Pairwise normalized compression distance (NCD) is a parameter-free, feature-free, alignment-free, similarity metric based on compression. We propose an NCD of multisets that is also metric. Previously, attempts to obtain such an NCD failed. For classification purposes it is superior to the pairwise NCD in accuracy and implementation complexity. We cover the entire trajectory from theoretical underpinning to feasible practice. It is applied to biological (stem cell, organelle transport) and OCR classification questions that were earlier treated with the pairwise NCD. With the new method we achieved significantly better results. The theoretic foundation is Kolmogorov complexity.

Kolmogorov complexity is the length of the ultimately compressed version of a file (i.e., anything which can be put in a computer). Formally, it is the length of a shortest program from which the file can be reconstructed. We discuss the incomputability of Kolmogorov complexity, which formal loopholes this leaves us with, recent approaches to compute or approximate Kolmogorov complexity, which approaches are problematic, and which approaches are viable.