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27
Factoring nonnegative matrices with linear programs
, 2012
"... This paper describes a new approach for computing nonnegative matrix factorizations (NMFs) with linear programming. The key idea is a datadriven model for the factorization, in which the most salient features in the data are used to express the remaining features. More precisely, given a data matri ..."
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This paper describes a new approach for computing nonnegative matrix factorizations (NMFs) with linear programming. The key idea is a datadriven model for the factorization, in which the most salient features in the data are used to express the remaining features. More precisely, given a data matrix X, the algorithm identifies a matrix C that satisfies X ≈ CX and some linear constraints. The matrix C selects features, which are then used to compute a lowrank NMF of X. A theoretical analysis demonstrates that this approach has the same type of guarantees as the recent NMF algorithm of Arora et al. (2012). In contrast with this earlier work, the proposed method (1) has better noise tolerance, (2) extends to more general noise models, and (3) leads to efficient, scalable algorithms. Experiments with synthetic and real datasets provide evidence that the new approach is also superior in practice. An optimized C++ implementation of the new algorithm can factor a multiGigabyte matrix in a matter of minutes.
Methods to find the number of latent skills
"... Identifying the skills that determine the success or failure to exercises and question items is a difficult task. Multiple skills may be involved at various degree of importance. Skills may overlap and correlate. Slip and guess factors affect item outcome and depend on the profile of the student’s s ..."
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Identifying the skills that determine the success or failure to exercises and question items is a difficult task. Multiple skills may be involved at various degree of importance. Skills may overlap and correlate. Slip and guess factors affect item outcome and depend on the profile of the student’s skill mastery and on item characteristics. In an effort towards the goal of finding the skills behind a set of items, we investigate two techniques to determine the number of salient latent skills. The Singular Value Decomposition (SVD) is a known technique to find latent factors. The singular values represent direct evidence of the strength of latent factors. Application of SVD to finding the number of latent skills is explored. A second technique is based on a wrapper approach. Linear models with different number of skills are built, and the one that yields the best prediction accuracy through cross validation is considered the most appropriate. The results show that both techniques are effective in identifying the latent factors of simulated data. Finally, an investigation with real data is reported. Both the SVD and wrapper methods yield results that have no simple interpretation, but one interpretation is consistent across the two methods, albeit not well aligned with the assessment of experts. 1.
Factorized point process intensities: A spatial analysis of professional basketball
 In Proceedings of the 31st International Conference on Machine Learning
, 2013
"... (Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. ..."
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Cited by 5 (2 self)
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters.
METHODOLOGY Open Access
"... RTPCR for quantifying bovine viral diarrhea virus type1 and its comparison with conventional RTPCR ..."
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RTPCR for quantifying bovine viral diarrhea virus type1 and its comparison with conventional RTPCR
RESEARCH ARTICLE Open Access
"... Expression cartography of human tissues using self organizing maps ..."
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Organizers:
, 2011
"... This was the seventeenth such workshop at NCSU. It brought together 34 graduate students from 26 different universities. Fifteen of the students were frommathematics programs, 18 fromstatistics, andone fromcomputer science. The goal of the IMSM workshop is to expose mathematics and statistics studen ..."
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This was the seventeenth such workshop at NCSU. It brought together 34 graduate students from 26 different universities. Fifteen of the students were frommathematics programs, 18 fromstatistics, andone fromcomputer science. The goal of the IMSM workshop is to expose mathematics and statistics students fromaroundthecountry to: realworld problemsfromindustryand government laboratories; interdisciplinary research involving mathematical, statistical and modeling components; as well as experience in a team approach to problem solving. On the morning of the first day, industrial and government scientists presented six research problems. Each presenter, together with a specially selected faculty mentor, thenguidedteamsof4–6studentsandhelpedthem todiscoverasolution. Incontrasttoneat, wellposedacademicexercisesthat are typically found in coursework or textbooks, the workshop problems are challenging real world problems that require the varied expertise and fresh
Contents
, 2012
"... This vignette describes how to produce different informative heatmaps from NMF objects, such as returned by the function nmf in the NMF package 1 [1]. The main drawing engine is implemented by the function aheatmap, which is a modification of the function pheatmap from the pheatmap package 2 [2], an ..."
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This vignette describes how to produce different informative heatmaps from NMF objects, such as returned by the function nmf in the NMF package 1 [1]. The main drawing engine is implemented by the function aheatmap, which is a modification of the function pheatmap from the pheatmap package 2 [2], and provides convenient and quick ways of producing high quality and customizable annotated heatmaps. Currently this function is part of the package NMF, but may eventually compose a separate package on its own.
An introduction to NMF package Version 0.8.5
, 2012
"... This vignette presents the NMF package 1 [8], which implements a framework for Nonnegative Matrix Factorization (NMF) algorithms in R [19]. The objective is to provide an implementation of some standard algorithms, while allowing the user to easily implement new methods that integrate into a common ..."
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This vignette presents the NMF package 1 [8], which implements a framework for Nonnegative Matrix Factorization (NMF) algorithms in R [19]. The objective is to provide an implementation of some standard algorithms, while allowing the user to easily implement new methods that integrate into a common framework, which facilitates analysis, result visualisation or performance benchmarking. If you use the package NMF package in your analysis and publications please cite: Renaud Gaujoux and Cathal Seoighe. “A flexible R package for nonnegative matrix factorization”.
License GPL3
, 2013
"... Enhances parallel Description The ’les ’ package estimates Loci of Enhanced Significance (LES) in tiling microarray data. These are regions of regulation such as found in differential transcription, CHiPchip, or DNA modification analysis. The package provides a universal framework suitable for ident ..."
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Enhances parallel Description The ’les ’ package estimates Loci of Enhanced Significance (LES) in tiling microarray data. These are regions of regulation such as found in differential transcription, CHiPchip, or DNA modification analysis. The package provides a universal framework suitable for identifying differential effects in tiling microarray data sets, and is independent of the underlying statistics at the level of single probes.