Using non-negative matrix factorization toward finding an informative basis in spin-image data

2008 ◽  
Author(s):  
Andrew J. Patterson ◽  
Nitesh N. Shah ◽  
Donald E. Waagen
Keyword(s):  
Matrix Factorization ◽  
Image Data ◽  
Spin Image ◽  
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 Non-negative matrix factorization framework for dimensionality reduction and unsupervised clustering

2007 ◽  
Author(s):  
Sayan Pathak
Keyword(s):  
Matrix Factorization ◽  
Gene Expression Analysis ◽  
Image Interpretation ◽  
Image Data ◽  
Brain Atlas ◽  
Noisy Image ◽  
Approach To Learning ◽  
Generic Framework ◽  
Specific Implementation ◽  
Non Negative Matrix Factorization

Non-negative Matrix Factorization (NMF) is a robust approach to learning spatially localized parts-based subspace patterns in applications such as document analysis, image interpretation, and gene expression analysis. NMF-based decomposition capabilities are lacking in the present ITK toolkit. We provide a generic framework for such decompositions. A specific implementation using a Kulback-Liebler type divergence function is provided to illustrate a possible extension of the base class along with test images to illustrate usage. We have found this method to be robust to noisy image data and show examples from our on-going research using the Allan Brain Atlas data to illustrate its ability to analyze higher dimension data.

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