Normalized Compression Distance of Multiples

Normalized compression distance (NCD) is a parameter-free similarity measure based on compression. The NCD between pairs of objects is not sufficient for all applications. We propose an NCD of finite multisets (multiples) of objacts that is metric and is better for many applications. Previously, attempts to obtain such an NCD failed. We use the theoretical notion of Kolmogorov complexity that for practical purposes is approximated from above by the length of the compressed version of the file involved, using a real-world compression program. We applied the new NCD for multiples to retinal progenitor cell questions that were earlier treated with the pairwise NCD. Here we get significantly better results. We also applied the NCD for multiples to synthetic time sequence data. The preliminary results are as good as nearest neighbor Euclidean classifier.