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Sparse projections onto the simplex
[article]
2013
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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]
2003
Lecture Notes in Computer Science
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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]
2016
arXiv
pre-print
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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]
2009
Lecture Notes in Computer Science
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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
2012
PLoS ONE
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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]
2014
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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
2014
Machine Learning
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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
2010
Image and Signal Processing for Remote Sensing XVI
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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
2008
Proceedings of the 25th international conference on Machine learning - ICML '08
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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]
2022
arXiv
pre-print
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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
2018
SIAM Journal on Optimization
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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
2012
IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing
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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]
2013
arXiv
pre-print
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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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