Normalized Compression Distance of Multisets with Applications

Normalized compression distance (NCD) is a parameter-free, feature-free, alignment-free, similarity measure between a pair of finite objects based on compression. However, it is not sufficient for all applications. We propose an NCD of finite nonempty multisets (a.k.a. multiples) of finite objects that is also a metric. Previously, attempts to obtain such an NCD failed. We cover the entire trajectory from theoretical underpinning to feasible practice. The new NCD for multisets is applied to retinal progenitor cell classification questions and to related synthetically generated data that were earlier treated with the pairwise NCD. With the new method we achieved significantly better results. Similarly for questions about axonal organelle transport. We also applied the new NCD to handwritten digit recognition and improved classification accuracy significantly over that of pairwise NCD by incorporating both the pairwise and NCD for multisets. In the analysis we use the incomputable 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. Index Terms— Normalized compression distance, multisets or multiples, pattern recognition, data mining, similarity, classification, Kolmogorov complexity, retinal progenitor cells, synthetic data, organelle transport, handwritten character recognition