Davies’ method of perturbed semigroups is a classical technique to obtain off-diagonal upper bounds on the heat kernel. However Davies’ method does not apply to anomalous diffusions due to the singularity of energy measures. In this note, we overcome the difficulty by modifying the Davies’ perturbation method to obtain sub-Gaussian upper bounds on the heat kernel. Our computations closely follo...

In the present paper a 2-means clustering-based anomaly detection technique is proposed. The presented method parses the set of training data, consisting of normal and anomaly data, and separates the data into two clusters. Each cluster is represented by its centroid one of the normal observations, and the other for the anomalies. The paper also provides appropriate methods for clustering, trai...