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Bidirectional Nonnegative Deep Model and Its Optimization in Learning

Xianhua Zeng, Zhengyi He, Hong Yu, Shengwei Qu
2016 Journal of Optimization  
Nonnegative matrix factorization (NMF) has been successfully applied in signal processing as a simple two-layer nonnegative neural network.  ...  In this paper, we combine the PNMF with deep learning and nonlinear fitting to propose a bidirectional nonnegative deep learning (BNDL) model and its optimization learning algorithm, which can obtain nonlinear  ...  Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant nos. 61672120, 61379114) and the Chongqing Natural Science Foundation Program (Grant no. cstc2015jcyjA40036  ... 
doi:10.1155/2016/5975120 fatcat:bjohpyvkqjdc3arcifhw3dbclm

Nonlinear Nonnegative Component Analysis

Stefanos Zafeiriou, Maria Petrou
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
framework where one can build a nonlinear nonnegative component analysis using kernels, the so-called Projected Gradient Kernel Nonnegative Matrix Factorization (PGKNMF).  ...  That is, motivated by a combination of the Nonnegative Matrix Factorization (NMF) algorithm and kernel theory, which has lead to an NMF algorithm in a polynomial feature space [1], we propose a general  ...  Acknowledgment This work has been supported by the EPSRC project EP/E028659/1 Face Recognition using Photometric Stereo.  ... 
doi:10.1109/cvpr.2009.5206584 dblp:conf/cvpr/ZafeiriouP09 fatcat:ccll3yzfvvfk5eqbpnjkz2acnu

Nonlinear Nonnegative Component Analysis

S. Zafeiriou, M. Petrou
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
framework where one can build a nonlinear nonnegative component analysis using kernels, the so-called Projected Gradient Kernel Nonnegative Matrix Factorization (PGKNMF).  ...  That is, motivated by a combination of the Nonnegative Matrix Factorization (NMF) algorithm and kernel theory, which has lead to an NMF algorithm in a polynomial feature space [1], we propose a general  ...  Acknowledgment This work has been supported by the EPSRC project EP/E028659/1 Face Recognition using Photometric Stereo.  ... 
doi:10.1109/cvprw.2009.5206584 fatcat:uimp3fiee5gdnazvmvn4e7zqh4

Comparison of reciprocity and closure enforcement methods for radiation view factors

Robert P. Taylor, Rogelio Luck
1995 Journal of thermophysics and heat transfer  
Among the least squares, the nonnegative projection scheme and the nonlinear-programming scheme yield almost identical results as expected, and the least squares without nonnegativity has very slightly  ...  Leersum’s rectified view factors fnii = Naive rectified view factors null-space component of view-factor vector, Eq. (19) Soi = nonlinear programming solution values fo = least-squares projection values  ... 
doi:10.2514/3.721 fatcat:73knmywdezgubfnt2refpkzr3u

Neighborhood Preserving Convex Nonnegative Matrix Factorization

Jiang Wei, Li Min, Zhang Yongqing
2014 Mathematical Problems in Engineering  
The convex nonnegative matrix factorization (CNMF) is a variation of nonnegative matrix factorization (NMF) in which each cluster is expressed by a linear combination of the data points and each data point  ...  This paper introduces a neighborhood preserving convex nonnegative matrix factorization (NPCNMF), which imposes an additional constraint on CNMF that each data point can be represented as a linear combination  ...  A Review of NMF and CNMF Nonnegative matrix factorization (NMF) factorizes the data matrix into one nonnegative basis matrix and one nonnegative coefficient matrix.  ... 
doi:10.1155/2014/154942 fatcat:cf5hbsobhreblp74eoeagje6wm

Computing non-negative tensor factorizations

Michael P. Friedlander, Kathrin Hatz
2008 Optimization Methods and Software  
We describe an approach for computing the NTF of a dataset that relies only on iterative linear-algebra techniques and that is comparable in cost to the nonnegative matrix factorization.  ...  (The better-known nonnegative matrix factorization is a special case of NTF and is also handled by our implementation.)  ...  Acknowledgments We are indebted to Tammy Kolda, who introduced us to the tensor factorization problem during her visit to UBC as a distinguished lecturer, and whos papers in this subject were invaluable  ... 
doi:10.1080/10556780801996244 fatcat:yb3gcutrwjdixhc5y23qfnpkbe

Online nonnegative matrix factorization based on kernel machines

Fei Zhu, Paul Honeine
2015 2015 23rd European Signal Processing Conference (EUSIPCO)  
Nonnegative matrix factorization (NMF) has been increasingly investigated for data analysis and dimension-reduction.  ...  So far, the online NMF has been limited to the linear model. This paper develops an online version of the nonlinear kernel-based NMF, where the decomposition is performed in the feature space.  ...  INTRODUCTION Nonnegative matrix factorization (NMF) consists in approximating a given nonnegative matrix by the product of two lowrank ones [1] , the left low-rank matrix is often called basis matrix  ... 
doi:10.1109/eusipco.2015.7362811 dblp:conf/eusipco/ZhuH15 fatcat:m34uqt67hza65k5ukm4ezgyzza

Sparse Deep Nonnegative Matrix Factorization [article]

Zhenxing Guo, Shihua Zhang
2017 arXiv   pre-print
Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning.  ...  In this paper, we proposed sparse deep nonnegative matrix factorization models to analyze complex data for more accurate classification and better feature interpretation.  ...  Another concern is why some nonlinear functions performs well while others not.  ... 
arXiv:1707.09316v1 fatcat:c6rzyvdmurdjlp6rdzof5fj37u

Robust nonnegative matrix factorization for nonlinear unmixing of hyperspectral images

Nicolas Dobigeon, Cedric Fevotte
2013 2013 5th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS)  
Simulation results obtained on synthetic and real data show that the proposed strategy competes with state-of-the-art linear and nonlinear unmixing methods.  ...  The standard nonnegativity and sum-to-one constraints inherent to spectral unmixing are coupled with a group-sparse constraint imposed on the nonlinearity component.  ...  The proposed decomposition relates to robust nonnegative matrix factorization (rNMF) as will be explained in more details in the following. The article is organized as follows.  ... 
doi:10.1109/whispers.2013.8080681 dblp:conf/whispers/DobigeonF13 fatcat:rtojkjpojvez7ghdglqujjrgze

NON-MATRIX FACTORIZATION FOR BLIND IMAGE SEPARATION

Ichsan Mardani
2019 Informatik  
Hyperspectral unmixing is a process to identify the constituent materials and estimate the corresponding fractions from the mixture, nonnegative matrix factions ( NMF ) is suitable as a candidate for the  ...  linear spectral mixture mode, has been applied to the unmixing hyperspectral data.  ...  To recognize that BSS for NNLM is a nonnegative matrix factorization, that is, to factorize into nonnegative and nonnegative , where nonnegative matrix factorization (NMF) technique is applicable.  ... 
doi:10.52958/iftk.v14i2.406 fatcat:ut3rpcfwfzfbbcfwfg5s7pmyba

Projected Gradients for Subclass Discriminant Nonnegative Subspace Learning

Symeon Nikitidis, Anastasios Tefas, Ioannis Pitas
2014 IEEE Transactions on Cybernetics  
Current discriminant nonnegative matrix factorization (NMF) methods either do not guarantee convergence to a stationary limit point or assume a compact data distribution inside classes, thus ignoring intra  ...  To address both limitations, we regard that data inside each class has a multimodal distribution, forming various subclasses and perform optimization using a projected gradients framework to ensure limit  ...  Projected Gradients for Subclass Discriminant Nonnegative Subspace Learning Symeon Nikitidis, Anastasios Tefas, and Ioannis Pitas Abstract-Current discriminant nonnegative matrix factorization (NMF) methods  ... 
doi:10.1109/tcyb.2014.2317174 pmid:24816629 fatcat:w3ggalzsqreqbfmqikl52elprq

Generalized bilinear model based nonlinear unmixing using semi-nonnegative matrix factorization

Naoto Yokoya, Jocelyn Chanussot, Akira Iwasaki
2012 2012 IEEE International Geoscience and Remote Sensing Symposium  
Index Termshyperspectral image, nonlinear unmixing, generalized bilinear model, semi-nonnegative matrix factorization  ...  Semi-nonnegative matrix factorization is used for optimization to process a whole image in a matrix form.  ...  Therefore, the minimization of (4) can be solved by Semi-NMF that factorizes a non-restricted matrix X into a non-restricted matrix F and a nonnegative matrix G T as X ≈ FG T [9] .  ... 
doi:10.1109/igarss.2012.6351282 dblp:conf/igarss/YokoyaCI12 fatcat:57p7l33z4bgovgjuz6jxs4236i

A "nonnegative PCA" algorithm for independent component analysis

M.D. Plumbley, E. Oja
2004 IEEE Transactions on Neural Networks  
Index Terms-Independent component analysis (ICA), nonlinear principal component analysis (nonlinear PCA), nonnegative matrix factorization, subspace learning rule.  ...  We propose the use of a "nonnegative principal component analysis (nonnegative PCA)" algorithm, which is a special case of the nonlinear PCA algorithm, but with a rectification nonlinearity, and we conjecture  ...  Centre for many interesting and stimulating discussions.  ... 
doi:10.1109/tnn.2003.820672 pmid:15387248 fatcat:fdc3utd4dbbfnaziyunior4mbq

An Efficient Nonnegative Matrix Factorization Approach in Flexible Kernel Space

Daoqiang Zhang, Wanquan Liu
2009 International Joint Conference on Artificial Intelligence  
In this paper, we propose a general formulation for kernel nonnegative matrix factorization with flexible kernels.  ...  Specifically, we propose the Gaussian nonnegative matrix factorization (GNMF) algorithm by using the Gaussian kernel in the framework.  ...  Acknowledgments We thank the the anonymous reviewers for their helpful comments and suggestions.  ... 
dblp:conf/ijcai/ZhangL09 fatcat:4ciifsm36redxdqq2zgdyuddra

Relationship Matrix Nonnegative Decomposition for Clustering

Ji-Yuan Pan, Jiang-She Zhang
2011 Mathematical Problems in Engineering  
Nonnegative matrix factorization (NMF) is a popular tool for analyzing the latent structure of nonnegative data.  ...  The RMND model is derived from the nonlinear NMF algorithm. RMND decomposes a pairwise similarity matrix into a product of three low rank nonnegative matrices.  ...  Specifically, KNMF is to find a set of nonnegative weights and nonnegative basis vectors such that the nonlinearly mapped training vectors can be written as linear combinations of nonlinear mapped nonnegative  ... 
doi:10.1155/2011/864540 fatcat:bnxt5zotcnfalagq6h3pqnagkq
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