  Although there is growing interest in measuring integrated information in
computational and cognitive systems, current methods for doing so in practice
are computationally unfeasible. Existing and novel integration measures are
investigated and classified by various desirable properties. A simple taxonomy
of Phi-measures is presented where they are each characterized by their choice
of factorization method (5 options), choice of probability distributions to
compare (3x4 options) and choice of measure for comparing probability
distributions (7 options). When requiring the Phi-measures to satisfy a minimum
of attractive properties, these hundreds of options reduce to a mere handful,
some of which turn out to be identical. Useful exact and approximate formulas
are derived that can be applied to real-world data from laboratory experiments
without posing unreasonable computational demands.
