2020/10/05 by Yufan Zhou, Zhou, Yufan, Changyou Chen +3 · 2 citations
Computer Science · Mathematics · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #cs.CV #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2010.01761
Accepted by NeurIPS 2020. Some typos have been corrected
openalex publication_date 2020/10/05 · arxiv created 2021/03/15 · arxiv updated 2021/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Manifold learning is a fundamental problem in machine learning with numerous applications. Most of the existing methods directly learn the low-dimensional embedding of the data in some high-dimensional space, and usually lack the flexibility of being directly applicable to down-stream applications. In this paper, we propose the concept of implicit manifold learning, where manifold information is implicitly obtained by learning the associated heat kernel. A heat kernel is the solution of the corresponding heat equation, which describes how "heat" transfers on the manifold, thus containing ample geometric information of the manifold. We provide both practical algorithm and theoretical analysis of our framework. The learned heat kernel can be applied to various kernel-based machine learning models, including deep generative models (DGM) for data generation and Stein Variational Gradient Descent for Bayesian inference. Extensive experiments show that our framework can achieve state-of-the-art results compared to existing methods for the two tasks.