Spectral Clustering using Expert Knowledge

We present results from an application of spectral clustering in which an algorithmically defined similarity measure is used in the domain of space object tracking. The current literature generally uses Gaussian kernels, which are well suited for Euclidean spaces, but the techniques could be more widely implemented in novel applications where expert knowledge and heuristics are required. Defining an algorithmic similarity measure allows such knowledge to be incorporated, which can be useful in a wide set of contexts. We show results for classifying space observations by object and present some theoretical justifications for its use. Advances in spectral clustering are utilized such as the use of a diffusion map to determine a low dimensional Euclidean representation of the data, which retains the non-linear associations, along with self-tuning parameters and the use of a local scaling to enhance results. Overall, this is meant to be an introduction to a set of classification tools through an example application.