Parametric Approximation Algorithms for High-Dimensional Euclidean Similarity

We introduce a spectrum of algorithms for measuring the similarity of high-dimensional vectors in Euclidean space. The algorithms proposed consist of a convex combination of two measures: one which contains summary data about the shape of a vector, and the other about the relative magnitudes of the coordinates. We present experiments on time-series data on labor statistics unemploymentfigures that show the effectiveness of the algorithm as a function of the parameter that combines the two parts.