scholarly journals Convex and Semi-Nonnegative Matrix Factorizations

2010 ◽  
Vol 32 (1) ◽  
pp. 45-55 ◽  
Author(s):  
C.H.Q. Ding ◽  
Tao Li ◽  
M.I. Jordan
Keyword(s):  
Nonnegative Matrix ◽  
Matrix Factorizations

A framework for least squares nonnegative matrix factorizations with Tikhonov regularization

2020 ◽  
Vol 387 ◽  
pp. 78-90
Author(s):  
Yueyang Teng ◽  
Shouliang Qi ◽  
Fangfang Han ◽  
Yudong Yao ◽  
Fenglei Fan ◽  
...  
Keyword(s):  
Least Squares ◽  
Tikhonov Regularization ◽  
Nonnegative Matrix ◽  
Matrix Factorizations

scholarly journals Nonnegative Matrix Factorizations Performing Object Detection and Localization

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
G. Casalino ◽  
N. Del Buono ◽  
M. Minervini
Keyword(s):  
Object Detection ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Matrix Factorizations ◽  
Prototype System ◽  
Image Objects ◽  
Template Image ◽  
General Object ◽  
Factorization Algorithms ◽  
Detection And Localization

We study the problem of detecting and localizing objects in still, gray-scale images making use of the part-based representation provided by nonnegative matrix factorizations. Nonnegative matrix factorization represents an emerging example of subspace methods, which is able to extract interpretable parts from a set of template image objects and then to additively use them for describing individual objects. In this paper, we present a prototype system based on some nonnegative factorization algorithms, which differ in the additional properties added to the nonnegative representation of data, in order to investigate if any additional constraint produces better results in general object detection via nonnegative matrix factorizations.

scholarly journals Integrative analysis of single cell genomics data by coupled nonnegative matrix factorizations

2018 ◽  
Author(s):  
Zhana Duren ◽  
Xi Chen ◽  
Mahdi Zamanighomi ◽  
Wanwen Zeng ◽  
Ansuman T Satpathy ◽  
...  
Keyword(s):  
Single Cell ◽  
Nonnegative Matrix ◽  
Integrative Analysis ◽  
Matrix Factorizations ◽  
Joint Analysis ◽  
Rna Seq ◽  
Single Cell Genomics ◽  
Clustering Problem ◽  
Two Samples ◽  
Different Types

AbstractWhen different types of functional genomics data are generated on single cells from different samples of cells from the same heterogeneous population, the clustering of cells in the different samples should be coupled. We formulate this “coupled clustering” problem as an optimization problem, and propose the method of coupled nonnegative matrix factorizations (coupled NMF) for its solution. The method is illustrated by the integrative analysis of single cell RNA-seq and single cell ATAC-seq data.Significance StatementsBiological samples are often heterogeneous mixtures of different types of cells. Suppose we have two single cell data sets, each providing information on a different cellular feature and generated on a different sample from this mixture. Then, the clustering of cells in the two samples should be coupled as both clusterings are reflecting the underlying cell types in the same mixture. This “coupled clustering” problem is a new problem not covered by existing clustering methods. In this paper we develop an approach for its solution based the coupling of two nonnegative matrix factorizations. The method should be useful for integrative single cell genomics analysis tasks such as the joint analysis of single cell RNA-seq and single cell ATAC-seq data.

A mixed iteration for nonnegative matrix factorizations

2013 ◽  
Vol 219 (18) ◽  
pp. 9847-9855 ◽  
Author(s):  
Ştefan M. Şoltuz ◽  
B.E. Rhoades
Keyword(s):  
Nonnegative Matrix ◽  
Matrix Factorizations
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