scholarly journals An Efficient Tensor Completion Method Combining Matrix Factorization and Smoothness

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Leiming Tang ◽  
Xunjie Cao ◽  
Weiyang Chen ◽  
Changbo Ye
Keyword(s):  
Matrix Factorization ◽  
Low Complexity ◽  
Low Rank ◽  
Total Variation Regularization ◽  
Tensor Completion ◽  
Alternating Direction ◽  
Factorization Model ◽  
Efficiency And Effectiveness ◽  
The Matrix ◽  
Accelerate Convergence

In this paper, the low-complexity tensor completion (LTC) scheme is proposed to improve the efficiency of tensor completion. On one hand, the matrix factorization model is established for complexity reduction, which adopts the matrix factorization into the model of low-rank tensor completion. On the other hand, we introduce the smoothness by total variation regularization and framelet regularization to guarantee the completion performance. Accordingly, given the proposed smooth matrix factorization (SMF) model, an alternating direction method of multiple- (ADMM-) based solution is further proposed to realize the efficient and effective tensor completion. Additionally, we employ a novel tensor initialization approach to accelerate convergence speed. Finally, simulation results are presented to confirm the system gain of the proposed LTC scheme in both efficiency and effectiveness.

scholarly journals Differentiating isoform functions with collaborative matrix factorization

2019 ◽  
Author(s):  
Keyao Wang ◽  
Jun Wang ◽  
Carlotta Domeniconi ◽  
Xiangliang Zhang ◽  
Guoxian Yu
Keyword(s):  
Matrix Factorization ◽  
Characteristic Curve ◽  
Function Prediction ◽  
Low Rank ◽  
Data Matrix ◽  
Supplementary Information ◽  
Genomic Databases ◽  
Gene Level ◽  
The Matrix ◽  
Level Function

Abstract Motivation Isoforms are alternatively spliced mRNAs of genes. They can be translated into different functional proteoforms, and thus greatly increase the functional diversity of protein variants (or proteoforms). Differentiating the functions of isoforms (or proteoforms) helps understanding the underlying pathology of various complex diseases at a deeper granularity. Since existing functional genomic databases uniformly record the annotations at the gene-level, and rarely record the annotations at the isoform-level, differentiating isoform functions is more challenging than the traditional gene-level function prediction. Results Several approaches have been proposed to differentiate the functions of isoforms. They generally follow the multi-instance learning paradigm by viewing each gene as a bag and the spliced isoforms as its instances, and push functions of bags onto instances. These approaches implicitly assume the collected annotations of genes are complete and only integrate multiple RNA-seq datasets. As such, they have compromised performance. We propose a data integrative solution (called DisoFun) to Differentiate isoform Functions with collaborative matrix factorization. DisoFun assumes the functional annotations of genes are aggregated from those of key isoforms. It collaboratively factorizes the isoform data matrix and gene-term data matrix (storing Gene Ontology (GO) annotations of genes) into low-rank matrices to simultaneously explore the latent key isoforms, and achieve function prediction by aggregating predictions to their originating genes. In addition, it leverages the PPI network and GO structure to further coordinate the matrix factorization. Extensive experimental results show that DisoFun improves the AUROC (area under the receiver-operating characteristic curve) and AUPRC (area under the precision-recall curve) of existing solutions by at least 7.7% and 28.9%, respectively. We further investigate DisoFun on four exemplar genes (LMNA, ADAM15, BCL2L1, and CFLAR) with known functions at the isoform-level, and observed that DisoFun can differentiate functions of their isoforms with 90.5% accuracy. Availability The code of DisoFun is available at mlda.swu.edu.cn/codes.php?name=DisoFun. Supplementary information Supplementary data are available at Bioinformatics online.

Matrix factorization for low-rank tensor completion using framelet prior

2018 ◽  
Vol 436-437 ◽  
pp. 403-417 ◽  
Author(s):  
Tai-Xiang Jiang ◽  
Ting-Zhu Huang ◽  
Xi-Le Zhao ◽  
Teng-Yu Ji ◽  
Liang-Jian Deng
Keyword(s):  
Matrix Factorization ◽  
Low Rank ◽  
Tensor Completion ◽  
Rank Tensor

Low-Rank Tensor Completion Based on Log-Det Rank Approximation and Matrix Factorization

2019 ◽  
Vol 80 (3) ◽  
pp. 1888-1912
Author(s):  
Chengfei Shi ◽  
Zhengdong Huang ◽  
Li Wan ◽  
Tifan Xiong
Keyword(s):  
Matrix Factorization ◽  
Low Rank ◽  
Tensor Completion ◽  
Rank Tensor ◽  
Rank Approximation

scholarly journals Followee Recommendation in Microblog Using Matrix Factorization Model with Structural Regularization

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yan Yu ◽  
Robin G. Qiu
Keyword(s):  
Social Network ◽  
Matrix Factorization ◽  
Information Sources ◽  
Quality Information ◽  
High Quality ◽  
Structure Information ◽  
Factorization Model ◽  
Proposed Model ◽  
The Matrix ◽  
High Quality Information

Microblog that provides us a new communication and information sharing platform has been growing exponentially since it emerged just a few years ago. To microblog users, recommending followees who can serve as high quality information sources is a competitive service. To address this problem, in this paper we propose a matrix factorization model with structural regularization to improve the accuracy of followee recommendation in microblog. More specifically, we adapt the matrix factorization model in traditional item recommender systems to followee recommendation in microblog and use structural regularization to exploit structure information of social network to constrain matrix factorization model. The experimental analysis on a real-world dataset shows that our proposed model is promising.

scholarly journals Convex Coupled Matrix and Tensor Completion

2018 ◽  
Vol 30 (11) ◽  
pp. 3095-3127 ◽  
Author(s):  
Kishan Wimalawarne ◽  
Makoto Yamada ◽  
Hiroshi Mamitsuka
Keyword(s):  
Optimal Solution ◽  
Real Data ◽  
Excess Risk ◽  
Low Rank ◽  
Trace Norm ◽  
Tensor Completion ◽  
The Matrix ◽  
Risk Bounds ◽  
Matrix Trace

We propose a set of convex low-rank inducing norms for coupled matrices and tensors (hereafter referred to as coupled tensors), in which information is shared between the matrices and tensors through common modes. More specifically, we first propose a mixture of the overlapped trace norm and the latent norms with the matrix trace norm, and then, propose a completion model regularized using these norms to impute coupled tensors. A key advantage of the proposed norms is that they are convex and can be used to find a globally optimal solution, whereas existing methods for coupled learning are nonconvex. We also analyze the excess risk bounds of the completion model regularized using our proposed norms and show that they can exploit the low-rankness of coupled tensors, leading to better bounds compared to those obtained using uncoupled norms. Through synthetic and real-data experiments, we show that the proposed completion model compares favorably with existing ones.

Tensor completion using total variation and low-rank matrix factorization

2016 ◽  
Vol 326 ◽  
pp. 243-257 ◽  
Author(s):  
Teng-Yu Ji ◽  
Ting-Zhu Huang ◽  
Xi-Le Zhao ◽  
Tian-Hui Ma ◽  
Gang Liu
Keyword(s):  
Total Variation ◽  
Matrix Factorization ◽  
Low Rank ◽  
Tensor Completion ◽  
Rank Matrix ◽  
Low Rank Matrix

Low-rank tensor completion via smooth matrix factorization

2019 ◽  
Vol 70 ◽  
pp. 677-695 ◽  
Author(s):  
Yu-Bang Zheng ◽  
Ting-Zhu Huang ◽  
Teng-Yu Ji ◽  
Xi-Le Zhao ◽  
Tai-Xiang Jiang ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Low Rank ◽  
Tensor Completion ◽  
Rank Tensor

scholarly journals Robust Asymmetric Bayesian Adaptive Matrix Factorization

2017 ◽  
Author(s):  
Xin Guo ◽  
Boyuan Pan ◽  
Deng Cai ◽  
Xiaofei He
Keyword(s):  
Real World ◽  
Matrix Factorization ◽  
State Of The Art ◽  
Low Rank ◽  
Data Sets ◽  
Real World Application ◽  
Factorization Model ◽  
Rank Matrix ◽  
Wide Range ◽  
Low Rank Matrix

Low rank matrix factorizations(LRMF) have attracted much attention due to its wide range of applications in computer vision, such as image impainting and video denoising. Most of the existing methods assume that the loss between an observed measurement matrix and its bilinear factorization follows symmetric distribution, like gaussian or gamma families. However, in real-world situations, this assumption is often found too idealized, because pictures under various illumination and angles may suffer from multi-peaks, asymmetric and irregular noises. To address these problems, this paper assumes that the loss follows a mixture of Asymmetric Laplace distributions and proposes robust Asymmetric Laplace Adaptive Matrix Factorization model(ALAMF) under bayesian matrix factorization framework. The assumption of Laplace distribution makes our model more robust and the asymmetric attribute makes our model more flexible and adaptable to real-world noise. A variational method is then devised for model inference. We compare ALAMF with other state-of-the-art matrix factorization methods both on data sets ranging from synthetic and real-world application. The experimental results demonstrate the effectiveness of our proposed approach.

Attribute interaction aware matrix factorization method for recommendation

2021 ◽  
Vol 25 (5) ◽  
pp. 1115-1130
Author(s):  
Yongquan Wan ◽  
Lihua Zhu ◽  
Cairong Yan ◽  
Bofeng Zhang
Keyword(s):  
Parallel Computing ◽  
Matrix Factorization ◽  
Time Complexity ◽  
Optimization Strategy ◽  
Computing Technology ◽  
Training Time ◽  
Latent Vector ◽  
Factorization Model ◽  
The Matrix ◽  
Original Rating

Matrix factorization (MF) models are effective and easy to expand and are widely used in industry, such as rating prediction and item recommendation. The basic MF model is relatively simple. In practical applications, side information such as attributes or implicit feedback is often combined to improve accuracy by modifying the model and optimizing the algorithm. In this paper, we propose an attribute interaction-aware matrix factorization (AIMF) method for recommendation tasks. We partition the original rating matrix into different sub-matrices according to the attribute interactions, train each sub-matrix independently, and merge all the latent vectors to generate the final score. Since the generated sub-matrices vary in size, an adaptive regularization coefficient optimization strategy and an adaptive latent vector dimension optimization strategy are proposed for sub-matrix training, and a variety of latent vector merging methods are put forward. The method AIMF has two advantages. When the original rating matrix is particularly large, the training time complexity of the MF-based model becomes higher and the update cost of the model is also higher. In AIMF, because each sub-matrix is usually much smaller than the original rating matrix, the training time complexity is greatly reduced after using parallel computing technology. Secondly, in AIMF, it is not necessary to modify the matrix factorization model to incorporate attributes and their interactive information into the model to improve the performance. The experimental results on the two classic public datasets MovieLens 1M and MovieLens 100k show that AIMF can not only effectively improve the accuracy of recommendation, but also make full use of parallel computing technology to improve training efficiency without modifying the matrix factorization model.

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