Parametric Approximation Algorithms for High-Dimensional Euclidean Similarity

  • Authors:
  • Ömer Egecioglu

  • Affiliations:
  • -

  • Venue:
  • PKDD '01 Proceedings of the 5th European Conference on Principles of Data Mining and Knowledge Discovery
  • Year:
  • 2001

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Abstract

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. The former is based on a concept called bin-score permutations and a metric to quantify similarity of permutations, the latter on another novel approximation for inner-product computations based on power symmetric functions, which generalizes the Cauchy-Schwarz inequality. We present experiments on time-series data on labor statistics unemployment figures that show the effectiveness of the algorithm as a function of the parameter that combines the two parts.