Gaussian mixture models in Hilbert spaces via kernel methods
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909021453156352 |
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| author | López-Montero, Daniel Álvarez-López, Antonio Matabuena, Marcos |
| author_facet | López-Montero, Daniel Álvarez-López, Antonio Matabuena, Marcos |
| contents | Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings, characterizing probability measures, for example, through densities, can be ill-defined or technically challenging. Motivated by clustering applications, we propose a Gaussian mixture framework for Hilbert-space-valued data based on kernel mean embeddings and develop efficient optimization algorithms for estimation. We establish theoretical guarantees showing that the proposed algorithm is well defined and that the model yields a dense class of approximations in infinite-dimensional spaces. We evaluate the framework through extensive experiments on diverse structures and data geometries, including $L^2$-functional data and random graphs in Laplacian spaces arising in modern medical applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05996 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gaussian mixture models in Hilbert spaces via kernel methods López-Montero, Daniel Álvarez-López, Antonio Matabuena, Marcos Machine Learning 62H30 (Primary), 62R10, 60B11, 28C20, 62R20 (Secondary) Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings, characterizing probability measures, for example, through densities, can be ill-defined or technically challenging. Motivated by clustering applications, we propose a Gaussian mixture framework for Hilbert-space-valued data based on kernel mean embeddings and develop efficient optimization algorithms for estimation. We establish theoretical guarantees showing that the proposed algorithm is well defined and that the model yields a dense class of approximations in infinite-dimensional spaces. We evaluate the framework through extensive experiments on diverse structures and data geometries, including $L^2$-functional data and random graphs in Laplacian spaces arising in modern medical applications. |
| title | Gaussian mixture models in Hilbert spaces via kernel methods |
| topic | Machine Learning 62H30 (Primary), 62R10, 60B11, 28C20, 62R20 (Secondary) |
| url | https://arxiv.org/abs/2605.05996 |