Hamm, Keaton; Henscheid, Nick; Kang, Shujie Wassmap: Wasserstein isometric mapping for image manifold learning. (English) Zbl 07726190 SIAM J. Math. Data Sci. 5, No. 2, 475-501 (2023). MSC: 68T10 49Q22 PDF BibTeX XML Cite \textit{K. Hamm} et al., SIAM J. Math. Data Sci. 5, No. 2, 475--501 (2023; Zbl 07726190) Full Text: DOI arXiv
Cartis, Coralia; Massart, Estelle; Otemissov, Adilet Global optimization using random embeddings. (English) Zbl 07700908 Math. Program. 200, No. 2 (B), 781-829 (2023). MSC: 65K05 90C30 90C26 49K45 PDF BibTeX XML Cite \textit{C. Cartis} et al., Math. Program. 200, No. 2 (B), 781--829 (2023; Zbl 07700908) Full Text: DOI arXiv
Li, Xiaohan; Polydorides, Nick Fast heat transfer simulation for laser powder bed fusion. (English) Zbl 07692998 Comput. Methods Appl. Mech. Eng. 412, Article ID 116107, 21 p. (2023). MSC: 78-XX 76-XX PDF BibTeX XML Cite \textit{X. Li} and \textit{N. Polydorides}, Comput. Methods Appl. Mech. Eng. 412, Article ID 116107, 21 p. (2023; Zbl 07692998) Full Text: DOI
Cartis, Coralia; Massart, Estelle; Otemissov, Adilet Bound-constrained global optimization of functions with low effective dimensionality using multiple random embeddings. (English) Zbl 07658269 Math. Program. 198, No. 1 (A), 997-1058 (2023). MSC: 65K05 90C30 90C26 49K45 15A52 PDF BibTeX XML Cite \textit{C. Cartis} et al., Math. Program. 198, No. 1 (A), 997--1058 (2023; Zbl 07658269) Full Text: DOI arXiv
Yang, Zhirong; Chen, Yuwei; Sedov, Denis; Kaski, Samuel; Corander, Jukka Stochastic cluster embedding. (English) Zbl 1499.62040 Stat. Comput. 33, No. 1, Paper No. 12, 14 p. (2023). MSC: 62-08 PDF BibTeX XML Cite \textit{Z. Yang} et al., Stat. Comput. 33, No. 1, Paper No. 12, 14 p. (2023; Zbl 1499.62040) Full Text: DOI arXiv
Pan, Guanru; Faulwasser, Timm NMPC in active subspaces: dimensionality reduction with recursive feasibility guarantees. (English) Zbl 1505.93057 Automatica 147, Article ID 110708, 9 p. (2023). MSC: 93B45 93B11 93C10 PDF BibTeX XML Cite \textit{G. Pan} and \textit{T. Faulwasser}, Automatica 147, Article ID 110708, 9 p. (2023; Zbl 1505.93057) Full Text: DOI arXiv
Liao, Wei; Liang, Taotao; Wang, Chen; Yang, Dayong A dimensionality reduction method for computing reachable tubes based on piecewise pseudo-time dependent Hamilton-Jacobi equation. (English) Zbl 1511.93017 Appl. Math. Comput. 441, Article ID 127696, 13 p. (2023). MSC: 93B03 49L12 93B11 PDF BibTeX XML Cite \textit{W. Liao} et al., Appl. Math. Comput. 441, Article ID 127696, 13 p. (2023; Zbl 1511.93017) Full Text: DOI
Bauer, Jan O.; Drabant, Bernhard Regression based thresholds in principal loading analysis. (English) Zbl 07626988 J. Multivariate Anal. 193, Article ID 105103, 10 p. (2023). MSC: 62Hxx 15A18 47H14 62H25 62J05 PDF BibTeX XML Cite \textit{J. O. Bauer} and \textit{B. Drabant}, J. Multivariate Anal. 193, Article ID 105103, 10 p. (2023; Zbl 07626988) Full Text: DOI arXiv
Ehre, Max; Papaioannou, Iason; Sudret, Bruno; Straub, Daniel Sequential active learning of low-dimensional model representations for reliability analysis. (English) Zbl 1493.62496 SIAM J. Sci. Comput. 44, No. 3, B558-B584 (2022). MSC: 62L99 62P30 62J02 65C05 PDF BibTeX XML Cite \textit{M. Ehre} et al., SIAM J. Sci. Comput. 44, No. 3, B558--B584 (2022; Zbl 1493.62496) Full Text: DOI arXiv
Zieliński, Przemysław; Hesthaven, Jan S. Discovery of slow variables in a class of multiscale stochastic systems via neural networks. (English) Zbl 1498.37127 J. Nonlinear Sci. 32, No. 4, Paper No. 51, 34 p. (2022). MSC: 37M99 65C30 70K70 PDF BibTeX XML Cite \textit{P. Zieliński} and \textit{J. S. Hesthaven}, J. Nonlinear Sci. 32, No. 4, Paper No. 51, 34 p. (2022; Zbl 1498.37127) Full Text: DOI arXiv
Gruber, Anthony; Gunzburger, Max; Ju, Lili; Wang, Zhu A comparison of neural network architectures for data-driven reduced-order modeling. (English) Zbl 1507.65157 Comput. Methods Appl. Mech. Eng. 393, Article ID 114764, 26 p. (2022). MSC: 65M22 65M60 PDF BibTeX XML Cite \textit{A. Gruber} et al., Comput. Methods Appl. Mech. Eng. 393, Article ID 114764, 26 p. (2022; Zbl 1507.65157) Full Text: DOI arXiv
Allerbo, Oskar; Jörnsten, Rebecka Non-linear, sparse dimensionality reduction via path Lasso penalized autoencoders. (English) Zbl 07626798 J. Mach. Learn. Res. 22, Paper No. 283, 28 p. (2021). MSC: 68T05 PDF BibTeX XML Cite \textit{O. Allerbo} and \textit{R. Jörnsten}, J. Mach. Learn. Res. 22, Paper No. 283, 28 p. (2021; Zbl 07626798) Full Text: arXiv Link
Gruber, Anthony; Gunzburger, Max; Ju, Lili; Teng, Yuankai; Wang, Zhu Nonlinear level set learning for function approximation on sparse data with applications to parametric differential equations. (English) Zbl 1499.65052 Numer. Math., Theory Methods Appl. 14, No. 4, 839-861 (2021). MSC: 65D15 65D40 PDF BibTeX XML Cite \textit{A. Gruber} et al., Numer. Math., Theory Methods Appl. 14, No. 4, 839--861 (2021; Zbl 1499.65052) Full Text: DOI arXiv
Girin, Laurent; Leglaive, Simon; Bie, Xiaoyu; Diard, Julien; Hueber, Thomas; Alameda-Pineda, Xavier Dynamical variational autoencoders: a comprehensive review. (English) Zbl 1491.68153 Found. Trends Mach. Learn. 15, No. 1-2, 1-175 (2021). MSC: 68T05 68T07 68-02 PDF BibTeX XML Cite \textit{L. Girin} et al., Found. Trends Mach. Learn. 15, No. 1--2, 1--175 (2021; Zbl 1491.68153) Full Text: DOI arXiv
Šehić, Kenan; Bredmose, Henrik; Sørensen, John D.; Karamehmedović, Mirza Low-dimensional offshore wave input for extreme event quantification. (English) Zbl 1483.76016 J. Eng. Math. 126, Paper No. 13, 18 p. (2021). MSC: 76B15 86A05 PDF BibTeX XML Cite \textit{K. Šehić} et al., J. Eng. Math. 126, Paper No. 13, 18 p. (2021; Zbl 1483.76016) Full Text: DOI arXiv Link
Sun, Zhihua; Chen, Feifei; Liang, Hua; Ruppert, David A projection-based consistent test incorporating dimension-reduction in partially linear models. (English) Zbl 1475.62172 Stat. Sin. 31, No. 3, 1489-1508 (2021). MSC: 62H15 62J02 PDF BibTeX XML Cite \textit{Z. Sun} et al., Stat. Sin. 31, No. 3, 1489--1508 (2021; Zbl 1475.62172) Full Text: DOI
Thrun, Michael C.; Ultsch, Alfred Swarm intelligence for self-organized clustering. (English) Zbl 1504.68191 Artif. Intell. 290, Article ID 103237, 24 p. (2021). MSC: 68T05 62H30 PDF BibTeX XML Cite \textit{M. C. Thrun} and \textit{A. Ultsch}, Artif. Intell. 290, Article ID 103237, 24 p. (2021; Zbl 1504.68191) Full Text: DOI arXiv
Chandler, Gabriel; Polonik, Wolfgang Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with applications. (English) Zbl 1468.62303 Ann. Stat. 49, No. 2, 988-1010 (2021). MSC: 62H30 62G07 62R20 PDF BibTeX XML Cite \textit{G. Chandler} and \textit{W. Polonik}, Ann. Stat. 49, No. 2, 988--1010 (2021; Zbl 1468.62303) Full Text: DOI arXiv
Bermanis, Amit; Salhov, Moshe; Averbuch, Amir Geometric component analysis and its applications to data analysis. (English) Zbl 1515.68282 Appl. Comput. Harmon. Anal. 54, 20-43 (2021). MSC: 68T09 PDF BibTeX XML Cite \textit{A. Bermanis} et al., Appl. Comput. Harmon. Anal. 54, 20--43 (2021; Zbl 1515.68282) Full Text: DOI
Altaher, Mohammad; Nomir, Omaima; ElMougy, Samir Intercepting a superior missile: trajectory optimization approach to a pursuit-evasion game. (English) Zbl 1478.93262 Int. Game Theory Rev. 22, No. 4, Article ID 2050004, 21 p. (2020). MSC: 93C10 49N75 91A24 53Z30 PDF BibTeX XML Cite \textit{M. Altaher} et al., Int. Game Theory Rev. 22, No. 4, Article ID 2050004, 21 p. (2020; Zbl 1478.93262) Full Text: DOI
Perea, Jose A. Sparse circular coordinates via principal \(\mathbb{Z}\)-bundles. (English) Zbl 1450.62140 Baas, Nils (ed.) et al., Topological data analysis. Proceedings of the Abel symposium 2018, Geiranger, Norway, June 4–8, 2018. Cham: Springer. Abel Symp. 15, 435-458 (2020). MSC: 62R40 62H35 55N31 PDF BibTeX XML Cite \textit{J. A. Perea}, Abel Symp. 15, 435--458 (2020; Zbl 1450.62140) Full Text: DOI arXiv
Turchetti, Claudio; Falaschetti, Laura A manifold learning approach to dimensionality reduction for modeling data. (English) Zbl 1451.68234 Inf. Sci. 491, 16-29 (2019). MSC: 68T05 62H12 68T09 PDF BibTeX XML Cite \textit{C. Turchetti} and \textit{L. Falaschetti}, Inf. Sci. 491, 16--29 (2019; Zbl 1451.68234) Full Text: DOI
Bao, Han; Liu, Wenbo; Chen, Mo Hidden extreme multistability and dimensionality reduction analysis for an improved non-autonomous memristive Fitzhugh-Nagumo circuit. (English) Zbl 1437.94103 Nonlinear Dyn. 96, No. 3, 1879-1894 (2019). MSC: 94C05 37M05 70K20 70K50 PDF BibTeX XML Cite \textit{H. Bao} et al., Nonlinear Dyn. 96, No. 3, 1879--1894 (2019; Zbl 1437.94103) Full Text: DOI
Amiri, Fatemeh; Ziaei-Rad, Saeed; Valizadeh, Navid; Rabczuk, Timon On the use of local maximum entropy approximants for Cahn-Hilliard phase-field models in 2D domains and on surfaces. (English) Zbl 1440.74370 Comput. Methods Appl. Mech. Eng. 346, 1-24 (2019). MSC: 74S05 65M60 74N20 PDF BibTeX XML Cite \textit{F. Amiri} et al., Comput. Methods Appl. Mech. Eng. 346, 1--24 (2019; Zbl 1440.74370) Full Text: DOI
Ibañez, R.; Abisset-Chavanne, E.; Cueto, E.; Ammar, A.; Duval, J.-L.; Chinesta, F. Some applications of compressed sensing in computational mechanics: model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction. (English) Zbl 1464.74394 Comput. Mech. 64, No. 5, 1259-1271 (2019). MSC: 74S99 PDF BibTeX XML Cite \textit{R. Ibañez} et al., Comput. Mech. 64, No. 5, 1259--1271 (2019; Zbl 1464.74394) Full Text: DOI HAL
Long, Andrew W.; Ferguson, Andrew L. Landmark diffusion maps (L-dMaps): accelerated manifold learning out-of-sample extension. (English) Zbl 1489.68228 Appl. Comput. Harmon. Anal. 47, No. 1, 190-211 (2019). MSC: 68T05 05C50 42B35 60J60 62R30 68Q25 92-10 PDF BibTeX XML Cite \textit{A. W. Long} and \textit{A. L. Ferguson}, Appl. Comput. Harmon. Anal. 47, No. 1, 190--211 (2019; Zbl 1489.68228) Full Text: DOI arXiv
López-Sánchez, Daniel; Corchado, Juan Manuel; González Arrieta, Angélica Data-independent random projections from the feature-map of the homogeneous polynomial kernel of degree two. (English) Zbl 1440.68230 Inf. Sci. 436-437, 214-226 (2018). MSC: 68T05 62H30 68U05 PDF BibTeX XML Cite \textit{D. López-Sánchez} et al., Inf. Sci. 436--437, 214--226 (2018; Zbl 1440.68230) Full Text: DOI Link
Grishagin, Vladimir; Israfilov, Ruslan; Sergeyev, Yaroslav Convergence conditions and numerical comparison of global optimization methods based on dimensionality reduction schemes. (English) Zbl 1426.90204 Appl. Math. Comput. 318, 270-280 (2018). MSC: 90C26 65K10 90C30 65K05 PDF BibTeX XML Cite \textit{V. Grishagin} et al., Appl. Math. Comput. 318, 270--280 (2018; Zbl 1426.90204) Full Text: DOI
Nakano, Naoto; Inatsu, Masaru; Kusuoka, Seiichiro; Saiki, Yoshitaka Empirical evaluated SDE modelling for dimensionality-reduced systems and its predictability estimates. (English) Zbl 1404.60054 Japan J. Ind. Appl. Math. 35, No. 2, 553-589 (2018). MSC: 60G25 62M10 62M20 PDF BibTeX XML Cite \textit{N. Nakano} et al., Japan J. Ind. Appl. Math. 35, No. 2, 553--589 (2018; Zbl 1404.60054) Full Text: DOI
Aggarwal, Charu C. Machine learning for text. (English) Zbl 1395.68001 Cham: Springer (ISBN 978-3-319-73530-6/hbk; 978-3-319-73531-3/ebook). xxiii, 493 p. (2018). Reviewer: Irina Ioana Mohorianu (Oxford) MSC: 68-01 68-02 62H30 68P20 68T05 68T50 PDF BibTeX XML Cite \textit{C. C. Aggarwal}, Machine learning for text. Cham: Springer (2018; Zbl 1395.68001) Full Text: DOI
Naor, Assaf A spectral gap precludes low-dimensional embeddings. (English) Zbl 1433.68312 Aronov, Boris (ed.) et al., 33rd international symposium on computational geometry. SoCG 2017, Brisbane, Australia, July 4–7, 2017. Proceedings. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 77, Article 50, 16 p. (2017). MSC: 68R12 05C50 15B51 46B85 PDF BibTeX XML Cite \textit{A. Naor}, LIPIcs -- Leibniz Int. Proc. Inform. 77, Article 50, 16 p. (2017; Zbl 1433.68312) Full Text: DOI arXiv
Alla, Alessandro; Kutz, J. Nathan Nonlinear model order reduction via dynamic mode decomposition. (English) Zbl 1373.65090 SIAM J. Sci. Comput. 39, No. 5, B778-B796 (2017). MSC: 65P99 37M05 PDF BibTeX XML Cite \textit{A. Alla} and \textit{J. N. Kutz}, SIAM J. Sci. Comput. 39, No. 5, B778--B796 (2017; Zbl 1373.65090) Full Text: DOI arXiv
Ding, Chao; Qi, Hou-Duo Convex optimization learning of faithful Euclidean distance representations in nonlinear dimensionality reduction. (English) Zbl 1391.90472 Math. Program. 164, No. 1-2 (A), 341-381 (2017). MSC: 90C25 90C33 PDF BibTeX XML Cite \textit{C. Ding} and \textit{H.-D. Qi}, Math. Program. 164, No. 1--2 (A), 341--381 (2017; Zbl 1391.90472) Full Text: DOI arXiv
Yang, Bo; Xiang, Ming; Zhang, Yupei Multi-manifold discriminant Isomap for visualization and classification. (English) Zbl 1412.68197 Pattern Recognition 55, 215-230 (2016). MSC: 68T05 62H30 68U05 PDF BibTeX XML Cite \textit{B. Yang} et al., Pattern Recognition 55, 215--230 (2016; Zbl 1412.68197) Full Text: DOI
Xing, Xianglei; Du, Sidan; Wang, Kejun Robust Hessian locally linear embedding techniques for high-dimensional data. (English) Zbl 1461.62075 Algorithms (Basel) 9, No. 2, Paper No. 36, 21 p. (2016). MSC: 62H12 62G35 62-08 68T10 PDF BibTeX XML Cite \textit{X. Xing} et al., Algorithms (Basel) 9, No. 2, Paper No. 36, 21 p. (2016; Zbl 1461.62075) Full Text: DOI
Tripathy, Rohit; Bilionis, Ilias; Gonzalez, Marcial Gaussian processes with built-in dimensionality reduction: applications to high-dimensional uncertainty propagation. (English) Zbl 1349.65049 J. Comput. Phys. 321, 191-223 (2016). MSC: 65C50 62F15 62H30 62J02 PDF BibTeX XML Cite \textit{R. Tripathy} et al., J. Comput. Phys. 321, 191--223 (2016; Zbl 1349.65049) Full Text: DOI arXiv
Wu, Xingyu; Mao, Xia; Chen, Lijiang; Xue, Yuli; Rovetta, Alberto Point context: an effective shape descriptor for RST-invariant trajectory recognition. (English) Zbl 1386.68183 J. Math. Imaging Vis. 56, No. 3, 441-454 (2016). MSC: 68T45 68U10 PDF BibTeX XML Cite \textit{X. Wu} et al., J. Math. Imaging Vis. 56, No. 3, 441--454 (2016; Zbl 1386.68183) Full Text: DOI arXiv
Zimmermann, R.; Willcox, K. An accelerated greedy missing point estimation procedure. (English) Zbl 1348.65045 SIAM J. Sci. Comput. 38, No. 5, A2827-A2850 (2016). MSC: 65C60 62F10 65H10 65F15 PDF BibTeX XML Cite \textit{R. Zimmermann} and \textit{K. Willcox}, SIAM J. Sci. Comput. 38, No. 5, A2827--A2850 (2016; Zbl 1348.65045) Full Text: DOI
Guhaniyogi, Rajarshi; Dunson, David B. Bayesian compressed regression. (English) Zbl 1373.62100 J. Am. Stat. Assoc. 110, No. 512, 1500-1514 (2015). MSC: 62F15 62J02 62J07 PDF BibTeX XML Cite \textit{R. Guhaniyogi} and \textit{D. B. Dunson}, J. Am. Stat. Assoc. 110, No. 512, 1500--1514 (2015; Zbl 1373.62100) Full Text: DOI arXiv
Deleforge, Antoine; Forbes, Florence; Horaud, Radu High-dimensional regression with Gaussian mixtures and partially-latent response variables. (English) Zbl 1332.62192 Stat. Comput. 25, No. 5, 893-911 (2015). MSC: 62H25 62J02 PDF BibTeX XML Cite \textit{A. Deleforge} et al., Stat. Comput. 25, No. 5, 893--911 (2015; Zbl 1332.62192) Full Text: DOI arXiv
Amsallem, David; Zahr, Matthew J.; Washabaugh, Kyle Fast local reduced basis updates for the efficient reduction of nonlinear systems with hyper-reduction. (English) Zbl 1331.65094 Adv. Comput. Math. 41, No. 5, 1187-1230 (2015). MSC: 65L05 34A34 35Q53 35Q35 65M99 78M34 PDF BibTeX XML Cite \textit{D. Amsallem} et al., Adv. Comput. Math. 41, No. 5, 1187--1230 (2015; Zbl 1331.65094) Full Text: DOI
Damelin, S. B.; Gu, Y.; Wunsch, D. C.; Xu, R. Fuzzy adaptive resonance theory, diffusion maps and their applications to clustering and biclustering. (English) Zbl 1380.94066 Math. Model. Nat. Phenom. 10, No. 3, 206-211 (2015). MSC: 94A15 94A08 PDF BibTeX XML Cite \textit{S. B. Damelin} et al., Math. Model. Nat. Phenom. 10, No. 3, 206--211 (2015; Zbl 1380.94066) Full Text: DOI arXiv
Iwen, M. A.; Krahmer, Felix Fast subspace approximation via greedy least-squares. (English) Zbl 1406.65012 Constr. Approx. 42, No. 2, 281-301 (2015). MSC: 65D15 41A46 68U05 90C59 PDF BibTeX XML Cite \textit{M. A. Iwen} and \textit{F. Krahmer}, Constr. Approx. 42, No. 2, 281--301 (2015; Zbl 1406.65012) Full Text: DOI arXiv
Peltonen, Jaakko; Lin, Ziyuan Information retrieval approach to meta-visualization. (English) Zbl 1331.68272 Mach. Learn. 99, No. 2, 189-229 (2015). MSC: 68U10 62-07 68P20 PDF BibTeX XML Cite \textit{J. Peltonen} and \textit{Z. Lin}, Mach. Learn. 99, No. 2, 189--229 (2015; Zbl 1331.68272) Full Text: DOI
Batenkov, Dmitry; Friedland, Omer; Yomdin, Yosef Sampling, metric entropy, and dimensionality reduction. (English) Zbl 1381.41026 SIAM J. Math. Anal. 47, No. 1, 786-796 (2015). MSC: 41A46 46E20 94A20 94A12 94A17 PDF BibTeX XML Cite \textit{D. Batenkov} et al., SIAM J. Math. Anal. 47, No. 1, 786--796 (2015; Zbl 1381.41026) Full Text: DOI arXiv
Wang, Heng; Huang, Shoudong; Khosoussi, Kasra; Frese, Udo; Dissanayake, Gamini; Liu, Bingbing Dimensionality reduction for point feature SLAM problems with spherical covariance matrices. (English) Zbl 1309.93191 Automatica 51, 149-157 (2015). MSC: 93E24 93E20 93C85 93B11 93C10 PDF BibTeX XML Cite \textit{H. Wang} et al., Automatica 51, 149--157 (2015; Zbl 1309.93191) Full Text: DOI Link
Gao, Xiaofang; Liang, Jiye An improved incremental nonlinear dimensionality reduction for isometric data embedding. (English) Zbl 1312.68166 Inf. Process. Lett. 115, No. 4, 492-501 (2015). MSC: 68T05 PDF BibTeX XML Cite \textit{X. Gao} and \textit{J. Liang}, Inf. Process. Lett. 115, No. 4, 492--501 (2015; Zbl 1312.68166) Full Text: DOI
Bates, Jonathan The embedding dimension of Laplacian eigenfunction maps. (English) Zbl 1304.58016 Appl. Comput. Harmon. Anal. 37, No. 3, 516-530 (2014). Reviewer: Alexander A. Borisenko (Khar’kov) MSC: 58J50 53C42 94A08 PDF BibTeX XML Cite \textit{J. Bates}, Appl. Comput. Harmon. Anal. 37, No. 3, 516--530 (2014; Zbl 1304.58016) Full Text: DOI arXiv
Monnig, Nathan D.; Fornberg, Bengt; Meyer, François G. Inverting nonlinear dimensionality reduction with scale-free radial basis function interpolation. (English) Zbl 1297.65015 Appl. Comput. Harmon. Anal. 37, No. 1, 162-170 (2014). MSC: 65D05 41A05 41A30 PDF BibTeX XML Cite \textit{N. D. Monnig} et al., Appl. Comput. Harmon. Anal. 37, No. 1, 162--170 (2014; Zbl 1297.65015) Full Text: DOI arXiv
Ma, Shujie; Zhang, Jun; Sun, Zihua; Liang, Hua Integrated conditional moment test for partially linear single index models incorporating dimension-reduction. (English) Zbl 1348.62141 Electron. J. Stat. 8, No. 1, 523-542 (2014). MSC: 62G08 62G10 62G20 62J02 62G09 PDF BibTeX XML Cite \textit{S. Ma} et al., Electron. J. Stat. 8, No. 1, 523--542 (2014; Zbl 1348.62141) Full Text: DOI Euclid
Millán, Daniel; Rosolen, Adrian; Arroyo, Marino Nonlinear manifold learning for meshfree finite deformation thin-shell analysis. (English) Zbl 1352.74176 Int. J. Numer. Methods Eng. 93, No. 7, 685-713 (2013). MSC: 74K25 74A05 74S05 PDF BibTeX XML Cite \textit{D. Millán} et al., Int. J. Numer. Methods Eng. 93, No. 7, 685--713 (2013; Zbl 1352.74176) Full Text: DOI Link
Escalante-B., Alberto N.; Wiskott, Laurenz How to solve classification and regression problems on high-dimensional data with a supervised extension of slow feature analysis. (English) Zbl 1318.62209 J. Mach. Learn. Res. 14, 3683-3719 (2013). MSC: 62H30 68T05 68T10 PDF BibTeX XML Cite \textit{A. N. Escalante-B.} and \textit{L. Wiskott}, J. Mach. Learn. Res. 14, 3683--3719 (2013; Zbl 1318.62209) Full Text: Link
Millán, Daniel; Arroyo, Marino Nonlinear manifold learning for model reduction in finite elastodynamics. (English) Zbl 1286.74021 Comput. Methods Appl. Mech. Eng. 261-262, 118-131 (2013). MSC: 74B20 PDF BibTeX XML Cite \textit{D. Millán} and \textit{M. Arroyo}, Comput. Methods Appl. Mech. Eng. 261--262, 118--131 (2013; Zbl 1286.74021) Full Text: DOI Link
Devaud, Denis; Manzoni, Andrea; Rozza, Gianluigi A combination between the reduced basis method and the ANOVA expansion: on the computation of sensitivity indices. (English. French summary) Zbl 1279.65137 C. R., Math., Acad. Sci. Paris 351, No. 15-16, 593-598 (2013). MSC: 65N99 35J60 PDF BibTeX XML Cite \textit{D. Devaud} et al., C. R., Math., Acad. Sci. Paris 351, No. 15--16, 593--598 (2013; Zbl 1279.65137) Full Text: DOI
Zhang, Lei-Hong; Liao, Li-Zhi; Ng, Michael K. Superlinear convergence of a general algorithm for the generalized Foley-Sammon discriminant analysis. (English) Zbl 1291.90249 J. Optim. Theory Appl. 157, No. 3, 853-865 (2013). Reviewer: Francisco Guerra Vazquez (Puebla) MSC: 90C30 PDF BibTeX XML Cite \textit{L.-H. Zhang} et al., J. Optim. Theory Appl. 157, No. 3, 853--865 (2013; Zbl 1291.90249) Full Text: DOI
Hur, Dongcheol; Suk, Heung-Il; Wallraven, Christian; Lee, Seong-Whan Biased manifold learning for view invariant body pose estimation. (English) Zbl 1258.68134 Int. J. Wavelets Multiresolut. Inf. Process. 10, No. 6, Paper No. 1250058, 24 p. (2012). MSC: 68T10 68Q32 PDF BibTeX XML Cite \textit{D. Hur} et al., Int. J. Wavelets Multiresolut. Inf. Process. 10, No. 6, Paper No. 1250058, 24 p. (2012; Zbl 1258.68134) Full Text: DOI
Ngo, T. T.; Bellalij, M.; Saad, Y. The trace ratio optimization problem. (English) Zbl 1251.65090 SIAM Rev. 54, No. 3, 545-569 (2012). MSC: 65K05 68T05 90C30 65F30 PDF BibTeX XML Cite \textit{T. T. Ngo} et al., SIAM Rev. 54, No. 3, 545--569 (2012; Zbl 1251.65090) Full Text: DOI Link
Christodoulou, George; Mirrokni, Vahab S.; Sidiropoulos, Anastasios Convergence and approximation in potential games. (English) Zbl 1251.91008 Theor. Comput. Sci. 438, 13-27 (2012). Reviewer: Ruxandra Stoean (Craiova) MSC: 91A10 91Axx PDF BibTeX XML Cite \textit{G. Christodoulou} et al., Theor. Comput. Sci. 438, 13--27 (2012; Zbl 1251.91008) Full Text: DOI
Gaubert, Stephane; McEneaney, William M. min-max spaces and complexity reduction in min-max expansions. (English) Zbl 1244.93051 Appl. Math. Optim. 65, No. 3, 315-348 (2012). MSC: 93B40 93B11 15A80 93C10 PDF BibTeX XML Cite \textit{S. Gaubert} and \textit{W. M. McEneaney}, Appl. Math. Optim. 65, No. 3, 315--348 (2012; Zbl 1244.93051) Full Text: DOI
Cao, Ying; Chen, Di-Rong On the regularized Laplacian eigenmaps. (English) Zbl 1237.62002 J. Stat. Plann. Inference 142, No. 7, 1627-1643 (2012). MSC: 62-07 68T05 65C60 46N30 PDF BibTeX XML Cite \textit{Y. Cao} and \textit{D.-R. Chen}, J. Stat. Plann. Inference 142, No. 7, 1627--1643 (2012; Zbl 1237.62002) Full Text: DOI
Wang, Jianzhong Geometric structure of high-dimensional data and dimensionality reduction. (English) Zbl 1250.68010 Berlin: Springer; Beijing: Higher Education Press (ISBN 978-3-642-27496-1; 978-7-04-031704-6/hbk). xix, 356 p. (2012). Reviewer: Catalin Stoean (Craiova) MSC: 68-02 68-00 68T01 68T05 62H30 68T10 PDF BibTeX XML Cite \textit{J. Wang}, Geometric structure of high-dimensional data and dimensionality reduction. Berlin: Springer; Beijing: Higher Education Press (2012; Zbl 1250.68010)
Kwak, Nojun Kernel discriminant analysis for regression problems. (English) Zbl 1233.68190 Pattern Recognition 45, No. 5, 2019-2031 (2012). MSC: 68T05 68T10 62H25 62J02 62H30 PDF BibTeX XML Cite \textit{N. Kwak}, Pattern Recognition 45, No. 5, 2019--2031 (2012; Zbl 1233.68190) Full Text: DOI
Vega-Vilca, José Carlos; Guzmán, Josué PLS and PCA regression as solution to the multicollinearity problem in multiple regression. (Spanish. English summary) Zbl 1307.62159 Rev. Mat. Teor. Apl. 18, No. 1, 9-20 (2011). MSC: 62H25 62J02 PDF BibTeX XML Cite \textit{J. C. Vega-Vilca} and \textit{J. Guzmán}, Rev. Mat. Teor. Apl. 18, No. 1, 9--20 (2011; Zbl 1307.62159) Full Text: DOI
Fornasier, Massimo; Haškovec, Jan; Vybíral, Jan Particle systems and kinetic equations modeling interacting agents in high dimension. (English) Zbl 1244.93010 Multiscale Model. Simul. 9, No. 4, 1727-1764 (2011). MSC: 93A14 93B11 35F25 65P99 PDF BibTeX XML Cite \textit{M. Fornasier} et al., Multiscale Model. Simul. 9, No. 4, 1727--1764 (2011; Zbl 1244.93010) Full Text: DOI arXiv
Krämer, Nicole; Sugiyama, Masashi The degrees of freedom of partial least squares regression. (English) Zbl 1232.62099 J. Am. Stat. Assoc. 106, No. 494, 697-705 (2011). MSC: 62J02 62H12 65C60 PDF BibTeX XML Cite \textit{N. Krämer} and \textit{M. Sugiyama}, J. Am. Stat. Assoc. 106, No. 494, 697--705 (2011; Zbl 1232.62099) Full Text: DOI arXiv
Guillemard, Mijail; Iske, Armin Curvature analysis of frequency modulated manifolds in dimensionality reduction. (English) Zbl 1211.94021 Calcolo 48, No. 1, 107-125 (2011). MSC: 94A20 94A12 57-04 94A05 PDF BibTeX XML Cite \textit{M. Guillemard} and \textit{A. Iske}, Calcolo 48, No. 1, 107--125 (2011; Zbl 1211.94021) Full Text: DOI
Lee, John A.; Verleysen, Michel On the role and impact of the metaparameters in \(t\)-distributed stochastic neighbor embedding. (English) Zbl 1436.62144 Lechevallier, Yves (ed.) et al., Proceedings of COMPSTAT’2010. 19th international conference on computational statistics, Paris, France, August 22–27, 2010. Keynote, invited and contributed papers. Heidelberg: Physica Verlag. 337-346 (2010). MSC: 62G08 62H11 62-08 PDF BibTeX XML Cite \textit{J. A. Lee} and \textit{M. Verleysen}, in: Proceedings of COMPSTAT'2010. 19th international conference on computational statistics, Paris, France, August 22--27, 2010. Keynote, invited and contributed papers. Heidelberg: Physica Verlag. 337--346 (2010; Zbl 1436.62144) Full Text: DOI
Liu, Bo; Zhang, Hongbin A manifold unfolding method based on boundary constraints. (Chinese. English summary) Zbl 1240.68194 Acta Autom. Sin. 36, No. 4, 488-498 (2010). MSC: 68T05 68T10 PDF BibTeX XML Cite \textit{B. Liu} and \textit{H. Zhang}, Acta Autom. Sin. 36, No. 4, 488--498 (2010; Zbl 1240.68194) Full Text: DOI
Chui, Charles K.; Wang, Jianzhong Randomized anisotropic transform for nonlinear dimensionality reduction. (English) Zbl 1204.68271 GEM. Int. J. Geomath. 1, No. 1, 23-50 (2010). MSC: 68W20 74N25 62-07 PDF BibTeX XML Cite \textit{C. K. Chui} and \textit{J. Wang}, GEM. Int. J. Geomath. 1, No. 1, 23--50 (2010; Zbl 1204.68271) Full Text: DOI
Liu, Yang; Liu, Yan; Chan, Keith C. C. Nonlinear dimensionality reduction with hybrid distance for trajectory representation of dynamic texture. (English) Zbl 1194.94112 Signal Process. 90, No. 8, 2375-2395 (2010). MSC: 94A12 PDF BibTeX XML Cite \textit{Y. Liu} et al., Signal Process. 90, No. 8, 2375--2395 (2010; Zbl 1194.94112) Full Text: DOI
Yin, Hujun; Huang, Weilin Adaptive nonlinear manifolds and their applications to pattern recognition. (English) Zbl 1205.68354 Inf. Sci. 180, No. 14, 2649-2662 (2010). MSC: 68T10 68U05 PDF BibTeX XML Cite \textit{H. Yin} and \textit{W. Huang}, Inf. Sci. 180, No. 14, 2649--2662 (2010; Zbl 1205.68354) Full Text: DOI Link
Zhu, Rong; Yao, Min Image feature optimization based on nonlinear dimensionality reduction. (English) Zbl 1211.68493 J. Zhejiang Univ., Sci. A 10, No. 12, 1720-1737 (2009). MSC: 68U10 68T05 PDF BibTeX XML Cite \textit{R. Zhu} and \textit{M. Yao}, J. Zhejiang Univ., Sci. A 10, No. 12, 1720--1737 (2009; Zbl 1211.68493) Full Text: DOI
Pan, Yaozhang; Ge, Shuzhi Sam; Mamun, Abdullah Al Weighted locally linear embedding for dimension reduction. (English) Zbl 1178.68453 Pattern Recognition 42, No. 5, 798-811 (2009). MSC: 68T05 68T10 PDF BibTeX XML Cite \textit{Y. Pan} et al., Pattern Recognition 42, No. 5, 798--811 (2009; Zbl 1178.68453) Full Text: DOI
Fan, Mingyu; Qiao, Hong; Zhang, Bo Intrinsic dimension estimation of manifolds by incising balls. (English) Zbl 1162.68405 Pattern Recognition 42, No. 5, 780-787 (2009). MSC: 68P05 68T10 PDF BibTeX XML Cite \textit{M. Fan} et al., Pattern Recognition 42, No. 5, 780--787 (2009; Zbl 1162.68405) Full Text: DOI
Jones, Peter W.; Maggioni, Mauro; Schul, Raanan Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels. (English) Zbl 1215.58012 Proc. Natl. Acad. Sci. USA 105, No. 6, 1803-1808 (2008). MSC: 58J35 58J50 PDF BibTeX XML Cite \textit{P. W. Jones} et al., Proc. Natl. Acad. Sci. USA 105, No. 6, 1803--1808 (2008; Zbl 1215.58012) Full Text: DOI
Meng, Deyu; Gu, Nannan; Xu, Zongben; Leung, Yee Nonlinear dimensionality reduction for data on manifold with rings. (Chinese. English summary) Zbl 1199.68225 J. Softw. 19, No. 11, 2908-2920 (2008). MSC: 68T05 68P05 PDF BibTeX XML Cite \textit{D. Meng} et al., J. Softw. 19, No. 11, 2908--2920 (2008; Zbl 1199.68225)
Gu, Siyang; Tu, Teng-Tao New face recognition algorithm based on nonlinear dimensionality reduction. (Chinese. English summary) Zbl 1175.94016 J. Comput. Appl. 28, No. 8, 2030-2032 (2008). MSC: 94A08 68U10 68T10 PDF BibTeX XML Cite \textit{S. Gu} and \textit{T.-T. Tu}, J. Comput. Appl. 28, No. 8, 2030--2032 (2008; Zbl 1175.94016) Full Text: DOI
Capobianco, Enrico Dimensionality reduction and greedy learning of convoluted stochastic dynamics. (English) Zbl 1156.91431 Nonlinear Anal., Real World Appl. 9, No. 5, 1928-1941 (2008). MSC: 91B62 42C40 62G08 PDF BibTeX XML Cite \textit{E. Capobianco}, Nonlinear Anal., Real World Appl. 9, No. 5, 1928--1941 (2008; Zbl 1156.91431) Full Text: DOI
Yu, Xuelian; Wang, Xuegang; Liu, Benyong Supervised kernel neighborhood preserving projections for radar target recognition. (English) Zbl 1151.94433 Signal Process. 88, No. 9, 2335-2339 (2008). MSC: 94A12 PDF BibTeX XML Cite \textit{X. Yu} et al., Signal Process. 88, No. 9, 2335--2339 (2008; Zbl 1151.94433) Full Text: DOI
Martínez-Montes, Eduardo; Sánchez-Bornot, José M.; Valdés-Sosa, Pedro A. Penalized PARAFAC analysis of spontaneous EEG recordings. (English) Zbl 1293.62143 Stat. Sin. 18, No. 4, 1449-1464 (2008). MSC: 62J02 62H11 62H25 62P10 92C55 94A12 PDF BibTeX XML Cite \textit{E. Martínez-Montes} et al., Stat. Sin. 18, No. 4, 1449--1464 (2008; Zbl 1293.62143) Full Text: Link
Wang, Na; Li, Xia Nonlinear dimensionality reduction using robust Isomap. (English) Zbl 1150.68485 J. Shenzhen Univ., Sci. Eng. 24, No. 3, 276-280 (2007). MSC: 68T30 68T05 PDF BibTeX XML Cite \textit{N. Wang} and \textit{X. Li}, J. Shenzhen Univ., Sci. Eng. 24, No. 3, 276--280 (2007; Zbl 1150.68485) Full Text: DOI
Li, Chi-Kwong; Li, Ren-Cang; Ye, Qiang Eigenvalues of an alignment matrix in nonlinear manifold learning. (English) Zbl 1135.65019 Commun. Math. Sci. 5, No. 2, 313-329 (2007). MSC: 65F15 15A42 PDF BibTeX XML Cite \textit{C.-K. Li} et al., Commun. Math. Sci. 5, No. 2, 313--329 (2007; Zbl 1135.65019) Full Text: DOI Euclid
Zhu, Liping; Yu, Zhou On spline approximation of sliced inverse regression. (English) Zbl 1125.62036 Sci. China, Ser. A 50, No. 9, 1289-1302 (2007). MSC: 62G08 62G20 62H12 62J02 PDF BibTeX XML Cite \textit{L. Zhu} and \textit{Z. Yu}, Sci. China, Ser. A 50, No. 9, 1289--1302 (2007; Zbl 1125.62036) Full Text: DOI
Choi, Heeyoul; Choi, Seungjin Robust kernel Isomap. (English) Zbl 1118.68188 Pattern Recognition 40, No. 3, 853-862 (2007). MSC: 68W05 68T05 PDF BibTeX XML Cite \textit{H. Choi} and \textit{S. Choi}, Pattern Recognition 40, No. 3, 853--862 (2007; Zbl 1118.68188) Full Text: DOI
Dai, Guang; Yeung, Dit-Yan; Qian, Yun-Tao Face recognition using a kernel fractional-step discriminant analysis algorithm. (English) Zbl 1103.68752 Pattern Recognition 40, No. 1, 229-243 (2007). MSC: 68T10 PDF BibTeX XML Cite \textit{G. Dai} et al., Pattern Recognition 40, No. 1, 229--243 (2007; Zbl 1103.68752) Full Text: DOI
Akkucuk, Ulas; Carroll, J. Douglas PARAMAP vs. Isomap: a comparison of two nonlinear mapping algorithms. (English) Zbl 1336.62167 J. Classif. 23, No. 2, 221-254 (2006). MSC: 62H30 PDF BibTeX XML Cite \textit{U. Akkucuk} and \textit{J. D. Carroll}, J. Classif. 23, No. 2, 221--254 (2006; Zbl 1336.62167) Full Text: DOI
Leith, D. J.; Leithead, W. E.; Murray-Smith, R. Inference of disjoint linear and nonlinear sub-domains of a nonlinear mapping. (English) Zbl 1137.93312 Automatica 42, No. 5, 849-858 (2006). MSC: 93B10 93B30 93B20 PDF BibTeX XML Cite \textit{D. J. Leith} et al., Automatica 42, No. 5, 849--858 (2006; Zbl 1137.93312) Full Text: DOI Link
Zhao, Deli Formulating LLE using alignment technique. (English) Zbl 1102.68644 Pattern Recognition 39, No. 11, 2233-2235 (2006). MSC: 68T10 PDF BibTeX XML Cite \textit{D. Zhao}, Pattern Recognition 39, No. 11, 2233--2235 (2006; Zbl 1102.68644) Full Text: DOI
Venna, Jarkko; Kaski, Samuel Local multidimensional scaling. (English) Zbl 1102.68601 Neural Netw. 19, No. 6-7, 889-899 (2006). MSC: 68T05 PDF BibTeX XML Cite \textit{J. Venna} and \textit{S. Kaski}, Neural Netw. 19, No. 6--7, 889--899 (2006; Zbl 1102.68601) Full Text: DOI
Chang, Hong; Yeung, Dit-Yan Robust locally linear embedding. (English) Zbl 1096.68713 Pattern Recognition 39, No. 6, 1053-1065 (2006). MSC: 68T10 PDF BibTeX XML Cite \textit{H. Chang} and \textit{D.-Y. Yeung}, Pattern Recognition 39, No. 6, 1053--1065 (2006; Zbl 1096.68713) Full Text: DOI
Wang, Meng; Yang, Jie; Xu, Zhi-Jie; Chou, Kuo-Chen SLLE for predicting membrane protein types. (English) Zbl 1442.92118 J. Theor. Biol. 232, No. 1, 7-15 (2005). MSC: 92D20 PDF BibTeX XML Cite \textit{M. Wang} et al., J. Theor. Biol. 232, No. 1, 7--15 (2005; Zbl 1442.92118) Full Text: DOI
Zhang, Zhenyue; Zha, Hongyuan Linear low-rank approximation and nonlinear dimensionality reduction. (English) Zbl 1117.65303 Sci. China, Ser. A 47, No. 6, 908-920 (2004). MSC: 65C60 62-07 65F20 PDF BibTeX XML Cite \textit{Z. Zhang} and \textit{H. Zha}, Sci. China, Ser. A 47, No. 6, 908--920 (2004; Zbl 1117.65303)
Zhang, Zhenyue; Zha, Hongyuan Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. (English) Zbl 1077.65042 SIAM J. Sci. Comput. 26, No. 1, 313-338 (2004). MSC: 65F30 65F15 65F50 PDF BibTeX XML Cite \textit{Z. Zhang} and \textit{H. Zha}, SIAM J. Sci. Comput. 26, No. 1, 313--338 (2004; Zbl 1077.65042) Full Text: DOI
Zhang, Changshui; Wang, Jun; Zhao, Nanyuan; Zhang, David Reconstruction and analysis of multi-pose face images based on nonlinear dimensionality reduction. (English) Zbl 1059.68124 Pattern Recognition 37, No. 2, 325-336 (2004). MSC: 68T10 PDF BibTeX XML Cite \textit{C. Zhang} et al., Pattern Recognition 37, No. 2, 325--336 (2004; Zbl 1059.68124) Full Text: DOI
Nicoleris, Theodoros; Yatracos, Yannis G. Rates of convergence of estimates, Kolmogorov’s entropy and the dimensionality reduction principle in regression. (English) Zbl 0909.62063 Ann. Stat. 25, No. 6, 2493-2511 (1997). Reviewer: Oleksandr Kukush (Kyiv) MSC: 62J02 62G20 62G05 62G30 PDF BibTeX XML Cite \textit{T. Nicoleris} and \textit{Y. G. Yatracos}, Ann. Stat. 25, No. 6, 2493--2511 (1997; Zbl 0909.62063) Full Text: DOI
Chaudhuri, Probal; Doksum, Kjell; Samarov, Alexander On average derivative quantile regression. (English) Zbl 0898.62082 Ann. Stat. 25, No. 2, 715-744 (1997). MSC: 62J02 62G20 62G99 62G05 PDF BibTeX XML Cite \textit{P. Chaudhuri} et al., Ann. Stat. 25, No. 2, 715--744 (1997; Zbl 0898.62082) Full Text: DOI
Chaudhuri, Probal; Doksum, Kjell; Samarov, Alexander Nonparametric estimation of global functionals of conditional quantiles. (English) Zbl 0845.62031 Rieder, Helmut (ed.), Robust statistics, data analysis, and computer intensive methods. In honor of Peter Huber’s 60th birthday. New York, NY: Springer-Verlag. Lect. Notes Stat., Springer-Verlag. 109, 63-78 (1996). MSC: 62G07 62J02 62G99 62J20 62G20 PDF BibTeX XML Cite \textit{P. Chaudhuri} et al., in: Robust statistics, data analysis, and computer intensive methods. In honor of Peter Huber's 60th birthday. New York, NY: Springer-Verlag. 63--78 (1996; Zbl 0845.62031)
Richter, Wolf-Dieter A geometric approach to the Gaussian law. (English) Zbl 0842.62038 Mammitzsch, Volker (ed.) et al., Proceedings of the 2nd Gauss symposium. Conference B: Statistical sciences, Munich, Germany, August 2-7, 1993. Berlin: Walter de Gruyter. Symposia Gaussiana. 25-45 (1995). MSC: 62H05 62J02 60F10 60D05 PDF BibTeX XML Cite \textit{W.-D. Richter}, in: Proceedings of the 2nd Gauss symposium. Conference B: Statistical sciences, Munich, Germany, August 2-7, 1993. Berlin: Walter de Gruyter. 25--45 (1995; Zbl 0842.62038)
Chen, Zehua Fitting multivariate regression functions by interaction spline models. (English) Zbl 0783.62029 J. R. Stat. Soc., Ser. B 55, No. 2, 473-491 (1993). MSC: 62G07 62J02 PDF BibTeX XML Cite \textit{Z. Chen}, J. R. Stat. Soc., Ser. B 55, No. 2, 473--491 (1993; Zbl 0783.62029)
Montvilas, Algirdas Mykolas A sequential nonlinear mapping for data analysis. (English) Zbl 0900.62442 Informatica, Vilnius 4, No. 1-2, 61-93 (1993). MSC: 62L10 62-07 PDF BibTeX XML Cite \textit{A. M. Montvilas}, Informatica, Vilnius 4, No. 1--2, 61--93 (1993; Zbl 0900.62442)