A context tree weighting algorithm with a finite window
Willems and colleagues proposed the context tree weighting (CTW) method. It is a method for probability estimation, by which the tree source serving the standard model for the data compression is compressed optimally in the quadratic sense with a high computational efficiency, under the condition th...
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| Vydané v: | Electronics & communications in Japan. Part 3, Fundamental electronic science Ročník 83; číslo 1; s. 21 - 30 |
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| Hlavní autori: | , |
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| Jazyk: | English |
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John Wiley & Sons, Inc
01.01.2000
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| ISSN: | 1042-0967, 1520-6440 |
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| Abstract | Willems and colleagues proposed the context tree weighting (CTW) method. It is a method for probability estimation, by which the tree source serving the standard model for the data compression is compressed optimally in the quadratic sense with a high computational efficiency, under the condition that the parameters are unknown and the model is unknown. This article intends to apply the CTW method to the nonstationary source, which is a problem that has not been investigated. A compression algorithm with a forgetting mechanism and with a finite window (FWCTW method) is proposed. As the first step, the CTW method in general is discussed. A lemma concerning inferior probability preservation is presented, which serves as a key to the various realization problems. Using that lemma, the validity of the realization of the FWCTW method is shown. Then, for the case of a stationary memoryless source, the redundancy has asymptotic optimality in regard to the window length. The effectiveness of the application to the general constant‐interval nonstationary tree source is shown by experiment. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 83(1): 21–30, 2000 |
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| AbstractList | Willems and colleagues proposed the context tree weighting (CTW) method. It is a method for probability estimation, by which the tree source serving the standard model for the data compression is compressed optimally in the quadratic sense with a high computational efficiency, under the condition that the parameters are unknown and the model is unknown. This article intends to apply the CTW method to the nonstationary source, which is a problem that has not been investigated. A compression algorithm with a forgetting mechanism and with a finite window (FWCTW method) is proposed. As the first step, the CTW method in general is discussed. A lemma concerning inferior probability preservation is presented, which serves as a key to the various realization problems. Using that lemma, the validity of the realization of the FWCTW method is shown. Then, for the case of a stationary memoryless source, the redundancy has asymptotic optimality in regard to the window length. The effectiveness of the application to the general constant‐interval nonstationary tree source is shown by experiment. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 83(1): 21–30, 2000 |
| Author | Sakaguchi, Hiroaki Kawabata, Tsutomu |
| Author_xml | – sequence: 1 givenname: Hiroaki surname: Sakaguchi fullname: Sakaguchi, Hiroaki organization: Department of Communications and Systems, University of Electro-Communications, Chofu, Japan 182 – sequence: 2 givenname: Tsutomu surname: Kawabata fullname: Kawabata, Tsutomu organization: Department of Communications and Systems, University of Electro-Communications, Chofu, Japan 182 |
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| Cites_doi | 10.1109/TIT.1981.1056331 10.1002/0471200611 10.1109/18.265494 10.1109/18.556608 10.1109/18.265504 10.1109/TIT.1986.1057210 10.1109/18.133247 10.1109/TIT.1983.1056741 10.1109/TIT.1977.1055714 10.1109/18.382012 10.1109/TIT.1978.1055934 10.1109/18.382011 |
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| References_xml | – reference: Johnson NL, Kotz S. Discrete distribution. Chapter 3. Wiley; 1969. – reference: Rissanen J. A universal data compression system. IEEE Trans Inf Theory 1983;IT-29:656-664. – reference: Han T. Recent advances in data compression theory [I], [II]. Proc IEICE 1984;2:185-191; 1984;3:286-292. – reference: Matsushima T, Inazumi H, Hirasawa S. A class of distortionless codes designed by Bayes decision theory. IEEE Trans Inf Theory 1991;37:1288-1293. – reference: Merhav N. On the minimum description length principle for sources with piecewise constant parameters. IEEE Trans Inf Theory 1993;39:1962-1967. – reference: Cover TM, Thomas JA. Elements of information theory. Wiley; 1991. – reference: Weinberger MJ, Rissanen JJ, Feder M. A universal finite memory source. IEEE Trans Inf Theory 1995;41:643-652. – reference: Ziv J, Lempel A. A universal algorithm for sequential data compression. IEEE Trans Inf Theory 1977;IT-23:337-343. – reference: Ziv J, Lempel A. Compression of individual sequences via variable-rate coding. IEEE Trans Inf Theory 1978;IT-24:530-536. – reference: Willems FMJ. Coding for a binary independent piecewise-identically distributed source. IEEE Trans Inf Theory 1996;42:2210-2217. – reference: Suzuki J. Some notes on universal noiseless coding. IEICE Trans Fundam 1995;E78-A:1840-1847. – reference: Kawabata T. Bayes coding and context tree weighting. Tech Rep IEICE 1994;IT-93-121. – reference: Morita H, Kobayashi K. On asymptotic optimality of a sliding window variation of Lempel-Ziv codes. IEEE Trans Inf Theory 1993;39:1840-1846. – reference: Willems FMJ, Shtarkov YM, Tjalkens TJ. The context tree weighting method: Basic properties. IEEE Trans Inf Theory 1995;41:653-664. – reference: Krichevsky RE, Trofimov VK. The performance of universal encoding. IEEE Trans Inf Theory 1981;IT-27:199-207. – reference: Rissanen J. Complexity of strings in the class of Markov sources. IEEE Trans Inf Theory 1986;32: 526-532. – volume: 42 start-page: 2210 year: 1996 end-page: 2217 article-title: Coding for a binary independent piecewise‐identically distributed source publication-title: IEEE Trans Inf Theory – start-page: 59 year: 1993 – volume: IT‐93‐121 year: 1994 article-title: Bayes coding and context tree weighting publication-title: Tech Rep IEICE – volume: 41 start-page: 643 year: 1995 end-page: 652 article-title: A universal finite memory source publication-title: IEEE Trans Inf Theory – volume: IT‐23 start-page: 337 year: 1977 end-page: 343 article-title: A universal algorithm for sequential data compression publication-title: IEEE Trans Inf Theory – volume: 37 start-page: 1288 year: 1991 end-page: 1293 article-title: A class of distortionless codes designed by Bayes decision theory publication-title: IEEE Trans Inf Theory – volume: IT‐24 start-page: 530 year: 1978 end-page: 536 article-title: Compression of individual sequences via variable‐rate coding publication-title: IEEE Trans Inf Theory – volume: 39 start-page: 1962 year: 1993 end-page: 1967 article-title: On the minimum description length principle for sources with piecewise constant parameters publication-title: IEEE Trans Inf Theory – year: 1969 – volume: 32 start-page: 526 year: 1986 end-page: 532 article-title: Complexity of strings in the class of Markov sources publication-title: IEEE Trans Inf Theory – volume: IT‐29 start-page: 656 year: 1983 end-page: 664 article-title: A universal data compression system publication-title: IEEE Trans Inf Theory – volume: 41 start-page: 653 year: 1995 end-page: 664 article-title: The context tree weighting method: Basic properties publication-title: IEEE Trans Inf Theory – volume: 2 start-page: 185 year: 1984 end-page: 191 article-title: Recent advances in data compression theory [I], [II] publication-title: Proc IEICE – year: 1991 – volume: 39 start-page: 1840 year: 1993 end-page: 1846 article-title: On asymptotic optimality of a 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10.1002/(SICI)1520-6440(200001)83:1<21::AID-ECJC3>3.0.CO;2-X-BIB4 publication-title: IEEE Trans Inf Theory doi: 10.1109/TIT.1978.1055934 – volume: 41 start-page: 643 year: 1995 ident: 10.1002/(SICI)1520-6440(200001)83:1<21::AID-ECJC3>3.0.CO;2-X-BIB16 publication-title: IEEE Trans Inf Theory doi: 10.1109/18.382011 – volume-title: Discrete distribution year: 1969 ident: 10.1002/(SICI)1520-6440(200001)83:1<21::AID-ECJC3>3.0.CO;2-X-BIB1 |
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| Title | A context tree weighting algorithm with a finite window |
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