Theoretical insights on the pre-image resolution in machine learning
While many nonlinear pattern recognition and data mining tasks rely on embedding the data into a latent space, one often needs to extract the patterns in the input space. Estimating the inverse of the nonlinear embedding is the so-called pre-image problem. Several strategies have been proposed to ad...
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| Published in: | Pattern recognition Vol. 156; p. 110800 |
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| Format: | Journal Article |
| Language: | English |
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01.12.2024
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| ISSN: | 0031-3203 |
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| Abstract | While many nonlinear pattern recognition and data mining tasks rely on embedding the data into a latent space, one often needs to extract the patterns in the input space. Estimating the inverse of the nonlinear embedding is the so-called pre-image problem. Several strategies have been proposed to address the estimation of the pre-image; However, there are no theoretical results so far to understand the pre-image problem and its resolution. In this paper, we provide theoretical underpinnings of the resolution of the pre-image problem in Machine Learning. These theoretical results are on the gradient descent optimization, the fixed-point iteration algorithm and Newton’s method. We provide sufficient conditions on the convexity/nonconvexity of the pre-image problem. Moreover, we show that the fixed-point iteration is a Newton update and prove that it is a Majorize-Minimization (MM) algorithm where the surrogate function is a quadratic function. These theoretical results are derived for the wide classes of radial kernels and projective kernels. We also provide other insights by connecting the resolution of this problem to the gradient density estimation problem with the so-called mean shift algorithm.
•Solid foundations on the resolution of the pre-image problem in Machine Learning•Relationship between the fixed-point iteration technique and Newton’s method•Fixed-point iteration is a Majorize-Minimization algorithm•General theoretical results for the wide classes of radial and projective kernels |
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| AbstractList | While many nonlinear pattern recognition and data mining tasks rely on embedding the data into a latent space, one often needs to extract the patterns in the input space. Estimating the inverse of the nonlinear embedding is the so-called pre-image problem. Several strategies have been proposed to address the estimation of the pre-image; However, there are no theoretical results so far to understand the pre-image problem and its resolution. In this paper, we provide theoretical underpinnings of the resolution of the pre-image problem in Machine Learning. These theoretical results are on the gradient descent optimization, the fixed-point iteration algorithm and Newton's method. We provide sufficient conditions on the convexity/nonconvexity of the pre-image problem. Moreover, we show that the fixed-point iteration is a Newton update and prove that it is a Majorize-Minimization (MM) algorithm where the surrogate function is a quadratic function. These theoretical results are derived for the wide classes of radial kernels and projective kernels. We also provide other insights by connecting the resolution of this problem to the gradient density estimation problem with the so-called mean shift algorithm. While many nonlinear pattern recognition and data mining tasks rely on embedding the data into a latent space, one often needs to extract the patterns in the input space. Estimating the inverse of the nonlinear embedding is the so-called pre-image problem. Several strategies have been proposed to address the estimation of the pre-image; However, there are no theoretical results so far to understand the pre-image problem and its resolution. In this paper, we provide theoretical underpinnings of the resolution of the pre-image problem in Machine Learning. These theoretical results are on the gradient descent optimization, the fixed-point iteration algorithm and Newton’s method. We provide sufficient conditions on the convexity/nonconvexity of the pre-image problem. Moreover, we show that the fixed-point iteration is a Newton update and prove that it is a Majorize-Minimization (MM) algorithm where the surrogate function is a quadratic function. These theoretical results are derived for the wide classes of radial kernels and projective kernels. We also provide other insights by connecting the resolution of this problem to the gradient density estimation problem with the so-called mean shift algorithm. •Solid foundations on the resolution of the pre-image problem in Machine Learning•Relationship between the fixed-point iteration technique and Newton’s method•Fixed-point iteration is a Majorize-Minimization algorithm•General theoretical results for the wide classes of radial and projective kernels |
| ArticleNumber | 110800 |
| Author | Honeine, Paul |
| Author_xml | – sequence: 1 givenname: Paul surname: Honeine fullname: Honeine, Paul email: paul.honeine@univ-rouen.fr organization: Univ Rouen Normandie, INSA Rouen Normandie, Université Le Havre Normandie, Normandie Univ, LITIS UR 4108, F-76000 Rouen, France |
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| Keywords | Majorize-minimization algorithm Newton’s method Fixed-point iteration Pattern recognition Machine learning Pre-image problem Pattern Recognition Newton's Method Fixed-point Iteration Majorize-Minimization Algorithm Machine Learning Pre-image Problem |
| Language | English |
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| References | Jia, Gaüzère, Honeine (b7) 2021 Arias-Castro, Mason, Pelletier (b35) 2016; 17 Fan, Chow (b5) 2018; 77 Aliyari Ghassabeh (b34) 2013; 34 C.S. Ong, X. Mary, S. Canu, A.J. Smola, Learning with non-positive kernels, in: Proc. 21st International Conference on Machine Learning, 2004, p. 81. Zhu, Honeine (b3) 2017; 131 Fukunaga, Hostetler (b30) 1975; 21 Li, Hu, Wu (b32) 2007; 40 S. Mika, B. Schölkopf, A. Smola, K.R. Müller, M. Scholz, G. Rätsch, Kernel PCA and de-noising in feature spaces, in: Proc. Conf. on Advances in Neural Information Processing Systems II, 1999, pp. 536–542. Honeine, Richard (b1) 2011; 28 Cheng (b20) 1995; 17 Tran Thi Phuong, Douzal, Yazdi, Honeine, Gallinari (b6) 2020; 286 Salazar, Rios, Aceros, Flórez-Vargas, Valencia (b4) 2021; 9 vor der Brück, Eger, Mehler (b18) 2015 Pandey, Schreurs, Suykens (b12) 2021; 135 Schölkopf (b17) 2000; 13 Celikkanat, Shen, Malliaros (b9) 2022 Fashing, Tomasi (b29) 2005; 27 Chen, Genovese, Wasserman (b39) 2014 Carreira-Perpinan (b27) 2000; 22 Pandey, De Meulemeester, De Moor, Suykens (b11) 2023; 554 Yamasaki, Tanaka (b37) 2024 Shankar, Fang, Guo, Fridovich-Keil, Schmidt, Ragan-Kelley, Recht (b13) 2020 He, He, Shi, Huang, Suykens (b19) 2023 Tax, Juszczak (b25) 2003; 17 Golub, Van Loan (b26) 1996 P. Esser, M. Fleissner, D. Ghoshdastidar, Non-parametric representation learning with kernels, in: Proceedings of the AAAI Conference on Artificial Intelligence, 2024, pp. 11910–11918. Yamasaki, Tanaka (b36) 2020; 42 Aliyari Ghassabeh (b21) 2015; 135 El Ahmad, Brogat-Motte, Laforgue, d’Alché Buc (b10) 2024 Cucker, Smale (b22) 2002; 39 Burges (b23) 1999 Comaniciu, Meer (b31) 2002; 24 Unser (b16) 2021; 21 M. Botsch, J.A. Nossek, Construction of interpretable radial basis function classifiers based on the random forest kernel, in: 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence), 2008, pp. 220–227. Schölkopf, Mika, Burges, Knirsch, Muller, Ratsch, Smola (b2) 1999; 10 Abedsoltan, Belkin, Pandit (b15) 2023 L. Jia, X. Ning, B. Gaüzère, P. Honeine, K. Riesen, Bridging distinct spaces in graph-based machine learning, in: M. Blumenstein, H. Lu, W. Yang, S.B. Cho (Eds.), Proceedings of the 7th Asian Conference on Pattern Recognition, ACPR, Kitakyushu, Japan, 2023. Carreira-Perpinan (b33) 2007; 29 Kwok, Tsang (b40) 2003 Yamasaki (10.1016/j.patcog.2024.110800_b36) 2020; 42 Cucker (10.1016/j.patcog.2024.110800_b22) 2002; 39 Li (10.1016/j.patcog.2024.110800_b32) 2007; 40 Honeine (10.1016/j.patcog.2024.110800_b1) 2011; 28 Schölkopf (10.1016/j.patcog.2024.110800_b2) 1999; 10 He (10.1016/j.patcog.2024.110800_b19) 2023 vor der Brück (10.1016/j.patcog.2024.110800_b18) 2015 Cheng (10.1016/j.patcog.2024.110800_b20) 1995; 17 Burges (10.1016/j.patcog.2024.110800_b23) 1999 Comaniciu (10.1016/j.patcog.2024.110800_b31) 2002; 24 Zhu (10.1016/j.patcog.2024.110800_b3) 2017; 131 10.1016/j.patcog.2024.110800_b38 Unser (10.1016/j.patcog.2024.110800_b16) 2021; 21 Kwok (10.1016/j.patcog.2024.110800_b40) 2003 Carreira-Perpinan (10.1016/j.patcog.2024.110800_b27) 2000; 22 Carreira-Perpinan (10.1016/j.patcog.2024.110800_b33) 2007; 29 Pandey (10.1016/j.patcog.2024.110800_b11) 2023; 554 10.1016/j.patcog.2024.110800_b8 Aliyari Ghassabeh (10.1016/j.patcog.2024.110800_b21) 2015; 135 10.1016/j.patcog.2024.110800_b14 Fukunaga (10.1016/j.patcog.2024.110800_b30) 1975; 21 Pandey (10.1016/j.patcog.2024.110800_b12) 2021; 135 Aliyari Ghassabeh (10.1016/j.patcog.2024.110800_b34) 2013; 34 Golub (10.1016/j.patcog.2024.110800_b26) 1996 Jia (10.1016/j.patcog.2024.110800_b7) 2021 Shankar (10.1016/j.patcog.2024.110800_b13) 2020 Yamasaki (10.1016/j.patcog.2024.110800_b37) 2024 Tax (10.1016/j.patcog.2024.110800_b25) 2003; 17 Chen (10.1016/j.patcog.2024.110800_b39) 2014 Fashing (10.1016/j.patcog.2024.110800_b29) 2005; 27 Celikkanat (10.1016/j.patcog.2024.110800_b9) 2022 Tran Thi Phuong (10.1016/j.patcog.2024.110800_b6) 2020; 286 10.1016/j.patcog.2024.110800_b28 Arias-Castro (10.1016/j.patcog.2024.110800_b35) 2016; 17 Salazar (10.1016/j.patcog.2024.110800_b4) 2021; 9 El Ahmad (10.1016/j.patcog.2024.110800_b10) 2024 Abedsoltan (10.1016/j.patcog.2024.110800_b15) 2023 Schölkopf (10.1016/j.patcog.2024.110800_b17) 2000; 13 Fan (10.1016/j.patcog.2024.110800_b5) 2018; 77 10.1016/j.patcog.2024.110800_b24 |
| References_xml | – volume: 286 year: 2020 ident: b6 article-title: Interpretable time series kernel analytics by pre-image estimation publication-title: Artificial Intelligence – reference: P. Esser, M. Fleissner, D. Ghoshdastidar, Non-parametric representation learning with kernels, in: Proceedings of the AAAI Conference on Artificial Intelligence, 2024, pp. 11910–11918. – reference: S. Mika, B. Schölkopf, A. Smola, K.R. Müller, M. Scholz, G. Rätsch, Kernel PCA and de-noising in feature spaces, in: Proc. Conf. on Advances in Neural Information Processing Systems II, 1999, pp. 536–542. – volume: 10 start-page: 1000 year: 1999 end-page: 1017 ident: b2 article-title: Input space versus feature space in kernel-based methods publication-title: IEEE Trans. Neural Netw. – start-page: 109 year: 2024 end-page: 117 ident: b10 article-title: Sketch in, sketch out: Accelerating both learning and inference for structured prediction with kernels publication-title: Proc. of the 27th International Conference on Artificial Intelligence and Statistics – volume: 554 year: 2023 ident: b11 article-title: Multi-view kernel PCA for time series forecasting publication-title: Neurocomputing – volume: 17 start-page: 333 year: 2003 end-page: 347 ident: b25 article-title: Kernel whitening for one-class classification publication-title: Int. J. Pattern Recognit. Artif. Intell. – volume: 24 start-page: 603 year: 2002 end-page: 619 ident: b31 article-title: Mean shift: a robust approach toward feature space analysis publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – reference: C.S. Ong, X. Mary, S. Canu, A.J. Smola, Learning with non-positive kernels, in: Proc. 21st International Conference on Machine Learning, 2004, p. 81. – start-page: 408 year: 2003 end-page: 415 ident: b40 article-title: The pre-image problem in kernel methods publication-title: Proc. 20th International Conference on Machine Learning – year: 1996 ident: b26 article-title: Matrix Computations – reference: M. Botsch, J.A. Nossek, Construction of interpretable radial basis function classifiers based on the random forest kernel, in: 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence), 2008, pp. 220–227. – start-page: 61 year: 2023 end-page: 78 ident: b15 article-title: Toward large kernel models publication-title: International Conference on Machine Learning – volume: 21 start-page: 32 year: 1975 end-page: 40 ident: b30 article-title: The estimation of the gradient of a density function, with applications in pattern recognition publication-title: IEEE Trans. Inform. Theory – volume: 131 start-page: 143 year: 2017 end-page: 153 ident: b3 article-title: Online kernel nonnegative matrix factorization publication-title: Signal Process. – volume: 34 start-page: 1423 year: 2013 end-page: 1427 ident: b34 article-title: On the convergence of the mean shift algorithm in the one-dimensional space publication-title: Pattern Recognit. Lett. – volume: 135 start-page: 177 year: 2021 end-page: 191 ident: b12 article-title: Generative restricted kernel machines: a framework for multi-view generation and disentangled feature learning publication-title: Neural Netw. – volume: 29 start-page: 767 year: 2007 end-page: 776 ident: b33 article-title: Gaussian mean-shift is an EM algorithm publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 135 start-page: 1 year: 2015 end-page: 10 ident: b21 article-title: A sufficient condition for the convergence of the mean shift algorithm with Gaussian kernel publication-title: J. Multivariate Anal. – volume: 27 start-page: 471 year: 2005 end-page: 474 ident: b29 article-title: Mean shift is a bound optimization publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – year: 2022 ident: b9 article-title: Multiple kernel representation learning on networks publication-title: IEEE Trans. Knowl. Data Eng. – volume: 28 start-page: 77 year: 2011 end-page: 88 ident: b1 article-title: Preimage problem in kernel-based machine learning publication-title: IEEE Signal Process. Mag. – volume: 21 start-page: 941 year: 2021 end-page: 960 ident: b16 article-title: A unifying representer theorem for inverse problems and machine learning publication-title: Found. Comput. Math. – volume: 17 start-page: 790 year: 1995 end-page: 799 ident: b20 article-title: Mean shift, mode seeking, and clustering publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – start-page: 216 year: 2021 end-page: 226 ident: b7 article-title: A graph pre-image method based on graph edit distances publication-title: Proc. IAPR Joint International Workshops on Statistical Techniques in Pattern Recognition (SPR) and Structural and Syntactic Pattern Recognition – volume: 42 start-page: 2273 year: 2020 end-page: 2286 ident: b36 article-title: Properties of mean shift publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – year: 2014 ident: b39 article-title: Generalized mode and ridge estimation – volume: 9 start-page: 101863 year: 2021 end-page: 101875 ident: b4 article-title: Kernel joint non-negative matrix factorization for genomic data publication-title: IEEE Access – volume: 39 start-page: 1 year: 2002 end-page: 49 ident: b22 article-title: On the mathematical foundations of learning publication-title: Bull. Amer. Math. Soc. – volume: 17 start-page: 1 year: 2016 end-page: 28 ident: b35 article-title: On the estimation of the gradient lines of a density and the consistency of the mean-shift algorithm publication-title: J. Mach. Learn. Res. – start-page: 89 year: 1999 end-page: 116 ident: b23 article-title: Geometry and invariance in kernel based methods publication-title: Advances in Kernel Methods: Support Vector Learning – start-page: 1 year: 2023 end-page: 12 ident: b19 article-title: Learning with asymmetric kernels: Least squares and feature interpretation publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 22 start-page: 1318 year: 2000 end-page: 1323 ident: b27 article-title: Mode-finding for mixtures of gaussian distributions publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – start-page: 103 year: 2015 end-page: 108 ident: b18 article-title: Complex decomposition of the negative distance kernel publication-title: 2015 IEEE 14th International Conference on Machine Learning and Applications – volume: 40 start-page: 1756 year: 2007 end-page: 1762 ident: b32 article-title: A note on the convergence of the mean shift publication-title: Pattern Recognit. – volume: 77 start-page: 378 year: 2018 end-page: 394 ident: b5 article-title: Non-linear matrix completion publication-title: Pattern Recognit. – start-page: 1 year: 2020 end-page: 10 ident: b13 article-title: Neural kernels without tangents publication-title: Proceedings of the 37th International Conference on Machine Learning – volume: 13 year: 2000 ident: b17 article-title: The kernel trick for distances publication-title: Adv. Neural Inf. Process. Syst. – reference: L. Jia, X. Ning, B. Gaüzère, P. Honeine, K. Riesen, Bridging distinct spaces in graph-based machine learning, in: M. Blumenstein, H. Lu, W. Yang, S.B. Cho (Eds.), Proceedings of the 7th Asian Conference on Pattern Recognition, ACPR, Kitakyushu, Japan, 2023. – start-page: 1 year: 2024 end-page: 11 ident: b37 article-title: Convergence analysis of mean shift publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 77 start-page: 378 year: 2018 ident: 10.1016/j.patcog.2024.110800_b5 article-title: Non-linear matrix completion publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2017.10.014 – volume: 22 start-page: 1318 year: 2000 ident: 10.1016/j.patcog.2024.110800_b27 article-title: Mode-finding for mixtures of gaussian distributions publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/34.888716 – volume: 21 start-page: 941 year: 2021 ident: 10.1016/j.patcog.2024.110800_b16 article-title: A unifying representer theorem for inverse problems and machine learning publication-title: Found. Comput. Math. doi: 10.1007/s10208-020-09472-x – start-page: 109 year: 2024 ident: 10.1016/j.patcog.2024.110800_b10 article-title: Sketch in, sketch out: Accelerating both learning and inference for structured prediction with kernels – volume: 40 start-page: 1756 year: 2007 ident: 10.1016/j.patcog.2024.110800_b32 article-title: A note on the convergence of the mean shift publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2006.10.016 – volume: 42 start-page: 2273 year: 2020 ident: 10.1016/j.patcog.2024.110800_b36 article-title: Properties of mean shift publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/TPAMI.2019.2913640 – volume: 29 start-page: 767 year: 2007 ident: 10.1016/j.patcog.2024.110800_b33 article-title: Gaussian mean-shift is an EM algorithm publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/TPAMI.2007.1057 – volume: 17 start-page: 1 year: 2016 ident: 10.1016/j.patcog.2024.110800_b35 article-title: On the estimation of the gradient lines of a density and the consistency of the mean-shift algorithm publication-title: J. Mach. Learn. Res. – ident: 10.1016/j.patcog.2024.110800_b38 doi: 10.1145/1015330.1015443 – volume: 28 start-page: 77 year: 2011 ident: 10.1016/j.patcog.2024.110800_b1 article-title: Preimage problem in kernel-based machine learning publication-title: IEEE Signal Process. Mag. doi: 10.1109/MSP.2010.939747 – year: 2022 ident: 10.1016/j.patcog.2024.110800_b9 article-title: Multiple kernel representation learning on networks publication-title: IEEE Trans. Knowl. Data Eng. doi: 10.1109/TKDE.2022.3172048 – volume: 17 start-page: 333 year: 2003 ident: 10.1016/j.patcog.2024.110800_b25 article-title: Kernel whitening for one-class classification publication-title: Int. J. Pattern Recognit. Artif. Intell. doi: 10.1142/S021800140300240X – start-page: 216 year: 2021 ident: 10.1016/j.patcog.2024.110800_b7 article-title: A graph pre-image method based on graph edit distances – volume: 17 start-page: 790 year: 1995 ident: 10.1016/j.patcog.2024.110800_b20 article-title: Mean shift, mode seeking, and clustering publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/34.400568 – ident: 10.1016/j.patcog.2024.110800_b8 doi: 10.1007/978-3-031-47637-2_1 – start-page: 1 year: 2020 ident: 10.1016/j.patcog.2024.110800_b13 article-title: Neural kernels without tangents – start-page: 61 year: 2023 ident: 10.1016/j.patcog.2024.110800_b15 article-title: Toward large kernel models – volume: 34 start-page: 1423 year: 2013 ident: 10.1016/j.patcog.2024.110800_b34 article-title: On the convergence of the mean shift algorithm in the one-dimensional space publication-title: Pattern Recognit. Lett. doi: 10.1016/j.patrec.2013.05.004 – start-page: 1 year: 2024 ident: 10.1016/j.patcog.2024.110800_b37 article-title: Convergence analysis of mean shift publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/TPAMI.2024.3385920 – ident: 10.1016/j.patcog.2024.110800_b14 doi: 10.1609/aaai.v38i11.29077 – volume: 21 start-page: 32 year: 1975 ident: 10.1016/j.patcog.2024.110800_b30 article-title: The estimation of the gradient of a density function, with applications in pattern recognition publication-title: IEEE Trans. Inform. Theory doi: 10.1109/TIT.1975.1055330 – start-page: 103 year: 2015 ident: 10.1016/j.patcog.2024.110800_b18 article-title: Complex decomposition of the negative distance kernel – volume: 554 year: 2023 ident: 10.1016/j.patcog.2024.110800_b11 article-title: Multi-view kernel PCA for time series forecasting publication-title: Neurocomputing doi: 10.1016/j.neucom.2023.126639 – year: 1996 ident: 10.1016/j.patcog.2024.110800_b26 – volume: 10 start-page: 1000 year: 1999 ident: 10.1016/j.patcog.2024.110800_b2 article-title: Input space versus feature space in kernel-based methods publication-title: IEEE Trans. Neural Netw. doi: 10.1109/72.788641 – start-page: 408 year: 2003 ident: 10.1016/j.patcog.2024.110800_b40 article-title: The pre-image problem in kernel methods – volume: 286 year: 2020 ident: 10.1016/j.patcog.2024.110800_b6 article-title: Interpretable time series kernel analytics by pre-image estimation publication-title: Artificial Intelligence – start-page: 89 year: 1999 ident: 10.1016/j.patcog.2024.110800_b23 article-title: Geometry and invariance in kernel based methods – volume: 13 year: 2000 ident: 10.1016/j.patcog.2024.110800_b17 article-title: The kernel trick for distances publication-title: Adv. Neural Inf. Process. Syst. – volume: 27 start-page: 471 year: 2005 ident: 10.1016/j.patcog.2024.110800_b29 article-title: Mean shift is a bound optimization publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/TPAMI.2005.59 – volume: 24 start-page: 603 year: 2002 ident: 10.1016/j.patcog.2024.110800_b31 article-title: Mean shift: a robust approach toward feature space analysis publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/34.1000236 – volume: 9 start-page: 101863 year: 2021 ident: 10.1016/j.patcog.2024.110800_b4 article-title: Kernel joint non-negative matrix factorization for genomic data publication-title: IEEE Access doi: 10.1109/ACCESS.2021.3096801 – volume: 39 start-page: 1 year: 2002 ident: 10.1016/j.patcog.2024.110800_b22 article-title: On the mathematical foundations of learning publication-title: Bull. Amer. Math. Soc. doi: 10.1090/S0273-0979-01-00923-5 – ident: 10.1016/j.patcog.2024.110800_b28 doi: 10.1109/IJCNN.2008.4633793 – start-page: 1 year: 2023 ident: 10.1016/j.patcog.2024.110800_b19 article-title: Learning with asymmetric kernels: Least squares and feature interpretation publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 135 start-page: 1 year: 2015 ident: 10.1016/j.patcog.2024.110800_b21 article-title: A sufficient condition for the convergence of the mean shift algorithm with Gaussian kernel publication-title: J. Multivariate Anal. doi: 10.1016/j.jmva.2014.11.009 – ident: 10.1016/j.patcog.2024.110800_b24 – year: 2014 ident: 10.1016/j.patcog.2024.110800_b39 – volume: 131 start-page: 143 year: 2017 ident: 10.1016/j.patcog.2024.110800_b3 article-title: Online kernel nonnegative matrix factorization publication-title: Signal Process. doi: 10.1016/j.sigpro.2016.08.011 – volume: 135 start-page: 177 year: 2021 ident: 10.1016/j.patcog.2024.110800_b12 article-title: Generative restricted kernel machines: a framework for multi-view generation and disentangled feature learning publication-title: Neural Netw. doi: 10.1016/j.neunet.2020.12.010 |
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