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Register a new userNormalized Information Distance
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Added by
Paul Vitanyi
Publication date
2008
fields
Informatics Engineering
and research's language is
English
Authors
Paul M.B. Vitanyi
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The normalized information distance is a universal distance measure for objects of all kinds. It is based on Kolmogorov complexity and thus uncomputable, but there are ways to utilize it. First, compression algorithms can be used to approximate the Kolmogorov complexity if the objects have a string representation. Second, for names and abstract concepts, page count statistics from the World Wide Web can be used. These practical realizations of the normalized information distance can then be applied to machine learning tasks, expecially clustering, to perform feature-free and parameter-free data mining. This chapter discusses the theoretical foundations of the normalized information distance and both practical realizations. It presents numerous examples of successful real-world applications based on these distance measures, ranging from bioinformatics to music clustering to machine translation.
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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.
Normalized information distance (NID) uses 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. This practical application is called normalized compression distance and it is trivially computable. It is a parameter-free similarity measure based on compression, and is used in pattern recognition, data mining, phylogeny, clustering, and classification. The complexity properties of its theoretical precursor, the NID, have been open. We show that the NID is neither upper semicomputable nor lower semicomputable.
In this paper we apply different techniques of information distortion on a set of classical books written in English. We study the impact that these distortions have upon the Kolmogorov complexity and the clustering by compression technique (the latter based on Normalized Compression Distance, NCD). We show how to decrease the complexity of the considered books introducing several modifications in them. We measure how the information contained in each book is maintained using a clustering error measure. We find experimentally that the best way to keep the clustering error is by means of modifications in the most frequent words. We explain the details of these information distortions and we compare with other kinds of modifications like random word distortions and unfrequent word distortions. Finally, some phenomenological explanations from the different empirical results that have been carried out are presented.
Collaborative filtering, a widely-used recommendation technique, predicts a users preference by aggregating the ratings from similar users. As a result, these measures cannot fully utilize the rating information and are not suitable for real world sparse data. To solve these issues, we propose a novel user distance measure named Preference Movers Distance (PMD) which makes full use of all ratings made by each user. Our proposed PMD can properly measure the distance between a pair of users even if they have no co-rated items. We show that this measure can be cast as an instance of the Earth Movers Distance, a well-studied transportation problem for which several highly efficient solvers have been developed. Experimental results show that PMD can help achieve superior recommendation accuracy than state-of-the-art methods, especially when training data is very sparse.
There is a great deal of work in cognitive psychology, linguistics, and computer science, about using word (or phrase) frequencies in context in text corpora to develop measures for word similarity or word association, going back to at least the 1960s. The goal of this chapter is to introduce the normalizedis a general way to tap the amorphous low-grade knowledge available for free on the Internet, typed in by local users aiming at personal gratification of diverse objectives, and yet globally achieving what is effectively the largest semantic electronic database in the world. Moreover, this database is available for all by using any search engine that can return aggregate page-count estimates for a large range of search-queries. In the paper introducing the NWD it was called `normalized Google distance (NGD), but since Google doesnt allow computer searches anymore, we opt for the more neutral and descriptive NWD. web distance (NWD) method to determine similarity between words and phrases. It
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