用随机投影加速子空间核计算，大幅节省内存。
Random Features for Grassmannian Kernels
- 基于随机投影的草图方法近似格拉斯曼流形核。
- 三种变体中两种使用二值化草图，内存减少显著。
- 适合大规模机器学习与模式识别中的子空间分析。
格拉斯曼流形 G(k, n) 在信号处理、计算机视觉和机器学习中广泛用于子空间分类、聚类与比较。本文提出一种基于草图的随机投影方法，用于近似格拉斯曼核。设计了三种核近似变体，其中两种依赖于二值化草图，带来显著内存节省。在 G(1, n) 特殊情形下建立了理论性质，并推广至一般 G(k, n)。实验表明，所提草图核性能接近标准格拉斯曼核，同时无需计算或存储完整核矩阵。该方法使大规模机器学习与模式识别中的格拉斯曼方法具备可扩展性。
原文摘要 · Abstract (English)
The Grassmannian manifold G(k, n) serves as a fundamental tool in signal processing, computer vision, and machine learning, where problems often involve classifying, clustering, or comparing subspaces. In this work, we propose a sketching-based approach to approximate Grassmannian kernels using random projections. We introduce three variations of kernel approximation, including two that rely on binarised sketches, offering substantial memory gains. We establish theoretical properties of our method in the special case of G(1, n) and extend it to general G(k, n). Experimental validation demonstrates that our sketched kernels closely match the performance of standard Grassmannian kernels while avoiding the need to compute or store the full kernel matrix. Our approach enables scalable Grassmannian-based methods for large-scale applications in machine learning and pattern recognition.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。