we can minimize the Frobenius norm of the error of the tensor Y and its estimate, e.g., using the Alternating Least Squares (ALS) algorithm to update sequentially the factor matrices [7][8][9][10], or the non-linear conjugate gradient method [11,12], the Levenberg-Marquardt (LM) algorithm [13,14], the Krylov LM algorithm [15,16], the nonlinear least squares (NLS) algorithm [17] to update all the parameters at a time. In practice, real-world data does not exactly admit the low-rank CPD.…”

Section: Introductionmentioning

confidence: 99%

Canonical Polyadic Tensor Decomposition With Low-Rank Factor Matrices

Phan

Tichavský

Sobolev

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper proposes a constrained canonical polyadic (CP) tensor decomposition method with low-rank factor matrices. In this way, we allow the CP decomposition with high rank while keeping the number of the model parameters small. First, we propose an algorithm to decompose the tensors into factor matrices of given ranks. Second, we propose an algorithm which can determine the ranks of the factor matrices automatically, such that the fitting error is bounded by a userselected constant. The algorithms are verified on the decomposition of a tensor of the MNIST hand-written image dataset.

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Partitioned Alternating Least Squares Technique for Canonical Polyadic Tensor Decomposition

Cited by 16 publications

References 12 publications

Research on Matrix Factorization Algorithm based on Multiple Kernel Learning in Collaborative Filtering

Research on Matrix Factorization Algorithm based on Multiple Kernel Learning in Collaborative Filtering

Recommender System Based Tensor Candecomp Parafact Algorithm-ALS to Handle Sparse Data in Food Commerce Information Services

Canonical Polyadic Tensor Decomposition With Low-Rank Factor Matrices

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