scholarly journals Efficient preconditioning for noisy separable nonnegative matrix factorization problems by successive projection based low-rank approximations

2017 ◽  
Vol 107 (4) ◽  
pp. 643-673 ◽  
Author(s):  
Tomohiko Mizutani ◽  
Mirai Tanaka
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Low Rank ◽  
Low Rank Approximations ◽  
Successive Projection

scholarly journals An Accelerated Symmetric Nonnegative Matrix Factorization Algorithm Using Extrapolation

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1187
Author(s):  
Peitao Wang ◽  
Zhaoshui He ◽  
Jun Lu ◽  
Beihai Tan ◽  
YuLei Bai ◽  
...  
Keyword(s):  
Real World ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Low Rank ◽  
Tensor Factorization ◽  
Real World Data ◽  
Restart Strategy ◽  
Extrapolation Scheme ◽  
Symmetric Nonnegative Matrix Factorization

Symmetric nonnegative matrix factorization (SNMF) approximates a symmetric nonnegative matrix by the product of a nonnegative low-rank matrix and its transpose. SNMF has been successfully used in many real-world applications such as clustering. In this paper, we propose an accelerated variant of the multiplicative update (MU) algorithm of He et al. designed to solve the SNMF problem. The accelerated algorithm is derived by using the extrapolation scheme of Nesterov and a restart strategy. The extrapolation scheme plays a leading role in accelerating the MU algorithm of He et al. and the restart strategy ensures that the objective function of SNMF is monotonically decreasing. We apply the accelerated algorithm to clustering problems and symmetric nonnegative tensor factorization (SNTF). The experiment results on both synthetic and real-world data show that it is more than four times faster than the MU algorithm of He et al. and performs favorably compared to recent state-of-the-art algorithms.

A hybrid algorithm for low-rank approximation of nonnegative matrix factorization

2019 ◽  
Vol 364 ◽  
pp. 129-137
Author(s):  
Peitao Wang ◽  
Zhaoshui He ◽  
Kan Xie ◽  
Junbin Gao ◽  
Michael Antolovich ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Hybrid Algorithm ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Rank Approximation

Underwater Image Enhancement with the Low-Rank Nonnegative Matrix Factorization Method

2021 ◽  
pp. 2154022
Author(s):  
Xiaopeng Liu ◽  
Cong Liu ◽  
Xiaochen Liu
Keyword(s):  
Image Enhancement ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Ground Truth ◽  
Factorization Method ◽  
Low Rank ◽  
Ground Truth Data ◽  
Underwater Image ◽  
Better Than

Due to the scattering and absorption effects in the undersea environment, underwater image enhancement is a challenging problem. To obtain the ground-truth data for training is also an open problem. So, the learning process is unavailable. In this paper, we propose a Low-Rank Nonnegative Matrix Factorization (LR-NMF) method, which only uses the degraded underwater image as input to generate the more clear and realistic image. According to the underwater image formation model, the degraded underwater image could be separated into three parts, the directed component, the back and forward scattering components. The latter two parts can be considered as scattering. The directed component is constrained to have a low rank. After that, the restored underwater image is obtained. The quantitative and qualitative analyses illustrate that the proposed method performed equivalent or better than the state-of-the-art methods. Yet, it’s simple to implement without the training process.

Low-rank nonnegative matrix factorization on Stiefel manifold

2020 ◽  
Vol 514 ◽  
pp. 131-148 ◽  
Author(s):  
Ping He ◽  
Xiaohua Xu ◽  
Jie Ding ◽  
Baichuan Fan
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Low Rank ◽  
Stiefel Manifold

scholarly journals Link Prediction via Convex Nonnegative Matrix Factorization on Multiscale Blocks

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Enming Dong ◽  
Jianping Li ◽  
Zheng Xie
Keyword(s):  
Matrix Factorization ◽  
Link Prediction ◽  
Latent Variable ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Prediction Method ◽  
Original Method ◽  
Divide And Conquer ◽  
Low Rank ◽  
Variable Model

Low rank matrices approximations have been used in link prediction for networks, which are usually global optimal methods and lack of using the local information. The block structure is a significant local feature of matrices: entities in the same block have similar values, which implies that links are more likely to be found within dense blocks. We use this insight to give a probabilistic latent variable model for finding missing links by convex nonnegative matrix factorization with block detection. The experiments show that this method gives better prediction accuracy than original method alone. Different from the original low rank matrices approximations methods for link prediction, the sparseness of solutions is in accord with the sparse property for most real complex networks. Scaling to massive size network, we use the block information mapping matrices onto distributed architectures and give a divide-and-conquer prediction method. The experiments show that it gives better results than common neighbors method when the networks have a large number of missing links.

scholarly journals A projective approach to nonnegative matrix factorization

2021 ◽  
Vol 37 ◽  
pp. 583-597
Author(s):  
Patrick Groetzner
Keyword(s):  
Matrix Factorization ◽  
Data Science ◽  
Nonnegative Matrix Factorization ◽  
Heuristic Method ◽  
Nonnegative Matrix ◽  
Type A ◽  
Low Rank ◽  
Feasibility Problem ◽  
Low Rank Approximation ◽  
Rank Approximation

In data science and machine learning, the method of nonnegative matrix factorization (NMF) is a powerful tool that enjoys great popularity. Depending on the concrete application, there exist several subclasses each of which performs a NMF under certain constraints. Consider a given square matrix $A$. The symmetric NMF aims for a nonnegative low-rank approximation $A\approx XX^T$ to $A$, where $X$ is entrywise nonnegative and of given order. Considering a rectangular input matrix $A$, the general NMF again aims for a nonnegative low-rank approximation to $A$ which is now of the type $A\approx XY$ for entrywise nonnegative matrices $X,Y$ of given order. In this paper, we introduce a new heuristic method to tackle the exact nonnegative matrix factorization problem (of type $A=XY$), based on projection approaches to solve a certain feasibility problem.

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