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. The book is outstanding and admirable in many respects. ... is necessary reading for all kinds of readers from undergraduate students to top authorities in the field. Journal of Symbolic Logic Written by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and their applications of Kolmogorov complexity. The book presents a thorough treatment of the subject with a wide range of illustrative applications. Such applications include the randomness of finite objects or infinite sequences, Martin-Loef tests for randomness, information theory, computational learning theory, the complexity of algorithms, and the thermodynamics of computing. It will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. The book is self-contained in that it contains the basic requirements from mathematics and computer science. Included are also numerous problem sets, comments, source references, and hints to solutions of problems. New topics in this edition include Omega numbers, KolmogorovLoveland randomness, universal learning, communication complexity, Kolmogorov's random graphs, time-limited universal distribution, Shannon information and others.