← 研踪 PaperTrailarXiv:2605.05996 · v2
Gaussian mixture models in Hilbert spaces via kernel methods
首次提交 2026-05-07 18:48
版本更新 2026-11-10 22:49
雷达观测 2026-11-11 13:08
摘要
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 data geometries, including $L^2$-functional data and graph signals arising in modern medical applications.
作者备注：39 pages, 14 figures
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v2 · 2026-11-10 22:49 · 最新观测版本
Gaussian mixture models in Hilbert spaces via kernel methods
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 data geometries, including $L^2$-functional data and graph signals arising in modern medical applications.
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