论文标题
扩散图：使用Semigroup属性进行参数调整
Diffusion Maps : Using the Semigroup Property for Parameter Tuning
论文作者
论文摘要
扩散图（DM）构成了一种经典的降低技术，对于位于或接近（相对）的低维歧管上的数据嵌入了更大的维空间。 DM过程包括从模拟的随机步行或数据集中的扩散路径构建频谱参数化。但是，DM很难在实践中调整。特别是，在构造扩散核矩阵时设置扩散时间t的任务至关重要。我们通过使用扩散操作员的半群属性来解决此问题。我们建议选择t的半群标准。实验表明，这种原则性的方法是有效且坚固的。
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.
