Using a Markov chain perspective of spectral clustering we present an algorithm to automatically find the number of stable clusters in a dataset. The Markov chain's behaviour is characterized by the spectral properties of the matrix of transition probabilities, from which we derive eigenflows along with their halflives. An eigenflow describes the flow of probabil- ity mass due to the Markov chain, and it is characterized by its eigen- value, or equivalently, by the halflife of its decay as the Markov chain is iterated. A ideal stable cluster is one with zero eigenflow and infi- nite half-life. The key insight in this paper is that bottlenecks between weakly coupled clusters can be identified by computing the sensitivity of the eigenflow's halflife to variations in the edge weights.

Clustering has gained widespread use, especially for static data. However, the rapid growth of spatio-temporal data from numerous instruments, such as earth-orbiting satellites, has created a need for spatio-temporal clustering methods to extract and monitor dynamic clusters. Dynamic spatio-temporal clustering faces two major challenges: First, the clusters are dynamic and may change in size, shape, and statistical properties over time. Second, numerous spatio-temporal data are incomplete, noisy, heterogeneous, and highly variable (over space and time). We propose a new spatio-temporal data mining paradigm, to autonomously identify dynamic spatio-temporal clusters in the presence of noise and missing data. Our proposed approach is more robust than traditional clustering and image segmentation techniques in the case of dynamic patterns, non-stationary, heterogeneity, and missing data. We demonstrate our method's performance on a real-world application of monitoring in-land water bodies on a global scale.