Normalized Google distance (NGD) is a relative semantic distance based on the World Wide Web (or any other large electronic database, for instance Wikipedia) and a search engine that returns aggregate page counts. The earlier NGD between pairs of search terms (including phrases) is not sufficient for all applications. We propose an NGD of finite multisets of search terms that is better for many applications. This gives a relative semantics shared by a multiset of search terms. We give applications and compare the results with those obtained using the pairwise NGD. The derivation of NGD method is based on Kolmogorov complexity.
If Kolmogorov complexity [25] measures information in one object and Information Distance measures information shared by two objects, how do we measure information shared by many objects? This paper provides an initial pragmatic study of this fundamental data mining question. Firstly, Em(x1,x2,...,xn) is defined to be the minimum amount of thermodynamic energy needed to convert from any xi to any xj. With this definition several theoretical problems have been solved. Second, our newly proposed theory is applied to select a comprehensive review and a specialized review from many reviews: (1) Core feature words, expanded words and dependent words are extracted respectively. (2) Comprehensive and specialized reviews are selected according to the information among them. This method of selecting a single review can be extended to select multiple reviews as well. Finally, experiments show that this comprehensive and specialized review mining method based on our new theory can do the job efficiently. 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. Information distance is a parameter-free similarity measure based on compression, used in pattern recognition, data mining, phylogeny, clustering and classification. The notion of information distance is extended from pairs to multiples (finite lists). We study maximal overlap, metricity, universality, minimal overlap, additivity and normalized information distance in multiples. We use the theoretical notion of Kolmogorov complexity which for practical purposes is approximated by the length of the compressed version of the file involved, using a real-world compression program.