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Sparse projections onto the simplex [article]

Anastasios Kyrillidis, Stephen Becker, Volkan Cevher and, Christoph Koch
2013 arXiv   pre-print
In this setting, we derive efficient sparse projections onto the simplex and its extension, and illustrate how to use them to solve high-dimensional learning problems in quantum tomography, sparse density  ...  Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the ℓ_1-norm.  ...  of our knowledge, explicitly sparse Euclidean projections onto the simplex and hyperplane constraints have not been considered before.  ... 
arXiv:1206.1529v5 fatcat:3fjlcg53dbffbpt3uw4k5ea23u

Fast Projection onto the Capped Simplex with Applications to Sparse Regression in Bioinformatics [article]

Andersen Ang, Jianzhu Ma, Nianjun Liu, Kun Huang, Yijie Wang
2021 arXiv   pre-print
We consider the problem of projecting a vector onto the so-called k-capped simplex, which is a hyper-cube cut by a hyperplane.  ...  We further illustrate the effectiveness of the proposed algorithm on solving sparse regression in a bioinformatics problem.  ...  Acknowledgments The presented materials are based upon the research supported by the Indiana University's Precision Health Initiative.  ... 
arXiv:2110.08471v4 fatcat:fzxo65udbrf5xgz6m45zdesg2q

Spherical Object Reconstruction Using Simplex Meshes from Sparse Data [chapter]

Pavel Matula, David Svoboda
2003 Lecture Notes in Computer Science  
The goal of this paper is to describe a modification of the method that is suitable also for sparse data. The performance of the proposed modification is demonstrated on real biomedical data.  ...  The method can handle volumetric as well as three-dimensional range data and is easy to use and relatively fast. The method, however, can yield wrong results for sparse data.  ...  Acknowledgements This work was supported by the Ministry of Education of the Czech Republic (Project No. MSM-143300002) and by the Academy of Sciences of the Czech Republic (Grants No.  ... 
doi:10.1007/978-3-540-39966-7_50 fatcat:5qnytuine5fa5bc6uh7z332734

Sparse Activity and Sparse Connectivity in Supervised Learning [article]

Markus Thom, Günther Palm
2016 arXiv   pre-print
The tool for achieving this is a sparseness-enforcing projection operator which finds the closest vector with a pre-defined sparseness for any given vector.  ...  In the theoretical part of this paper, a comprehensive theory for such a projection is developed.  ...  Acknowledgments The authors wish to thank Patrik O. Hoyer and Xiaojing Ye for sharing the source code of their algorithms.  ... 
arXiv:1603.08367v1 fatcat:z3wewgqptrbwtew7mtwctkbwza

Blind Decomposition of Spectral Imaging Microscopy: A Study on Artificial and Real Test Data [chapter]

Fabian J. Theis, Richard Neher, Andre Zeug
2009 Lecture Notes in Computer Science  
In some cases, however, additional cost function terms such as sparseness enhancement are necessary to arrive at a satisfactory decomposition.  ...  Applying the algorithm, we are able to successfully extract the dye distributions from the images.  ...  FT gratefully acknowledges partial financial support by the Helmholtz Alliance on Systems Biology (project 'CoReNe').  ... 
doi:10.1007/978-3-642-00599-2_69 fatcat:x7uv2asnjnabdi5xent77ixtyy

Conic Sampling: An Efficient Method for Solving Linear and Quadratic Programming by Randomly Linking Constraints within the Interior

Oliver Serang, Jérémie Bourdon
2012 PLoS ONE  
The conic sampling method is then adapted and applied to solve a certain quadratic program, which compute a projection onto a polytope; the proposed method is shown to outperform the proprietary software  ...  Mathematica on large, sparse QP problems constructed from mass spectometry-based proteomics.  ...  This work is dedicated to the memory of Paul Tseng, who generously shared his expertise. Author Contributions  ... 
doi:10.1371/journal.pone.0043706 pmid:22952741 pmcid:PMC3428371 fatcat:cpm3sp4iibaathvchzlfju2bzu

Representing Data by a Mixture of Activated Simplices [article]

Chunyu Wang, John Flynn, Yizhou Wang, Alan L. Yuille
2014 arXiv   pre-print
While the total number of bases used to build the simplices is a parameter of the model, the dimensions of the individual activated simplices are learned from the data.  ...  We call the boundary facets of the convex hull that are close to the data Activated Simplices.  ...  We've observed that the best projection of y (j) onto the optimal simplices is the projection of y (j) onto the convex hull of the bases.  ... 
arXiv:1412.4102v1 fatcat:czz3d4yllbcazowmqsiiwxq44e

Wasserstein k-means with sparse simplex projection [article]

Takumi Fukunaga, Hiroyuki Kasai
2020 arXiv   pre-print
We designate this proposed algorithm as sparse simplex projection based Wasserstein k-means, or SSPW k-means.  ...  Furthermore, we dynamically reduced the computational complexity by removing lower-valued data samples and harnessing sparse simplex projection while keeping the degradation of clustering quality lower  ...  Moreover, with regard to the different projection types, the case in which the sparse simplex projection is performed onto both the centroid and data sample requires the shortest computation time, as expected  ... 
arXiv:2011.12542v1 fatcat:anbkxsvkgbekvgncwcyzb3snoy

SAGA: sparse and geometry-aware non-negative matrix factorization through non-linear local embedding

Nicolas Courty, Xing Gong, Jimmy Vandel, Thomas Burger
2014 Machine Learning  
This paper presents a new non-negative matrix factorization technique which (1) allows the decomposition of the original data on multiple latent factors accounting for the geometrical structure of the  ...  It operates by coding the data with respect to local neighbors with non-linear weights. This locality is obtained as a consequence of the simultaneous sparsity and convexity constraints.  ...  (Asterix project). and the Prospectom project (Mastodons 2012 CNRS challenge).  ... 
doi:10.1007/s10994-014-5463-y fatcat:djud7urtbzdafcubootv3dw6zu

Hyperspectral unmixing: geometrical, statistical, and sparse regression-based approaches

José M. Bioucas-Dias, Antonio Plaza, Lorenzo Bruzzone
2010 Image and Signal Processing for Remote Sensing XVI  
The presentations is organized into four main topics: i) mixing models, ii) signal subspace identification, iii) geometrical-based spectral unmixing, (iv) statistical-based spectral unmixing, and (v) sparse  ...  Very often, however, owing to low spatial resolution of the scanner or to the presence of intimate mixtures (mixing of the materials at a very small scale) in the scene, the spectral vectors (collection  ...  The selected vectors are then projected onto this subspace, and a simplex is found by a MV procedure.  ... 
doi:10.1117/12.870780 fatcat:6n6ywqiajfhejhr2cbes5ymfvy

Efficient projections onto thel1-ball for learning in high dimensions

John Duchi, Shai Shalev-Shwartz, Yoram Singer, Tushar Chandra
2008 Proceedings of the 25th international conference on Machine learning - ICML '08  
We describe efficient algorithms for projecting a vector onto the ℓ 1 -ball. We present two methods for projection.  ...  The first performs exact projection in O(n) expected time, where n is the dimension of the space.  ...  Acknowledgments We thank the anonymous reviewers for their helpful and insightful comments.  ... 
doi:10.1145/1390156.1390191 dblp:conf/icml/DuchiSSC08 fatcat:teibrsxryzhhfpjrjcp5idndjm

Distributed Projections onto a Simplex [article]

Yongzheng Dai, Chen Chen
2022 arXiv   pre-print
Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems.  ...  Our method is especially effective when the projection is highly sparse; which is the case, for instance, in large-scale problems with i.i.d. entries.  ...  As a particular example, projection onto a simplex can be used to project onto the parity polytope (see e.g. Wasson et al.  ... 
arXiv:2204.08153v2 fatcat:r6lhgyelk5azpofbcttio4mj6a

Proximal Mapping for Symmetric Penalty and Sparsity

Amir Beck, Nadav Hallak
2018 SIAM Journal on Optimization  
It is shown that many important symmetric sets, such as the 1 , 2 , ∞-balls, the simplex and the fullsimplex, satisfy this SOM property.  ...  Essential properties of the sparse prox are proved, and an efficient method for computing the sparse prox in the general case is derived.  ...  Lemma A.10 suggests that the projection onto the α-simplex might be sparse even without a sparsity constraint.  ... 
doi:10.1137/17m1116544 fatcat:kp6rewej7fhvvajck7s27xvwfq

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

José M. Bioucas-Dias, Antonio Plaza, Nicolas Dobigeon, Mario Parente, Qian Du, Paul Gader, Jocelyn Chanussot
2012 IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing  
This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed.  ...  Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel.  ...  The authors also acknowledge the Army Geospatial Center, US Army Corps of Engineers, for making the HYDICE Rterrain data set available to the community.  ... 
doi:10.1109/jstars.2012.2194696 fatcat:s66a35xjd5dqzkw5wwihq6ux64

Efficient Sparseness-Enforcing Projections [article]

Markus Thom, Günther Palm
2013 arXiv   pre-print
We improve on this by adaptation of a linear time algorithm for projecting onto simplexes.  ...  We propose a linear time and constant space algorithm for computing Euclidean projections onto sets on which a normalized sparseness measure attains a constant value.  ...  Acknowledgments The authors would like to thank Michael Gabb for helpful discussions. This work was supported by Daimler AG, Germany.  ... 
arXiv:1303.5259v1 fatcat:isk5vjsqkbdfxbbbkb63kf3yya
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