scholarly journals Non-negative Matrix Factorization and Its Extensions for Spectral Image Data Analysis

2019 ◽  
Vol 17 (0) ◽  
pp. 148-154
Author(s):  
Motoki Shiga ◽  
Shunsuke Muto
Keyword(s):  
Data Analysis ◽  
Matrix Factorization ◽  
Image Data ◽  
Spectral Image ◽  
Non Negative Matrix Factorization

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 Optimal Recovery of Missing Values for Non-negative Matrix Factorization

2019 ◽  
Author(s):  
Rebecca Chen ◽  
Lav R. Varshney
Keyword(s):  
Matrix Factorization ◽  
Missing Values ◽  
Image Data ◽  
Optimal Recovery ◽  
Upper Bounds ◽  
Biological Data ◽  
Geometric Conditions ◽  
Theoretic Technique ◽  
Better Than ◽  
Non Negative Matrix Factorization

AbstractWe extend the approximation-theoretic technique of optimal recovery to the setting of imputing missing values in clustered data, specifically for non-negative matrix factorization (NMF), and develop an implementable algorithm. Under certain geometric conditions, we prove tight upper bounds on NMF relative error, which is the first bound of this type for missing values. We also give probabilistic bounds for the same geometric assumptions. Experiments on image data and biological data show that this theoretically-grounded technique performs as well as or better than other imputation techniques that account for local structure.

scholarly journals Raman imaging reveals in-situ microchemistry of cuticle and epidermis of spruce needles

Plant Methods ◽  
2021 ◽  
Vol 17 (1) ◽  
Author(s):  
Nadia Sasani ◽  
Peter Bock ◽  
Martin Felhofer ◽  
Notburga Gierlinger
Keyword(s):  
Data Analysis ◽  
Matrix Factorization ◽  
Abiotic Stresses ◽  
Protective Layer ◽  
Raman Imaging ◽  
Chemical Extraction ◽  
Chemical Heterogeneity ◽  
Coumaric Acid ◽  
Biotic And Abiotic Stresses ◽  
Non Negative Matrix Factorization

Abstract Background The cuticle is a protective layer playing an important role in plant defense against biotic and abiotic stresses. So far cuticle structure and chemistry was mainly studied by electron microscopy and chemical extraction. Thus, analysing composition involved sample destruction and the link between chemistry and microstructure remained unclear. In the last decade, Raman imaging showed high potential to link plant anatomical structure with microchemistry and to give insights into orientation of molecules. In this study, we use Raman imaging and polarization experiments to study the native cuticle and epidermal layer of needles of Norway spruce, one of the economically most important trees in Europe. The acquired hyperspectral dataset is the basis to image the chemical heterogeneity using univariate (band integration) as well as multivariate data analysis (cluster analysis and non-negative matrix factorization). Results Confocal Raman microscopy probes the cuticle together with the underlying epidermis in the native state and tracks aromatics, lipids, carbohydrates and minerals with a spatial resolution of 300 nm. All three data analysis approaches distinguish a waxy, crystalline layer on top, in which aliphatic chains and coumaric acid are aligned perpendicular to the surface. Also in the lipidic amorphous cuticle beneath, strong signals of coumaric acid and flavonoids are detected. Even the unmixing algorithm results in mixed endmember spectra and confirms that lipids co-locate with aromatics. The underlying epidermal cell walls are devoid of lipids but show strong aromatic Raman bands. Especially the upper periclinal thicker cell wall is impregnated with aromatics. At the interface between epidermis and cuticle Calcium oxalate crystals are detected in a layer-like fashion. Non-negative matrix factorization gives the purest component spectra, thus the best match with reference spectra and by this promotes band assignments and interpretation of the visualized chemical heterogeneity. Conclusions Results sharpen our view about the cuticle as the outermost layer of plants and highlight the aromatic impregnation throughout. In the future, developmental studies tracking lipid and aromatic pathways might give new insights into cuticle formation and comparative studies might deepen our understanding why some trees and their needle and leaf surfaces are more resistant to biotic and abiotic stresses than others.

scholarly journals Microbiome Data Analysis by Symmetric Non-negative Matrix Factorization With Local and Global Regularization

2021 ◽  
Vol 8 ◽  
Author(s):  
Junmin Zhao ◽  
Yuanyuan Ma ◽  
Lifang Liu
Keyword(s):  
Data Analysis ◽  
Matrix Factorization ◽  
Original Data ◽  
Biological Data ◽  
Fine Grained ◽  
Laplacian Graph ◽  
Fine Grained Structure ◽  
Microbiome Data ◽  
Global And Local ◽  
Non Negative Matrix Factorization

A network is an efficient tool to organize complicated data. The Laplacian graph has attracted more and more attention for its good properties and has been applied to many tasks including clustering, feature selection, and so on. Recently, studies have indicated that though the Laplacian graph can capture the global information of data, it lacks the power to capture fine-grained structure inherent in network. In contrast, a Vicus matrix can make full use of local topological information from the data. Given this consideration, in this paper we simultaneously introduce Laplacian and Vicus graphs into a symmetric non-negative matrix factorization framework (LVSNMF) to seek and exploit the global and local structure patterns that inherent in the original data. Extensive experiments are conducted on three real datasets (cancer, cell populations, and microbiome data). The experimental results show the proposed LVSNMF algorithm significantly outperforms other competing algorithms, suggesting its potential in biological data analysis.

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