论文标题
多尺度聚类的相变级联
Cascade of Phase Transitions for Multi-Scale Clustering
论文作者
论文摘要
我们提出了一个新的框架，利用在对期望最大化算法的模拟退火期间，发生的相变的级联对于具有多尺度结构的群集数据集。使用加权的局部协方差，我们可以提取后验，而无需任何先验知识，有关不同尺度的簇数及其大小的信息。我们还研究了迭代方案的线性稳定性，以得出第一次过渡的阈值并显示如何近似下一个阈值。最后，我们将模拟退火与最新的正规高斯混合模型的发展相结合，从空间结构化数据集中学习主要图，这些图也可以表现出许多尺度。
We present a novel framework exploiting the cascade of phase transitions occurring during a simulated annealing of the Expectation-Maximisation algorithm to cluster datasets with multi-scale structures. Using the weighted local covariance, we can extract, a posteriori and without any prior knowledge, information on the number of clusters at different scales together with their size. We also study the linear stability of the iterative scheme to derive the threshold at which the first transition occurs and show how to approximate the next ones. Finally, we combine simulated annealing together with recent developments of regularised Gaussian mixture models to learn a principal graph from spatially structured datasets that can also exhibit many scales.
