Nguyen, Du Families of costs with zero and nonnegative MTW tensor in optimal transport. arXiv:2401.00953 Preprint, arXiv:2401.00953 [math.AP] (2024). MSC: 58C05 49Q22 53C80 57Z20 57Z25 68T05 26B25 BibTeX Cite \textit{D. Nguyen}, ``Families of costs with zero and nonnegative MTW tensor in optimal transport'', Preprint, arXiv:2401.00953 [math.AP] (2024) Full Text: arXiv OA License
Nguyen, Du Operator-valued formulas for Riemannian gradient and Hessian and families of tractable metrics in Riemannian optimization. (English) Zbl 1515.65169 J. Optim. Theory Appl. 198, No. 1, 135-164 (2023). MSC: 65K10 58C05 49Q12 53C25 57Z20 57Z25 68T05 PDFBibTeX XMLCite \textit{D. Nguyen}, J. Optim. Theory Appl. 198, No. 1, 135--164 (2023; Zbl 1515.65169) Full Text: DOI arXiv
Bello-Rivas, Juan M.; Georgiou, Anastasia; Guckenheimer, John; Kevrekidis, Ioannis G. Staying the course: iteratively locating equilibria of dynamical systems on Riemannian manifolds defined by point-clouds. (English) Zbl 1515.37090 J. Math. Chem. 61, No. 3, 600-629 (2023). MSC: 37M05 37M21 53Z50 68T05 PDFBibTeX XMLCite \textit{J. M. Bello-Rivas} et al., J. Math. Chem. 61, No. 3, 600--629 (2023; Zbl 1515.37090) Full Text: DOI arXiv
Sun, Ke Local measurements of nonlinear embeddings with information geometry. (English) Zbl 1524.68300 Nielsen, Frank (ed.) et al., Geometry and statistics. Amsterdam: Elsevier/Academic Press. Handb. Stat. 46, 257-281 (2022). MSC: 68T05 53B12 62B11 PDFBibTeX XMLCite \textit{K. Sun}, Handb. Stat. 46, 257--281 (2022; Zbl 1524.68300) Full Text: Link
Nguyen, Du Closed-form geodesics and optimization for Riemannian logarithms of Stiefel and flag manifolds. (English) Zbl 1500.53056 J. Optim. Theory Appl. 194, No. 1, 142-166 (2022). MSC: 53C22 14M15 58E10 65K10 58C05 53C25 57Z20 57Z25 68T05 68T45 PDFBibTeX XMLCite \textit{D. Nguyen}, J. Optim. Theory Appl. 194, No. 1, 142--166 (2022; Zbl 1500.53056) Full Text: DOI arXiv
Hanika, Tom; Schneider, Friedrich Martin; Stumme, Gerd Intrinsic dimension of geometric data sets. (English) Zbl 1491.68188 Tôhoku Math. J. (2) 74, No. 1, 23-52 (2022). Reviewer: Jialong Deng (Beijing) MSC: 68T09 53C23 68P05 68T05 PDFBibTeX XMLCite \textit{T. Hanika} et al., Tôhoku Math. J. (2) 74, No. 1, 23--52 (2022; Zbl 1491.68188) Full Text: DOI arXiv
Cabanes, Yann; Nielsen, Frank Classification in the Siegel space for vectorial autoregressive data. (English) Zbl 1490.53021 Nielsen, Frank (ed.) et al., Geometric science of information. 5th international conference, GSI 2021, Paris, France, July 21–23, 2021. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12829, 693-700 (2021). MSC: 53B12 94A12 53A35 68T05 15B48 PDFBibTeX XMLCite \textit{Y. Cabanes} and \textit{F. Nielsen}, Lect. Notes Comput. Sci. 12829, 693--700 (2021; Zbl 1490.53021) Full Text: DOI
Kileel, Joe; Moscovich, Amit; Zelesko, Nathan; Singer, Amit Manifold learning with arbitrary norms. (English) Zbl 07395100 J. Fourier Anal. Appl. 27, No. 5, Paper No. 82, 56 p. (2021). MSC: 68T05 53B50 62R30 PDFBibTeX XMLCite \textit{J. Kileel} et al., J. Fourier Anal. Appl. 27, No. 5, Paper No. 82, 56 p. (2021; Zbl 07395100) Full Text: DOI arXiv
Zhang, Ruda; Ghanem, Roger Normal-bundle bootstrap. (English) Zbl 1475.62292 SIAM J. Math. Data Sci. 3, No. 2, 573-592 (2021). MSC: 62R30 62G09 37M22 53A07 68T05 PDFBibTeX XMLCite \textit{R. Zhang} and \textit{R. Ghanem}, SIAM J. Math. Data Sci. 3, No. 2, 573--592 (2021; Zbl 1475.62292) Full Text: DOI arXiv
Becker, Simon; Li, Wuchen Quantum statistical learning via quantum Wasserstein natural gradient. (English) Zbl 1460.81008 J. Stat. Phys. 182, No. 1, Paper No. 7, 26 p. (2021). MSC: 81P45 81P50 53B12 81P16 46L05 68T05 PDFBibTeX XMLCite \textit{S. Becker} and \textit{W. Li}, J. Stat. Phys. 182, No. 1, Paper No. 7, 26 p. (2021; Zbl 1460.81008) Full Text: DOI arXiv
Schnörr, Christoph Assignment flows. (English) Zbl 1512.37099 Grohs, Philipp (ed.) et al., Handbook of variational methods for nonlinear geometric data. Cham: Springer. 235-260 (2020). MSC: 37M99 53B12 62B11 68T05 68T09 PDFBibTeX XMLCite \textit{C. Schnörr}, in: Handbook of variational methods for nonlinear geometric data. Cham: Springer. 235--260 (2020; Zbl 1512.37099) Full Text: DOI
Budninskiy, Max; Yin, Gloria; Feng, Leman; Tong, Yiying; Desbrun, Mathieu Parallel transport unfolding: a connection-based manifold learning approach. (English) Zbl 1425.53019 SIAM J. Appl. Algebra Geom. 3, No. 2, 266-291 (2019). MSC: 53B20 53B05 68T05 PDFBibTeX XMLCite \textit{M. Budninskiy} et al., SIAM J. Appl. Algebra Geom. 3, No. 2, 266--291 (2019; Zbl 1425.53019) Full Text: DOI arXiv
Ache, Antonio G.; Warren, Micah W. Ricci curvature and the manifold learning problem. (English) Zbl 1415.93297 Adv. Math. 342, 14-66 (2019). Reviewer: Kurt Marti (München) MSC: 93E35 53A07 53A05 68T05 PDFBibTeX XMLCite \textit{A. G. Ache} and \textit{M. W. Warren}, Adv. Math. 342, 14--66 (2019; Zbl 1415.93297) Full Text: DOI arXiv
Li, Wuchen; Montúfar, Guido Natural gradient via optimal transport. (English) Zbl 1409.62022 Inf. Geom. 1, No. 2, 181-214 (2018). MSC: 62B10 68T05 53C80 60E05 PDFBibTeX XMLCite \textit{W. Li} and \textit{G. Montúfar}, Inf. Geom. 1, No. 2, 181--214 (2018; Zbl 1409.62022) Full Text: DOI arXiv
Minh, Hà Quang; Murino, Vittorio Covariances in computer vision and machine learning. (English) Zbl 1380.68005 Synthesis Lectures on Computer Vision 13. San Rafael, CA: Morgan & Claypool Publishers (ISBN 978-1-68173-013-4/pbk; 978-1-68173-014-1/ebook). xiii, 156 p. (2018). MSC: 68-02 15B48 47B32 53B21 62H35 68T05 68T45 PDFBibTeX XMLCite \textit{H. Q. Minh} and \textit{V. Murino}, Covariances in computer vision and machine learning. San Rafael, CA: Morgan \& Claypool Publishers (2018; Zbl 1380.68005) Full Text: DOI
Minh, Hà Quang (ed.); Murino, Vittorio (ed.) Algorithmic advances in Riemannian geometry and applications. For machine learning, computer vision, statistics, and optimization. (English) Zbl 1357.53004 Advances in Computer Vision and Pattern Recognition. Cham: Springer (ISBN 978-3-319-45025-4/hbk; 978-3-319-45026-1/ebook). xiv, 208 p. (2016). MSC: 53-06 53C21 68U05 68T05 00B15 PDFBibTeX XMLCite \textit{H. Q. Minh} (ed.) and \textit{V. Murino} (ed.), Algorithmic advances in Riemannian geometry and applications. For machine learning, computer vision, statistics, and optimization. Cham: Springer (2016; Zbl 1357.53004) Full Text: DOI
Amari, Shun-ichi Information geometry and its applications. (English) Zbl 1350.94001 Applied Mathematical Sciences 194. Tokyo: Springer (ISBN 978-4-431-55977-1/hbk; 978-4-431-55978-8/ebook). xiii, 374 p. (2016). Reviewer: Athanase Papadopoulos (Strasbourg) MSC: 94-01 62-01 53-01 94A15 94A17 52B10 62E10 62F12 53B05 62B10 62H30 62M10 68T05 PDFBibTeX XMLCite \textit{S.-i. Amari}, Information geometry and its applications. Tokyo: Springer (2016; Zbl 1350.94001) Full Text: DOI
Uwano, Yoshio All the trajectories of an extended averaged Hebbian learning equation on the quantum state space are the e-geodesics. arXiv:1601.07983 Preprint, arXiv:1601.07983 [math.DS] (2016). MSC: 37D40 53C22 68T05 81P45 BibTeX Cite \textit{Y. Uwano}, ``All the trajectories of an extended averaged Hebbian learning equation on the quantum state space are the e-geodesics'', Preprint, arXiv:1601.07983 [math.DS] (2016) Full Text: arXiv OA License
Ollivier, Yann Riemannian metrics for neural networks. II: Recurrent networks and learning symbolic data sequences. (English) Zbl 1380.68338 Inf. Inference 4, No. 2, 154-193 (2015). MSC: 68T05 53B20 94A17 PDFBibTeX XMLCite \textit{Y. Ollivier}, Inf. Inference 4, No. 2, 154--193 (2015; Zbl 1380.68338) Full Text: DOI arXiv
Ollivier, Yann Riemannian metrics for neural networks. I: Feedforward networks. (English) Zbl 1380.68337 Inf. Inference 4, No. 2, 108-153 (2015). MSC: 68T05 53B20 94A17 PDFBibTeX XMLCite \textit{Y. Ollivier}, Inf. Inference 4, No. 2, 108--153 (2015; Zbl 1380.68337) Full Text: DOI arXiv
Chazal, Frédéric; Huang, Ruqi; Sun, Jian Gromov-Hausdorff approximation of filamentary structures using Reeb-type graphs. (English) Zbl 1315.68252 Discrete Comput. Geom. 53, No. 3, 621-649 (2015). MSC: 68U05 53C23 68R10 68T05 PDFBibTeX XMLCite \textit{F. Chazal} et al., Discrete Comput. Geom. 53, No. 3, 621--649 (2015; Zbl 1315.68252) Full Text: DOI arXiv
Bavafaye, Haghighi Elham; Rahmati, Mohamad; Palm, Guenther; Shiry, Ghidary Saeed Learning inductive Riemannian manifold in abstract form by modeling embedded dynamical system. (English) Zbl 1387.68194 Informatica, Vilnius 25, No. 3, 361-384 (2014). MSC: 68T05 53B21 62H11 PDFBibTeX XMLCite \textit{H. E. Bavafaye} et al., Informatica, Vilnius 25, No. 3, 361--384 (2014; Zbl 1387.68194) Full Text: Link
Chazal, Frédéric; Sun, Jian Gromov-Hausdorff approximation of filament structure using Reeb-type graph (extended abstract). (English) Zbl 1395.68296 Proceedings of the 30th annual symposium on computational geometry, SoCG ’14, Kyoto, Japan, June 8–11, 2014. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-2594-3). 491-500 (2014). MSC: 68U05 53C23 68R10 68T05 PDFBibTeX XMLCite \textit{F. Chazal} and \textit{J. Sun}, in: Proceedings of the 30th annual symposium on computational geometry, SoCG '14, Kyoto, Japan, June 8--11, 2014. New York, NY: Association for Computing Machinery (ACM). 491--500 (2014; Zbl 1395.68296) Full Text: DOI
Xu, Qing; Li, Fanzhang; Zou, Peng The \(k\)-means algorithm based on Finsler geometry. (Chinese. English summary) Zbl 1324.68123 J. Univ. Sci. Technol. China 44, No. 7, 570-575 (2014). MSC: 68T05 53C60 PDFBibTeX XMLCite \textit{Q. Xu} et al., J. Univ. Sci. Technol. China 44, No. 7, 570--575 (2014; Zbl 1324.68123) Full Text: DOI
Rosman, Guy; Bronstein, Michael M.; Bronstein, Alexander M.; Kimmel, Ron Nonlinear dimensionality reduction by topologically constrained isometric embedding. (English) Zbl 1477.68489 Int. J. Comput. Vis. 89, No. 1, 56-68 (2010). MSC: 68U05 53B12 68T05 PDFBibTeX XMLCite \textit{G. Rosman} et al., Int. J. Comput. Vis. 89, No. 1, 56--68 (2010; Zbl 1477.68489) Full Text: DOI
Ivancevic, Tijana T.; Pearce, Charles E. M.; Bottema, Murk; Jain, Lakhmi C. A differential geometry-based neurodynamical classifier. (English) Zbl 1252.53022 Facta Univ., Ser. Mech. Autom. Control Robot. 6(2007), No. Special Issue, 221-230 (2009). MSC: 53B20 68T05 92B20 PDFBibTeX XMLCite \textit{T. T. Ivancevic} et al., Facta Univ., Ser. Mech. Autom. Control Robot. 6, No. Special Issue, 221--230 (2009; Zbl 1252.53022)
Ye, Gui-Bo; Zhou, Ding-Xuan SVM learning and \(L^{p}\) approximation by Gaussians on Riemannian manifolds. (English) Zbl 1175.68346 Anal. Appl., Singap. 7, No. 3, 309-339 (2009). MSC: 68T05 53C21 62J02 PDFBibTeX XMLCite \textit{G.-B. Ye} and \textit{D.-X. Zhou}, Anal. Appl., Singap. 7, No. 3, 309--339 (2009; Zbl 1175.68346) Full Text: DOI
Baraniuk, Richard G.; Wakin, Michael B. Random projections of smooth manifolds. (English) Zbl 1172.53005 Found. Comput. Math. 9, No. 1, 51-77 (2009). Reviewer: Hans-Peter Schröcker (Innsbruck) MSC: 53A07 62H99 65C99 68P30 68T05 94A12 94A29 PDFBibTeX XMLCite \textit{R. G. Baraniuk} and \textit{M. B. Wakin}, Found. Comput. Math. 9, No. 1, 51--77 (2009; Zbl 1172.53005) Full Text: DOI Link
Amari, Shun-ichi; Park, Hyeyoung; Ozeki, Tomoko Geometry of learning in multilayer perceptrons. (English) Zbl 1139.62326 Antoch, Jaromir (ed.), COMPSTAT. Proceedings in computational statistics. 16th symposium, Prague, Czech Republic, August 23-27, 2004. With CD-ROM. Heidelberg: Physica-Verlag (ISBN 3-7908-1554-3/pbk). 49-60 (2004). MSC: 62M45 68T05 53B99 PDFBibTeX XMLCite \textit{S.-i. Amari} et al., in: COMPSTAT. Proceedings in computational statistics. 16th symposium, Prague, Czech Republic, August 23-27, 2004. With CD-ROM. Heidelberg: Physica-Verlag. 49--60 (2004; Zbl 1139.62326)
Najarian, Kayvan On stochastic stability of dynamic neural models in presence of noise. (English) Zbl 1090.68565 Discrete Contin. Dyn. Syst. 2003, Suppl. Vol., 656-663 (2003). MSC: 68T05 53C35 93E15 PDFBibTeX XMLCite \textit{K. Najarian}, Discrete Contin. Dyn. Syst. 2003, 656--663 (2003; Zbl 1090.68565)
Burdet, G.; Combe, Ph.; Nencka, H. Statistical manifolds, self-parallel curves and learning processes. (English) Zbl 0947.62004 Dalang, Robert C. (ed.) et al., Seminar on Stochastic analysis, random fields and applications. Centro Stefano Franscini, Ascona, Italy, September 1996. Basel: Birkhäuser. Prog. Probab. 45, 87-99 (1999). Reviewer: Serguey M.Pokas (Odessa) MSC: 62A01 62B10 53A15 94A17 68T05 PDFBibTeX XMLCite \textit{G. Burdet} et al., Prog. Probab. 45, 87--99 (1999; Zbl 0947.62004)
Combe, P.; Nencka, H. Information geometry and learning in formal neural networks. (English) Zbl 0878.68098 Nencka, Hanna (ed.) et al., Geometry and nature: in memory of W. K. Clifford. A conference on new trends in geometrical and topological methods, July 30–August 5, 1995, Madeira, Portugal. Providence, RI: American Mathematical Society. Contemp. Math. 203, 105-116 (1997). Reviewer: S.M.Pokas (Odessa) MSC: 68T05 53C99 94A17 62B10 PDFBibTeX XMLCite \textit{P. Combe} and \textit{H. Nencka}, Contemp. Math. 203, 105--116 (1997; Zbl 0878.68098)
Amari, Shun-Ichi Mathematical methods of neurocomputing. (English) Zbl 0821.92003 Barndorff-Nielsen, O. E. (ed.) et al., Networks and chaos: statistical and probabilistic aspects. Revised versions of papers given at the first European statistical seminar on chaos and neural networks, held at Sandbjerg/Aarhus University from 25 April to 7 May 1992. London: Chapman and Hall. Monogr. Stat. Appl. Probab. 50, 1-39 (1993). MSC: 92B20 68T05 62B10 53B05 PDFBibTeX XMLCite \textit{S.-I. Amari}, Monogr. Stat. Appl. Probab. 50, 1--39 (1993; Zbl 0821.92003)
Wyvill, G.; Cao, En; Trotman, A. The Cao En surface: A new approach to freeform geometric models. (English. Russian original) Zbl 0875.68912 Program. Comput. Softw. 18, No. 4, 135-145 (1992); translation from Programmirovanie 1992, No. 4, 4-16 (1992). MSC: 68U05 53A05 68T05 PDFBibTeX XMLCite \textit{G. Wyvill} et al., Program. Comput. Softw. 18, No. 4, 135--145 (1992; Zbl 0875.68912); translation from Programmirovanie 1992, No. 4, 4--16 (1992)