Multilinear Kernel Regression and Imputation via Manifold Learning
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916116459159552 |
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| author | Nguyen, Duc Thien Slavakis, Konstantinos |
| author_facet | Nguyen, Duc Thien Slavakis, Konstantinos |
| contents | This paper introduces a novel nonparametric framework for data imputation, coined multilinear kernel regression and imputation via the manifold assumption (MultiL-KRIM). Motivated by manifold learning, MultiL-KRIM models data features as a point cloud located in or close to a user-unknown smooth manifold embedded in a reproducing kernel Hilbert space. Unlike typical manifold-learning routes, which seek low-dimensional patterns via regularizers based on graph-Laplacian matrices, MultiL-KRIM builds instead on the intuitive concept of tangent spaces to manifolds and incorporates collaboration among point-cloud neighbors (regressors) directly into the data-modeling term of the loss function. Multiple kernel functions are allowed to offer robustness and rich approximation properties, while multiple matrix factors offer low-rank modeling, integrate dimensionality reduction, and streamline computations with no need of training data. Two important application domains showcase the functionality of MultiL-KRIM: time-varying-graph-signal (TVGS) recovery, and reconstruction of highly accelerated dynamic-magnetic-resonance-imaging (dMRI) data. Extensive numerical tests on real and synthetic data demonstrate MultiL-KRIM's remarkable speedups over its predecessors, and outperformance over prevalent "shallow" data-imputation techniques, with a more intuitive and explainable pipeline than deep-image-prior methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multilinear Kernel Regression and Imputation via Manifold Learning Nguyen, Duc Thien Slavakis, Konstantinos Signal Processing Machine Learning This paper introduces a novel nonparametric framework for data imputation, coined multilinear kernel regression and imputation via the manifold assumption (MultiL-KRIM). Motivated by manifold learning, MultiL-KRIM models data features as a point cloud located in or close to a user-unknown smooth manifold embedded in a reproducing kernel Hilbert space. Unlike typical manifold-learning routes, which seek low-dimensional patterns via regularizers based on graph-Laplacian matrices, MultiL-KRIM builds instead on the intuitive concept of tangent spaces to manifolds and incorporates collaboration among point-cloud neighbors (regressors) directly into the data-modeling term of the loss function. Multiple kernel functions are allowed to offer robustness and rich approximation properties, while multiple matrix factors offer low-rank modeling, integrate dimensionality reduction, and streamline computations with no need of training data. Two important application domains showcase the functionality of MultiL-KRIM: time-varying-graph-signal (TVGS) recovery, and reconstruction of highly accelerated dynamic-magnetic-resonance-imaging (dMRI) data. Extensive numerical tests on real and synthetic data demonstrate MultiL-KRIM's remarkable speedups over its predecessors, and outperformance over prevalent "shallow" data-imputation techniques, with a more intuitive and explainable pipeline than deep-image-prior methods. |
| title | Multilinear Kernel Regression and Imputation via Manifold Learning |
| topic | Signal Processing Machine Learning |
| url | https://arxiv.org/abs/2402.03648 |