Unsupervised cluster discovery using statistics in scale space

This paper presents a method of the unsupervised discovery of valid clusters using statistics on the modes of the probability density function in scale space. First, a Gaussian scale-space theory is applied to the kernel density estimation to derive the hierarchical relationships among the modes of the probability density function in scale space. The data points are classified into clusters according to the mode hierarchy. Second, the algorithm of cluster discovery is presented. The valid clusters are discovered by testing whether each cluster is distinguishable from spurious clusters obtained from uniformly random points. The statistical hypothesis test for cluster discovery requires distribution forms of annihilation scales of the modes estimated from the uniformly random points. The distribution forms are experimentally shown to be unimodal. Finally, cluster discovery is demonstrated using synthetic data and benchmark data.