Birnbaum, T. (2017). A similarity measure for complex numbers. Poster session presented at NSE PhD Day 2017, Brussels, Belgium.

@conference{a924152e565c4c9da4390c710d0783dc,
title = "A similarity measure for complex numbers",
abstract = "Complex numbers are encountered in many applications due to integral transforms such as Fourier or Laplace or simply due to implicit wave phenomena. But while countless similarity measures exist for real valued data, its difficult to compare two complex datasets. One has to resort to either comparing the data in parts, e.g. real/imaginary or absolute value/phase, or resort to error measures based on the mean squared error (MSE). Often applications provide a good intuition of which mismatches are tolerable. We therefore propose a versatile similarity measure that allows an easy local and global interpretation. It is specifically crafted for complex-valued data and guarantees scale invariance, invariance under constant phase shifts, symmetry with respect to the arguments, but can be freely adjusted to match the desired notion of similarity. We show that it globally matches the MSE and hope to provide a useful template for anybody required to compare complex-valued datasets.",
author = "Tobias Birnbaum",
year = "2017",
month = jun,
day = "8",
language = "English",
note = "NSE PhD Day 2017 ; Conference date: 08-06-2017",
}