scholarly journals Nonnegative matrix factorization for spectral data analysis

2006 ◽  
Vol 416 (1) ◽  
pp. 29-47 ◽  
Author(s):  
V. Paul Pauca ◽  
J. Piper ◽  
Robert J. Plemmons
2020 ◽  
Vol 21 (S6) ◽  
Author(s):  
Yuanyuan Ma ◽  
Junmin Zhao ◽  
Yingjun Ma

Abstract Background With the rapid development of high-throughput technique, multiple heterogeneous omics data have been accumulated vastly (e.g., genomics, proteomics and metabolomics data). Integrating information from multiple sources or views is challenging to obtain a profound insight into the complicated relations among micro-organisms, nutrients and host environment. In this paper we propose a multi-view Hessian regularization based symmetric nonnegative matrix factorization algorithm (MHSNMF) for clustering heterogeneous microbiome data. Compared with many existing approaches, the advantages of MHSNMF lie in: (1) MHSNMF combines multiple Hessian regularization to leverage the high-order information from the same cohort of instances with multiple representations; (2) MHSNMF utilities the advantages of SNMF and naturally handles the complex relationship among microbiome samples; (3) uses the consensus matrix obtained by MHSNMF, we also design a novel approach to predict the classification of new microbiome samples. Results We conduct extensive experiments on two real-word datasets (Three-source dataset and Human Microbiome Plan dataset), the experimental results show that the proposed MHSNMF algorithm outperforms other baseline and state-of-the-art methods. Compared with other methods, MHSNMF achieves the best performance (accuracy: 95.28%, normalized mutual information: 91.79%) on microbiome data. It suggests the potential application of MHSNMF in microbiome data analysis. Conclusions Results show that the proposed MHSNMF algorithm can effectively combine the phylogenetic, transporter, and metabolic profiles into a unified paradigm to analyze the relationships among different microbiome samples. Furthermore, the proposed prediction method based on MHSNMF has been shown to be effective in judging the types of new microbiome samples.


2014 ◽  
Vol 971-973 ◽  
pp. 1874-1883
Author(s):  
Akio Ishida ◽  
Kei Fujii ◽  
Naoki Yamamoto ◽  
Jun Murakami ◽  
Satoko Saito ◽  
...  

In recent years, we have been studied about medical data analysis, especially for the rehabilitation data provided by a hospital, and extracted the recovery tendency of patients from their Functional Independence Measure (FIM) data. This time, we adopt the nonnegative Tucker decomposition (NTD) method, which is known as an extension of the nonnegative matrix factorization (NMF) to higher-dimensional data, to the medical data built up by piling each FIM data at some time points for several patients. Since the all elements of the tensor and matrices obtained by the NTD are nonnegative, it is expected that this method makes the interpretation of the characteristic vectors which are obtained from the resulting matrices easy and intelligible in comparison with our former approach, which used the multi-dimensional principal component analysis (MPCA). The experimental results show the effectiveness of proposed approach.


2012 ◽  
Vol 24 (4) ◽  
pp. 1085-1105 ◽  
Author(s):  
Nicolas Gillis ◽  
François Glineur

Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational biology, and clustering. In this letter, we consider two well-known algorithms designed to solve NMF problems: the multiplicative updates of Lee and Seung and the hierarchical alternating least squares of Cichocki et al. We propose a simple way to significantly accelerate these schemes, based on a careful analysis of the computational cost needed at each iteration, while preserving their convergence properties. This acceleration technique can also be applied to other algorithms, which we illustrate on the projected gradient method of Lin. The efficiency of the accelerated algorithms is empirically demonstrated on image and text data sets and compares favorably with a state-of-the-art alternating nonnegative least squares algorithm.


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