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Optimal control on special Euclidean group via natural gradient algorithm

Chunhui Li, Erchuan Zhang, Lin Jiu, Huafei Sun
<span title="2016-10-10">2016</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ikvx2lmj7rew7jpw4lygqgjpby" style="color: black;">Science China Information Sciences</a> </i> &nbsp;
Furthermore, some numerical simulations are shown to illustrate our outcomes based on the natural gradient descent algorithm for optimizing the control system of the special Euclidean group.  ...  Considering the optimal control problem about the control system of the special Euclidean group whose output only depends on its input is meaningful in practical applications.  ...  Acknowledgements This work was supported by National Natural Science Foundations of China (Grant Nos. 61179031, 10932002).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11432-015-0096-3">doi:10.1007/s11432-015-0096-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/okvvcanysnebro5hn4hkfr3zl4">fatcat:okvvcanysnebro5hn4hkfr3zl4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200510160956/http://engine.scichina.com/doi/pdf/de1471b71dc3415f8318dda12a5d1a2a" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ea/2b/ea2b848c46d9d7adec51756f56ba907359d4544b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11432-015-0096-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Optimization on the space of rigid and flexible motions: An alternative manifold optimization approach

Pirooz Vakili, Hanieh Mirzaei, Shahrooz Zarbafian, Ioannis Ch. Paschalidis, Dima Kozakov, Sandor Vajda
<span title="">2014</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6lxj4fexcfalpdclkghtt47hlu" style="color: black;">53rd IEEE Conference on Decision and Control</a> </i> &nbsp;
We present a unified setting for formulating this problem as an optimization on an appropriately defined manifold for which efficient manifold optimizations can be developed.  ...  This setting is based on a Lie group representation of the rigid movements of a body that is different from what is commonly used for this purpose.  ...  AN ALTERNATIVE GROUP OF RIGID BODY TRANSFORMATIONS In this section we begin by clarifying the distinction between the common representation of the rigid movement of a body via the Special Euclidean group  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2014.7040301">doi:10.1109/cdc.2014.7040301</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/25774073">pmid:25774073</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4357846/">pmcid:PMC4357846</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4m7hrbaytnc5nadyxax4anadky">fatcat:4m7hrbaytnc5nadyxax4anadky</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808042713/https://structure.bu.edu/sites/default/files/07040301.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2c/d1/2cd13390a7686e2384c3163fb5086803a2cc3e17.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2014.7040301"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4357846" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Optimizing quantum circuits with Riemannian gradient flow [article]

Roeland Wiersema, Nathan Killoran
<span title="2022-05-11">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Since quantum circuits are elements of the special unitary group, we can consider an alternative optimization perspective that depends on the structure of this group.  ...  In this work, we investigate a Riemannian optimization scheme over the special unitary group and we discuss its implementation on a quantum computer.  ...  Roeland would like to thank David Wakeham and Jack Ceroni from the I.C. for the weekly discussions on differential geometry and Josh Izaac for his help with implementing Riemannian gradient-flow in Pen-nyLane  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2202.06976v2">arXiv:2202.06976v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bx37u2wxvbc6hi44tjvnjkp5ni">fatcat:bx37u2wxvbc6hi44tjvnjkp5ni</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220217022313/https://arxiv.org/pdf/2202.06976v1.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0b/9f/0b9fda3aaa9b1444ce85b9cc8eb1f1f75e7d2a3c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2202.06976v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A new approach to rigid body minimization with application to molecular docking

Hanieh Mirzaei, Dima Kozakov, Dmitri Beglov, Ioannis Ch. Paschalidis, Sandor Vajda, Pirooz Vakili
<span title="">2012</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wjd7b2sxyfahnaei4xvi46vwsu" style="color: black;">2012 IEEE 51st IEEE Conference on Decision and Control (CDC)</a> </i> &nbsp;
Our computational results for a local optimization algorithm developed based on the new approach show that it is about an order of magnitude faster than a state of art local minimization algorithms for  ...  We introduce a novel representation of rigid body motion that leads to a natural formulation of the energy minimization problem as an optimization on the manifold, rather than the commonly used SE(3).  ...  The space of rigid body transformations in is commonly represented by the Special Euclidean group (or simply the Euclidean group) SE(3), a Lie group (see, e.g. [4] ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2012.6426267">doi:10.1109/cdc.2012.6426267</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/24763338">pmid:24763338</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC3992991/">pmcid:PMC3992991</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cdc/MirzaeiKBPVV12.html">dblp:conf/cdc/MirzaeiKBPVV12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6yzp3gbtrzaavaiszdsy7mp3vu">fatcat:6yzp3gbtrzaavaiszdsy7mp3vu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200430051658/http://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC3992991&amp;blobtype=pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a7/2d/a72ddddbc5664912bcb4a1ee9a05ec616f703f83.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2012.6426267"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3992991" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Optimal Data Fitting on Lie Groups: a Coset Approach [chapter]

C. Lageman, R. Sepulchre
<span title="">2010</span> <i title="Springer Berlin Heidelberg"> Recent Advances in Optimization and its Applications in Engineering </i> &nbsp;
For biinvariant Riemannian distances we provide an algorithm based on the Karcher mean gradient algorithm. We illustrate our approach by some examples on SO(n).  ...  This work considers the problem of fitting data on a Lie group by a coset of a compact subgroup.  ...  Acknowledgments This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-12598-0_15">doi:10.1007/978-3-642-12598-0_15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jee5kybjebe7ralj22o4764sbm">fatcat:jee5kybjebe7ralj22o4764sbm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170816051730/http://orbi.ulg.ac.be/bitstream/2268/78593/1/LS10.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c8/af/c8afd33d3c11e5ac3fb56705b7862188ccbc2bd3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-12598-0_15"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Steepest Descent Algorithms for Optimization Under Unitary Matrix Constraint

Traian E. Abrudan, Jan Eriksson, Visa Koivunen
<span title="">2008</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gkn2pu46ozb4tmkxczacnmtvkq" style="color: black;">IEEE Transactions on Signal Processing</a> </i> &nbsp;
We derive steepest descent (SD) algorithms on the Lie group of unitary matrices ( ). The proposed algorithms move towards the optimum along the geodesics, but other alternatives are also considered.  ...  In many engineering applications we deal with constrained optimization problems with respect to complex-valued matrices.  ...  CONCLUSION In this paper, Riemannian optimization algorithms on the Lie group of unitary matrices have been introduced. Expression for Riemannian gradient needed in the optimization has been derived.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsp.2007.908999">doi:10.1109/tsp.2007.908999</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/75kgratdcbd7zaa5dtsyelhwtm">fatcat:75kgratdcbd7zaa5dtsyelhwtm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829221448/http://www.cs.ox.ac.uk/files/6675/AbrEriKoi08TSP__SD_algorithms_for_optimization_under_unitary_matrix_constraint.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5d/c4/5dc44bc1148ae8e001fcc27596512f752cbb69ec.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsp.2007.908999"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Least-Squares on the Real Symplectic Group [article]

Simone Fiori
<span title="2013-03-07">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The resulting non-linear minimization problem on manifold may be tackled by means of a gradient-descent algorithm tailored to the geometry of the space at hand.  ...  In turn, gradient steepest descent on manifold may be implemented through a geodesic-based stepping method.  ...  . • The resulting sum-of-squared-distance minimization problem on manifold may be tackled via a gradient-based descent algorithm tailored to the geometry of the symplectic group through a geodesic-based  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1001.0829v2">arXiv:1001.0829v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rkonq352wnatvktmi6pah2jdjm">fatcat:rkonq352wnatvktmi6pah2jdjm</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1001.0829/1001.0829.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bf/24/bf2428fb6e15fa88fa49f87e0859c78b2c7efb24.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1001.0829v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Collaborative filtering via euclidean embedding

Mohammad Khoshneshin, W. Nick Street
<span title="">2010</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/vxvef3lblbcxbliuugiju5sify" style="color: black;">Proceedings of the fourth ACM conference on Recommender systems - RecSys &#39;10</a> </i> &nbsp;
One of the most accurate and scalable collaborative filtering algorithms is matrix factorization, which is based on a latent factor model.  ...  Our experimental results confirm these advantages and show that collaborative filtering via Euclidean embedding is a promising approach for online recommender systems.  ...  A key advantage of Euclidean embedding over matrix factorization is that the nature of the mapped space allows candidate retrieval via neighborhood search.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1864708.1864728">doi:10.1145/1864708.1864728</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/recsys/KhoshneshinS10.html">dblp:conf/recsys/KhoshneshinS10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hklx2aetfzax3kwntzqsezmwsa">fatcat:hklx2aetfzax3kwntzqsezmwsa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110331182027/http://dollar.biz.uiowa.edu/~street/research/recsys10_cfmds.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7f/43/7f437f273c9a7775c7e11b8ecb5b7c3cf220b4c0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1864708.1864728"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Geometric Direct Search Algorithms for Image Registration

Seok Lee, Minseok Choi, Hyungmin Kim, Frank Chongwoo Park
<span title="">2007</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dhlhr4jqkbcmdbua2ca45o7kru" style="color: black;">IEEE Transactions on Image Processing</a> </i> &nbsp;
In this paper, we present coordinate-invariant, geometric versions of the Nelder-Mead optimization algorithm on the groups (3), and their various subgroups, that are applicable to a wide class of image  ...  Because the algorithms respect the geometric structure of the underlying groups, they are numerically more stable, and exhibit better convergence properties than existing local coordinate-based algorithms  ...  either of the rigid body type, i.e., belonging to the special Euclidean group , or of a more general volume preserving type, i.e., belonging to the special linear group .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tip.2007.901809">doi:10.1109/tip.2007.901809</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/17784595">pmid:17784595</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4akahfs375dupejclzvzqbp5oe">fatcat:4akahfs375dupejclzvzqbp5oe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170830012100/http://robotics.snu.ac.kr/fcp/files/_pdf_files_publications/geometric_direct_search_algorithms_for_image_registration.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/66/77/66777c21c0e00c99436c7b89c8c4f4c9d344683e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tip.2007.901809"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Quantum multiobservable control

Raj Chakrabarti, Rebing Wu, Herschel Rabitz
<span title="2008-06-30">2008</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/iedolmzeofgc3ezyedga7h4eba" style="color: black;">Physical Review A. Atomic, Molecular, and Optical Physics</a> </i> &nbsp;
The effects of multiple control objectives on the structure and complexity of optimal fields are examined.  ...  Unlike optimal control approaches based on cost function optimization, quantum multiobservable tracking control (MOTC) is capable of tracking predetermined homotopic trajectories to target expectation  ...  that optimize scalar objective functions of the form (2) or (3) , with a specific focus on gradient algorithms.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.77.063425">doi:10.1103/physreva.77.063425</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/grjoad7fgnfpplwrppbk3bf3ta">fatcat:grjoad7fgnfpplwrppbk3bf3ta</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-0805.1556/0805.1556.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.77.063425"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

Geometric Optimization Methods for Adaptive Filtering [article]

Steven Thomas Smith
<span title="2013-05-08">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Some classical optimization techniques on Euclidean space are generalized to Riemannian manifolds.  ...  Specifically, two new algorithms, which can be thought of as Newton's method and the conjugate gradient method on Riemannian manifolds, are presented and shown to possess quadratic and superlinear convergence  ...  analogous to the optimization algorithms on Euclidean space discussed above.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1305.1886v1">arXiv:1305.1886v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q3vvafkqfjazndl4vvm2m5c4ba">fatcat:q3vvafkqfjazndl4vvm2m5c4ba</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200823204214/https://arxiv.org/pdf/1305.1886v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e3/d6/e3d692bb56c4733f80d486df4a077bf3f2a3db47.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1305.1886v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Generalized Sparse and Low-Rank Optimization for Ultra-Dense Networks [article]

Yuanming Shi and Jun Zhang and Wei Chen and Khaled B. Letaief
<span title="2017-09-26">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A special attention is paid on algorithmic approaches to deal with nonconvex objective functions and constraints, as well as computational scalability.  ...  This motivates the recent introduction of highly structured and generalizable models for network optimization.  ...  We have seen recent progress on nonconvex procedures based on various algorithms (e.g., projected/stochastic/conditional gradient methods, Riemannian manifold optimization algorithms) for a class of high-dimensional  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1709.09103v1">arXiv:1709.09103v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gtamszsp7zhatewx23el6jfuw4">fatcat:gtamszsp7zhatewx23el6jfuw4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200929220522/https://arxiv.org/pdf/1709.09103v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/95/69/956978f6a7eee6b4b9a1e69275ea6e9258f77ed7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1709.09103v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Bayesian Optimization Meets Riemannian Manifolds in Robot Learning [article]

Noémie Jaquier, Leonel Rozo, Sylvain Calinon, Mathias Bürger
<span title="2019-10-11">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach  ...  Our approach, built on Riemannian manifold theory, allows BO to properly measure similarities in the parameter space through geometry-aware kernel functions and to optimize the acquisition function on  ...  The authors thank Andras Kupcsik and Lukas Fröhlich for their useful feedback on this manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.04998v1">arXiv:1910.04998v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gy7d6nv37banhkp2ehobxedfoy">fatcat:gy7d6nv37banhkp2ehobxedfoy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200928010453/https://arxiv.org/pdf/1910.04998v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/77/ec/77ec4adb3249bfe519403af0049d2f9165bb204a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.04998v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Extrinsic Geometrical Methods for Neural Blind Deconvolution

Simone Fiori
<span title="">2006</span> <i title="AIP"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3jzz7zp4afbbpdcvegp6zk7rp4" style="color: black;">AIP Conference Proceedings</a> </i> &nbsp;
The present contribution discusses a Riemannian-gradient-based algorithm and a projection-based learning algorithm over a curved parameter space for single-neuron learning.  ...  The learning rule naturally arises from a criterion-function minimization over the unitary hyper-sphere setting.  ...  Recent studies have shown that learning algorithms based on natural gradient, which takes into account the geometrical structure of the neural manifold, do seem to be less affected by this difficulty  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1063/1.2423271">doi:10.1063/1.2423271</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sczkhfymfrbobaygbq2alrbbku">fatcat:sczkhfymfrbobaygbq2alrbbku</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705062209/http://djafari.free.fr/maxent2006/Finals/092_Fiori.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/69/7c/697c7c3dc9a6230cc24214c90f5aafcb206767ad.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1063/1.2423271"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Browser-based Hyperbolic Visualization of Graphs [article]

Jacob Miller, Stephen Kobourov, Vahan Huroyan
<span title="2022-05-16">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
With this in mind, we designed, implemented, and analyzed three methods for hyperbolic visualization of networks in the browser based on inverse projections, generalized force-directed algorithms, and  ...  Hyperbolic geometry offers a natural focus + context for data visualization and has been shown to underlie real-world complex networks.  ...  The layout is obtained by reducing the energy of the system via gradient descent.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2205.08028v1">arXiv:2205.08028v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w3c4fhpknrhrna7unxisdn74p4">fatcat:w3c4fhpknrhrna7unxisdn74p4</a> </span>
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