9,214 research outputs found
Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality
We survey diverse approaches to the notion of information: from Shannon
entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov
complexity are presented: randomness and classification. The survey is divided
in two parts published in a same volume. Part II is dedicated to the relation
between logic and information system, within the scope of Kolmogorov
algorithmic information theory. We present a recent application of Kolmogorov
complexity: classification using compression, an idea with provocative
implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses
how Kolmogorov complexity, besides being a foundation to randomness, is also
related to classification. Another approach to classification is also
considered: the so-called "Google classification". It uses another original and
attractive idea which is connected to the classification using compression and
to Kolmogorov complexity from a conceptual point of view. We present and unify
these different approaches to classification in terms of Bottom-Up versus
Top-Down operational modes, of which we point the fundamental principles and
the underlying duality. We look at the way these two dual modes are used in
different approaches to information system, particularly the relational model
for database introduced by Codd in the 70's. This allows to point out diverse
forms of a fundamental duality. These operational modes are also reinterpreted
in the context of the comprehension schema of axiomatic set theory ZF. This
leads us to develop how Kolmogorov's complexity is linked to intensionality,
abstraction, classification and information system.Comment: 43 page
Normalized Web Distance and Word Similarity
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 doesn't allow computer searches anymore, we opt for the more
neutral and descriptive NWD. web distance (NWD) method to determine similarity
between words and phrases. ItComment: Latex, 20 pages, 7 figures, to appear in: Handbook of Natural
Language Processing, Second Edition, Nitin Indurkhya and Fred J. Damerau
Eds., CRC Press, Taylor and Francis Group, Boca Raton, FL, 2010, ISBN
978-142008592
Algorithmic Complexity for Short Binary Strings Applied to Psychology: A Primer
Since human randomness production has been studied and widely used to assess
executive functions (especially inhibition), many measures have been suggested
to assess the degree to which a sequence is random-like. However, each of them
focuses on one feature of randomness, leading authors to have to use multiple
measures. Here we describe and advocate for the use of the accepted universal
measure for randomness based on algorithmic complexity, by means of a novel
previously presented technique using the the definition of algorithmic
probability. A re-analysis of the classical Radio Zenith data in the light of
the proposed measure and methodology is provided as a study case of an
application.Comment: To appear in Behavior Research Method
Normalized Information Distance
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.Comment: 33 pages, 12 figures, pdf, in: Normalized information distance, in:
Information Theory and Statistical Learning, Eds. M. Dehmer, F.
Emmert-Streib, Springer-Verlag, New-York, To appea
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