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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Vydané v:IEEE transactions on information theory Ročník 54; číslo 4; s. 1626 - 1636
Hlavný autor: Ziv, J.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York, NY IEEE 01.04.2008
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
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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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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2008.917666