Tensor Completion Algorithms in Big Data Analytics

Song, Qingquan; Ge, Hancheng; Caverlee, James; Hu, Xia

doi:10.48550/arxiv.1711.10105

Cited by 4 publications

(5 citation statements)

References 138 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast to most works (see our introduction and the overviews [Cichocki et al, 2017, Song et al, 2018), the tensors in this paper only appear after a discretization of the feature space determined by the labelled data set. Discretizations are of course always needed when a discrete tensor approximates an infinite dimensional function.…”

Section: Related Workmentioning

confidence: 99%

TTML: tensor trains for general supervised machine learning

Vandereycken¹,

Voorhaar²

2022

Preprint

View full text Add to dashboard Cite

This work proposes a novel general-purpose estimator for supervised machine learning (ML) based on tensor trains (TT). The estimator uses TTs to parametrize discretized functions, which are then optimized using Riemannian gradient descent under the form of a tensor completion problem. Since this optimization is sensitive to initialization, it turns out that the use of other ML estimators for initialization is crucial. This results in a competitive, fast ML estimator with lower memory usage than many other ML estimators, like the ones used for the initialization.

show abstract

Section: Related Workmentioning

confidence: 99%

TTML: tensor trains for general supervised machine learning

Vandereycken¹,

Voorhaar²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…There are other models such as RESCAL [3], Tuckerbased methods [2] etc that have been considered for tensor completion tasks. We refer the interested reader to a recent survey for more information [13].…”

Section: Related Workmentioning

confidence: 99%

“…Most tensor datasets encountered in the above settings are not fully observed. This leads to tensor completion, the problem of predicting the missing entries, given a small number of observations from the tensor [2,13]. In order to recover the missing entries, it is important to take into account the data efficiency of the tensor completion model.…”

Section: Introductionmentioning

confidence: 99%

Recovery Guarantees for Quadratic Tensors with Limited Observations

Zhang¹,

Sharan²,

Charikar³

et al. 2018

Preprint

View full text Add to dashboard Cite

We consider the tensor completion problem of predicting the missing entries of a tensor. The commonly used CP model has a triple product form, but an alternate family of quadratic models which are the sum of pairwise products instead of a triple product have emerged from applications such as recommendation systems. Non-convex methods are the method of choice for learning quadratic models, and this work examines their sample complexity and error guarantee. Our main result is that with the number of samples being only linear in the dimension, all local minima of the mean squared error objective are global minima and recover the original tensor accurately. The techniques lead to simple proofs showing that convex relaxation can recover quadratic tensors provided with linear number of samples. We substantiate our theoretical results with experiments on synthetic and real-world data, showing that quadratic models have better performance than CP models in scenarios where there are limited amount of observations available.

show abstract

“…Tensor decomposition, as a multi-dimensional generalization of matrix decomposition, is a multi-decades-old mathematical technique in multi-way data analysis since the 1960s, see [13] and references therein; tensor decompositions are widely applied in areas from signal processing such as blind source separation and multi-modal data fusion to machine learning such as model compression and learning latent variable models [3,64]. Tensor computing recently emerges as a promising solution for big data processing due to its ability to model wide variety of data such as graphical, tabular, discrete, and continuous data [42,66,78]; algorithms to cater for different data quality / veracity or missing data [65] and provide real-time analytics for big data velocity such as streaming analytics [68,69]; and able to capture the complex correlation structure in data with large volume and generate valuable insights for many big data distributed applications [12,14]. Tensor network computing, on the other hand, is a well-established technique among the numerical community; the technique provides unprecedented large-scale scientific computing with performance comparable to competing techniques such as sparse-grid methods [37,38].…”

Section: Introductionmentioning

confidence: 99%

Protecting Big Data Privacy Using Randomized Tensor Network Decomposition and Dispersed Tensor Computation

Ong,

Ng,

Tjuawinata

et al. 2021

Preprint

View full text Add to dashboard Cite

Data privacy is an important issue for organizations and enterprises to securely outsource data storage, sharing, and computation on clouds / fogs. However, data encryption is complicated in terms of the key management and distribution; existing secure computation techniques are expensive in terms of computational / communication cost and therefore do not scale to big data computation. Tensor network decomposition and distributed tensor computation have been widely used in signal processing and machine learning for dimensionality reduction and large-scale optimization. However, the potential of distributed tensor networks for big data privacy preservation have not been considered before, this motivates the current study. Our primary intuition is that tensor network representations are mathematically non-unique, unlinkable, and uninterpretable; tensor network representations naturally support a range of multilinear operations for compressed and distributed / dispersed computation. Therefore, we propose randomized algorithms to decompose big data into randomized tensor network representations and analyze the privacy leakage for 1D to 3D data tensors. The randomness mainly comes from the complex structural information commonly found in big data; randomization is based on controlled perturbation applied to the tensor blocks prior to decomposition. The distributed tensor representations are dispersed on multiple clouds / fogs or servers / devices with metadata privacy, this provides both distributed trust and management to seamlessly secure big data storage, communication, sharing, and computation. Experiments show that the proposed randomization techniques are helpful for big data anonymization and efficient for big data storage and computation.

show abstract

Tensor Completion Algorithms in Big Data Analytics

Cited by 4 publications

References 138 publications

TTML: tensor trains for general supervised machine learning

TTML: tensor trains for general supervised machine learning

Recovery Guarantees for Quadratic Tensors with Limited Observations

Protecting Big Data Privacy Using Randomized Tensor Network Decomposition and Dispersed Tensor Computation

Contact Info

Product

Resources

About