Instantaneous Versus Convolutive Non-Negative Matrix Factorization

2010 ◽  
pp. 353-370 ◽  
Author(s):  
Wenwu Wang
Keyword(s):  
Machine Learning ◽  
Performance Evaluation ◽  
Data Analysis ◽  
Matrix Factorization ◽  
Temporal Structure ◽  
Low Rank ◽  
Basis Matrix ◽  
And Performance ◽  
Separation Problems ◽  
Non Negative Matrix Factorization

Non-negative matrix factorization (NMF) is an emerging technique for data analysis and machine learning, which aims to find low-rank representations for non-negative data. Early works in NMF are mainly based on the instantaneous model, i.e. using a single basis matrix to represent the data. Recent works have shown that the instantaneous model may not be satisfactory for many audio application tasks. The convolutive NMF model, which has an advantage of revealing the temporal structure possessed by many signals, has been proposed. This chapter intends to provide a brief overview of the models and algorithms for both the instantaneous and the convolutive NMF, with a focus on the theoretical analysis and performance evaluation of the convolutive NMF algorithms, and their applications to audio pattern separation problems.

scholarly journals Application of non-negative matrix factorization to multispectral FLIM data analysis

2012 ◽  
Vol 3 (9) ◽  
pp. 2244 ◽  
Author(s):  
Paritosh Pande ◽  
Brian E. Applegate ◽  
Javier A. Jo
Keyword(s):  
Data Analysis ◽  
Matrix Factorization ◽  
Non Negative Matrix Factorization

scholarly journals A Quantum-inspired Classical Algorithm for Separable Non-negative Matrix Factorization

2019 ◽  
Author(s):  
Zhihuai Chen ◽  
Yinan Li ◽  
Xiaoming Sun ◽  
Pei Yuan ◽  
Jialin Zhang
Keyword(s):  
Image Processing ◽  
Polynomial Time ◽  
Matrix Factorization ◽  
Text Analysis ◽  
Low Rank ◽  
Nonnegative Matrices ◽  
Classical Algorithm ◽  
Data Points ◽  
Conical Hull ◽  
Non Negative Matrix Factorization

Non-negative Matrix Factorization (NMF) asks to decompose a (entry-wise) non-negative matrix into the product of two smaller-sized nonnegative matrices, which has been shown intractable in general. In order to overcome this issue, separability assumption is introduced which assumes all data points are in a conical hull. This assumption makes NMF tractable and widely used in text analysis and image processing, but still impractical for huge-scale datasets. In this paper, inspired by recent development on dequantizing techniques, we propose a new classical algorithm for separable NMF problem. Our new algorithm runs in polynomial time in the rank and logarithmic in the size of input matrices, which achieves an exponential speedup in the low-rank setting.

scholarly journals Adaptive-Weighted Multiview Deep Basis Matrix Factorization for Multimedia Data Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Shicheng Li ◽  
Qinghua Liu ◽  
Jiangyan Dai ◽  
Wenle Wang ◽  
Xiaolin Gui ◽  
...  
Keyword(s):  
Data Analysis ◽  
Matrix Factorization ◽  
Feature Learning ◽  
Representation Learning ◽  
Feature Representation ◽  
Multimedia Data ◽  
Basis Matrix ◽  
Rich Information ◽  
Low Dimensional ◽  
Better Than

Feature representation learning is a key issue in artificial intelligence research. Multiview multimedia data can provide rich information, which makes feature representation become one of the current research hotspots in data analysis. Recently, a large number of multiview data feature representation methods have been proposed, among which matrix factorization shows the excellent performance. Therefore, we propose an adaptive-weighted multiview deep basis matrix factorization (AMDBMF) method that integrates matrix factorization, deep learning, and view fusion together. Specifically, we first perform deep basis matrix factorization on data of each view. Then, all views are integrated to complete the procedure of multiview feature learning. Finally, we propose an adaptive weighting strategy to fuse the low-dimensional features of each view so that a unified feature representation can be obtained for multiview multimedia data. We also design an iterative update algorithm to optimize the objective function and justify the convergence of the optimization algorithm through numerical experiments. We conducted clustering experiments on five multiview multimedia datasets and compare the proposed method with several excellent current methods. The experimental results demonstrate that the clustering performance of the proposed method is better than those of the other comparison methods.

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