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.

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

A PSO Based Approach for Producing Optimized Latent Factor in Special Reference to Big Data

2016 ◽  
Vol 7 (3) ◽  
pp. 55-70 ◽  
Author(s):  
Bharat Singh ◽  
Om Prakash Vyas
Keyword(s):  
Big Data ◽  
Matrix Factorization ◽  
Nonnegative Matrix ◽  
Low Rank ◽  
Data Matrix ◽  
Experimental Result ◽  
Low Rank Approximation ◽  
Latent Factor ◽  
New Approach ◽  
Rank Approximation

Now a day's application deal with Big Data has tremendously been used in the popular areas. To tackle with such kind of data various approaches have been developed by researchers in the last few decades. A recent investigated techniques to factored the data matrix through a known latent factor in a lower size space is the so called matrix factorization. In addition, one of the problems with the NMF approaches, its randomized valued could not provide absolute optimization in limited iteration, but having local optimization. Due to this, the authors have proposed a new approach that considers the initial values of the decomposition to tackle the issues of computationally expensive. They have devised an algorithm for initializing the values of the decomposed matrix based on the PSO. In this paper, the auhtors have intended a genetic algorithm based technique while incorporating the nonnegative matrix factorization. Through the experimental result, they will show the proposed method converse very fast in comparison to other low rank approximation like simple NMF multiplicative, and ACLS technique.

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.

scholarly journals Coordinate Descent-Based Sparse Nonnegative Matrix Factorization for Robust Cancer-Class Discovery and Microarray Data Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Melisew Tefera Belachew
Keyword(s):  
Microarray Data ◽  
Matrix Factorization ◽  
Data Science ◽  
Nonnegative Matrix Factorization ◽  
Real Life ◽  
Nonnegative Matrix ◽  
Descent Method ◽  
Coordinate Descent ◽  
Microarray Data Analysis ◽  
Robust Clustering

Determining the number of clusters in high-dimensional real-life datasets and interpreting the final outcome are among the challenging problems in data science. Discovering the number of classes in cancer and microarray data plays a vital role in the treatment and diagnosis of cancers and other related diseases. Nonnegative matrix factorization (NMF) plays a paramount role as an efficient data exploratory tool for extracting basis features inherent in massive data. Some algorithms which are based on incorporating sparsity constraints in the nonconvex NMF optimization problem are applied in the past for analyzing microarray datasets. However, to the best of our knowledge, none of these algorithms use block coordinate descent method which is known for providing closed form solutions. In this paper, we apply an algorithm developed based on columnwise partitioning and rank-one matrix approximation. We test this algorithm on two well-known cancer datasets: leukemia and multiple myeloma. The numerical results indicate that the proposed algorithm performs significantly better than related state-of-the-art methods. In particular, it is shown that this method is capable of robust clustering and discovering larger cancer classes in which the cluster splits are stable.

scholarly journals Incremental Matrix Factorization: A Linear Feature Transformation Perspective

2017 ◽  
Author(s):  
Xunpeng Huang ◽  
Le Wu ◽  
Enhong Chen ◽  
Hengshu Zhu ◽  
Qi Liu ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Low Rank ◽  
Feature Transformation ◽  
Low Rank Approximation ◽  
Linear Feature ◽  
Special Cases ◽  
Rank Approximation ◽  
Training Error ◽  
Real World Datasets ◽  
And Storage

Matrix Factorization (MF) is among the most widely used techniques for collaborative filtering based recommendation. Along this line, a critical demand is to incrementally refine the MF models when new ratings come in an online scenario. However, most of existing incremental MF algorithms are limited by specific MF models or strict use restrictions. In this paper, we propose a general incremental MF framework by designing a linear transformation of user and item latent vectors over time. This framework shows a relatively high accuracy with a computation and space efficient training process in an online scenario. Meanwhile, we explain the framework with a low-rank approximation perspective, and give an upper bound on the training error when this framework is used for incremental learning in some special cases. Finally, extensive experimental results on two real-world datasets clearly validate the effectiveness, efficiency and storage performance of the proposed framework.

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