This paper introduces a novel method for embedding data in low-dimensional Euclidean spaces using Gaussian processes and heat kernels. The approach focuses on approximating diffusion distances and maintaining robustness to outliers. By sketching the heat kernel matrix, the authors demonstrate the advantages of their method over traditional approaches.
Recent success in analyzing high-dimensional data is attributed to underlying low-dimensional structures. The paper introduces a novel method for embedding data in low-dimensional spaces based on Gaussian processes and heat kernels. The approach aims to approximate diffusion distances by combining eigenvectors/functions, preserving small-scale information neglected by other methods.
Gaussian process embeddings are shown to be almost surely embeddings when certain conditions are met, providing insights into the extrinsic geometry of manifolds embedded in high dimensions. The method relies on constructing a Gaussian process on the data and computing embeddings via specific formulas.
Experimental results show that Gaussian process embeddings perform well with robustness to outliers and are computationally efficient compared to traditional methods like diffusion maps. The paper also discusses theoretical justifications for the approach based on previous work on Gaussian processes.
Overall, the method presented offers a promising way to embed high-dimensional data into low-dimensional spaces efficiently while preserving important structural information.
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