Application of Positional Entropy to Fast Shannon Entropy Estimation for Samples of Digital Signals
This paper introduces a new method of estimating Shannon entropy. The proposed method can be successfully used for large data samples and enables fast computations to rank the data samples according to their Shannon entropy. Original definitions of positional entropy and integer entropy are discusse...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/10/1173 |
| _version_ | 1797550561124417536 |
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| author | Marcin Cholewa Bartłomiej Płaczek |
| author_facet | Marcin Cholewa Bartłomiej Płaczek |
| author_sort | Marcin Cholewa |
| collection | DOAJ |
| description | This paper introduces a new method of estimating Shannon entropy. The proposed method can be successfully used for large data samples and enables fast computations to rank the data samples according to their Shannon entropy. Original definitions of positional entropy and integer entropy are discussed in details to explain the theoretical concepts that underpin the proposed approach. Relations between positional entropy, integer entropy and Shannon entropy were demonstrated through computational experiments. The usefulness of the introduced method was experimentally verified for various data samples of different type and size. The experimental results clearly show that the proposed approach can be successfully used for fast entropy estimation. The analysis was also focused on quality of the entropy estimation. Several possible implementations of the proposed method were discussed. The presented algorithms were compared with the existing solutions. It was demonstrated that the algorithms presented in this paper estimate the Shannon entropy faster and more accurately than the state-of-the-art algorithms. |
| first_indexed | 2024-03-10T15:31:05Z |
| format | Article |
| id | doaj.art-f9e137fe67ab4dd5a31df6a49cdd9b78 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T15:31:05Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-f9e137fe67ab4dd5a31df6a49cdd9b782023-11-20T17:38:58ZengMDPI AGEntropy1099-43002020-10-012210117310.3390/e22101173Application of Positional Entropy to Fast Shannon Entropy Estimation for Samples of Digital SignalsMarcin Cholewa0Bartłomiej Płaczek1Institute of Computer Science, University of Silesia, Będzińska 39, 41–205 Sosnowiec, PolandInstitute of Computer Science, University of Silesia, Będzińska 39, 41–205 Sosnowiec, PolandThis paper introduces a new method of estimating Shannon entropy. The proposed method can be successfully used for large data samples and enables fast computations to rank the data samples according to their Shannon entropy. Original definitions of positional entropy and integer entropy are discussed in details to explain the theoretical concepts that underpin the proposed approach. Relations between positional entropy, integer entropy and Shannon entropy were demonstrated through computational experiments. The usefulness of the introduced method was experimentally verified for various data samples of different type and size. The experimental results clearly show that the proposed approach can be successfully used for fast entropy estimation. The analysis was also focused on quality of the entropy estimation. Several possible implementations of the proposed method were discussed. The presented algorithms were compared with the existing solutions. It was demonstrated that the algorithms presented in this paper estimate the Shannon entropy faster and more accurately than the state-of-the-art algorithms.https://www.mdpi.com/1099-4300/22/10/1173entropy estimationShannon entropypositional entropy |
| spellingShingle | Marcin Cholewa Bartłomiej Płaczek Application of Positional Entropy to Fast Shannon Entropy Estimation for Samples of Digital Signals Entropy entropy estimation Shannon entropy positional entropy |
| title | Application of Positional Entropy to Fast Shannon Entropy Estimation for Samples of Digital Signals |
| title_full | Application of Positional Entropy to Fast Shannon Entropy Estimation for Samples of Digital Signals |
| title_fullStr | Application of Positional Entropy to Fast Shannon Entropy Estimation for Samples of Digital Signals |
| title_full_unstemmed | Application of Positional Entropy to Fast Shannon Entropy Estimation for Samples of Digital Signals |
| title_short | Application of Positional Entropy to Fast Shannon Entropy Estimation for Samples of Digital Signals |
| title_sort | application of positional entropy to fast shannon entropy estimation for samples of digital signals |
| topic | entropy estimation Shannon entropy positional entropy |
| url | https://www.mdpi.com/1099-4300/22/10/1173 |
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