تقرير
Sketching the Heat Kernel: Using Gaussian Processes to Embed Data
| العنوان: | Sketching the Heat Kernel: Using Gaussian Processes to Embed Data |
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| المؤلفون: | Gilbert, Anna C., O'Neill, Kevin |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics Statistics |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Mathematics - Numerical Analysis, Statistics - Machine Learning |
| الوصف: | This paper introduces a novel, non-deterministic method for embedding data in low-dimensional Euclidean space based on computing realizations of a Gaussian process depending on the geometry of the data. This type of embedding first appeared in (Adler et al, 2018) as a theoretical model for a generic manifold in high dimensions. In particular, we take the covariance function of the Gaussian process to be the heat kernel, and computing the embedding amounts to sketching a matrix representing the heat kernel. The Karhunen-Lo\`eve expansion reveals that the straight-line distances in the embedding approximate the diffusion distance in a probabilistic sense, avoiding the need for sharp cutoffs and maintaining some of the smaller-scale structure. Our method demonstrates further advantage in its robustness to outliers. We justify the approach with both theory and experiments. Comment: 28 pages |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2403.07929Test |
| رقم الانضمام: | edsarx.2403.07929 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |