Projected Gradient Methods for Nonnegative Matrix Factorization

Lin, Chih-Jen

doi:10.1162/neco.2007.19.10.2756

Cited by 1,481 publications

(1,110 citation statements)

References 14 publications

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“…The non-negativity constraint generally leads to a sparse, part-based representation of the original data set, which is often semantically more meaningful than other factorization methods. While it is difficult to find the optimal solution of NMF because of the non-convexity of the objective function, several efficient approximation algorithms exist (e.g., multiplicative update [4], projective gradient decent [5]). Here we use multiplicative update because of its simplicity.…”

Section: B Feature Groupingmentioning

confidence: 99%

RolX: Role Extraction and Mining in Large Networks

Henderson¹,

Gallagher²,

Eliassi-Rad³

et al. 2011

204

287

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Abstract-Given a graph, how can we automatically discover roles for nodes? Roles could be, eg., 'bridges', or 'peripherynodes', etc. Roles are compact summaries of a node's behavior that generalize across networks. They enable numerous novel and useful network mining tasks, such as sense-making, searching for similar nodes, and node classification. We propose RolX (Role eXtraction), a scalable (linear in the number of edges), unsupervised learning approach for automatically extracting roles from general network data. We demonstrate the effectiveness of RolX on several network mining tasks, from exploratory data analysis to network transfer learning. Moreover, we compare network role discovery with network community discovery. We highlight fundamental differences between the two (e.g., roles generalize across disconnected networks, communities do not).

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Section: B Feature Groupingmentioning

confidence: 99%

RolX: Role Extraction and Mining in Large Networks

Henderson¹,

Gallagher²,

Eliassi-Rad³

et al. 2011

204

287

View full text Add to dashboard Cite

show abstract

“…is the Frobenius inner product. Parameters β and σ in our experiments have been set to β = 0.1 and σ = 0.01, which is an efficient parameter selection, as has been verified in other studies [24], [25].…”

Section: ) Maximum Margin Projection Matrix Update For Fixed W Omentioning

confidence: 80%

“…An efficient approach for setting an appropriate value to the learning step parameter λ t based on the Armijo rule [23] is presented in [24], which is also adopted in this work. According to this strategy, the learning step takes the form λ t = β g t , where g t is the first non-negative integer value found satisfying: (15) where operator ., .…”

Section: ) Maximum Margin Projection Matrix Update For Fixed W Omentioning

confidence: 99%

Maximum Margin Projection Subspace Learning for Visual Data Analysis

Nikitidis

Tefas

Pitas

2014

IEEE Trans. on Image Process.

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Abstract-Visual pattern recognition from images often involves dimensionality reduction as a key step to discover a lower dimensional image data representation and obtain a more manageable problem. Contrary to what is commonly practiced today in various recognition applications where dimensionality reduction and classification are independently treated, we propose a novel dimensionality reduction method appropriately combined with a classification algorithm. The proposed method called maximum margin projection pursuit, aims to identify a low dimensional projection subspace, where samples form classes that are better discriminated, i.e., are separated with maximum margin. The proposed method is an iterative alternate optimization algorithm that computes the maximum margin projections exploiting the separating hyperplanes obtained from training a support vector machine classifier in the identified low dimensional space. Experimental results on both artificial data, as well as, on popular databases for facial expression, face and object recognition verified the superiority of the proposed method against various state-of-the-art dimensionality reduction algorithms.

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“…, 2006). In our work, we applied the algorithm of projected gradient method for NMF presented by Chih-Jen Lin (Lin, 2007). Due to its good convergence, this algorithm works much faster than the multiplicative method presented by Lee and Seung (Lee & Seung 2001).…”

Section: Non-negative Matrix Factorization In Briefmentioning

confidence: 99%

Determining Projections of Grain Boundaries from Diffraction Data in Transmission Electron Microscope

Kiss

Lábár

2016

Microsc Microanal

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Keywords: grain boundary plane, non-negative matrix factorization, electron diffraction, computer program, polycrystalline thin films Microscopy and Microanalysis, a Cambridge University Press journal AbstractGrain boundaries (GB) are characterized by disorientation of the neighboring grains and the direction of the boundary plane between them. A new approach presented here determines the projection of grain boundaries that can be used to determine the latter one. The novelty is that an additional parameter of GB-s is quantified in addition to the ones provided by the orientation maps, namely the width of the projection of the GB is measured from the same set of diffraction patterns that were recorded for the orientation map, without the need to take any additional images. The diffraction patterns are collected in nanobeam diffraction (NBD) mode in a transmission electron microscope (TEM) pixel-by-pixel from an area containing two neighboring grains and the boundary between them. In our case the diffraction patterns were recorded using the beam scanning function of the a commercially available ASTAR system (ASTAR). Our method is based on non-negative matrix factorization (NMF) applied to the mentioned set of diffraction patterns. The method is encoded in a MATLAB environment, making the results easy to interpret and visualize. The measured GB-projection width is used to determine the orientation of the grain boundary plane, as given in Microsc. Microanal. 21, 422-435Kiss et al., 2015.

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Projected Gradient Methods for Nonnegative Matrix Factorization

Cited by 1,481 publications

References 14 publications

RolX: Role Extraction and Mining in Large Networks

RolX: Role Extraction and Mining in Large Networks

Maximum Margin Projection Subspace Learning for Visual Data Analysis

Determining Projections of Grain Boundaries from Diffraction Data in Transmission Electron Microscope

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