扩散映射：利用半群性质进行参数调整
Diffusion Maps : Using the Semigroup Property for Parameter Tuning
摘要：
扩散图（DM）构成了一个经典的降维技术，数据躺在或接近一个（相对）低维流形嵌入在一个更大的维空间。DM过程包括从数据集上的模拟随机游动或扩散路径构造流形的谱参数化。然而，DM在实践中很难调整。特别地，在构造扩散核矩阵时设置扩散时间t的任务是关键的。我们解决这个问题，通过使用扩散算子的半群性质。我们提出了一个挑选t的半群准则。实验结果表明，该方法是有效的，鲁棒性好.
英文摘要：
Diffusion maps (DM) constitute a classic dimension reduction technique, for data lying on or close to a (relatively) low-dimensional manifold embedded in a much larger dimensional space. The DM procedure consists in constructing a spectral parametrization for the manifold from simulated random walks or diffusion paths on the data set. However, DM is hard to tune in practice. In particular, the task to set a diffusion time t when constructing the diffusion kernel matrix is critical. We address this problem by using the semigroup property of the diffusion operator. We propose a semigroup criterion for picking t. Experiments show that this principled approach is effective and robust.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
