On Finite Memory Universal Data Compression and Classification of Individual Sequences

Consider the case where consecutive blocks of letters of a semi-infinite individual sequence over a finite-alphabet are being compressed into binary sequences by some one-to-one mapping. No a priori information about is available at the encoder, which must therefore adopt a universal data-compressio...

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Vydáno v:	IEEE transactions on information theory Ročník 54; číslo 4; s. 1626 - 1636
Hlavní autor:	Ziv, J.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.04.2008 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithms Applied sciences Binary sequences Biological system modeling Classifiers Coding, codes Compressing Compression algorithms Computational biology Context-tree coding Data compression Data transmission Encoders Exact sciences and technology H infinity control Information analysis Information processing Information theory Information, signal and communications theory Jacobian matrices Mathematical analysis Signal and communications theory Signal representation. Spectral analysis Signal, noise Telecommunications and information theory Testing Training Turing machines universal classification universal compression Alphabet Automatic classification Probabilistic approach Lempel Ziv algorithm Data compression Context tree Mapping universal compression Signal classification Discriminator Learning Binary sequence Space complexity Context-tree coding Coding A priori estimation universal classification
ISSN:	0018-9448, 1557-9654
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Popis
Shrnutí:	Consider the case where consecutive blocks of letters of a semi-infinite individual sequence over a finite-alphabet are being compressed into binary sequences by some one-to-one mapping. No a priori information about is available at the encoder, which must therefore adopt a universal data-compression algorithm. It is known that if the universal Lempel-Ziv (LZ) data compression algorithm is successively applied to -blocks then the best error-free compression, for the particular individual sequence is achieved as tends to infinity. The best possible compression that may be achieved by any universal data compression algorithm for finite -blocks is discussed. It is demonstrated that context tree coding essentially achieves it. Next, consider a device called classifier (or discriminator) that observes an individual training sequence . The classifier's task is to examine individual test sequences of length and decide whether the test -sequence has the same features as those that are captured by the training sequence , or is sufficiently different, according to some appropriate criterion. Here again, it is demonstrated that a particular universal context classifier with a storage-space complexity that is linear in , is essentially optimal. This may contribute a theoretical ldquoindividual sequencerdquo justification for the Probabilistic Suffix Tree (PST) approach in learning theory and in computational biology.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2008.917666