A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo Sampling
The two-dimensional sample entropy marks a significant advance in evaluating the regularity and predictability of images in the information domain. Unlike the direct computation of sample entropy, which incurs a time complexity of <inline-formula><math xmlns="http://www.w3.org/1998/Mat...
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| Format: | Article |
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MDPI AG
2024-02-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/26/2/155 |
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| author | Zeheng Zhou Ying Jiang Weifeng Liu Ruifan Wu Zerong Li Wenchao Guan |
| author_facet | Zeheng Zhou Ying Jiang Weifeng Liu Ruifan Wu Zerong Li Wenchao Guan |
| author_sort | Zeheng Zhou |
| collection | DOAJ |
| description | The two-dimensional sample entropy marks a significant advance in evaluating the regularity and predictability of images in the information domain. Unlike the direct computation of sample entropy, which incurs a time complexity of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><msup><mi>N</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula> for the series with <i>N</i> length, the Monte Carlo-based algorithm for computing one-dimensional sample entropy (MCSampEn) markedly reduces computational costs by minimizing the dependence on <i>N</i>. This paper extends MCSampEn to two dimensions, referred to as MCSampEn2D. This new approach substantially accelerates the estimation of two-dimensional sample entropy, outperforming the direct method by more than a thousand fold. Despite these advancements, MCSampEn2D encounters challenges with significant errors and slow convergence rates. To counter these issues, we have incorporated an upper confidence bound (UCB) strategy in MCSampEn2D. This strategy involves assigning varied upper confidence bounds in each Monte Carlo experiment iteration to enhance the algorithm’s speed and accuracy. Our evaluation of this enhanced approach, dubbed UCBMCSampEn2D, involved the use of medical and natural image data sets. The experiments demonstrate that UCBMCSampEn2D achieves a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>40</mn><mo>%</mo></mrow></semantics></math></inline-formula> reduction in computational time compared to MCSampEn2D. Furthermore, the errors with UCBMCSampEn2D are only <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>30</mn><mo>%</mo></mrow></semantics></math></inline-formula> of those observed in MCSampEn2D, highlighting its improved accuracy and efficiency. |
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| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-07T22:33:29Z |
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| spelling | doaj.art-5117bad52f0a429a9779d52ddf56b8192024-02-23T15:15:44ZengMDPI AGEntropy1099-43002024-02-0126215510.3390/e26020155A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo SamplingZeheng Zhou0Ying Jiang1Weifeng Liu2Ruifan Wu3Zerong Li4Wenchao Guan5School of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, ChinaSchool of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, ChinaSchool of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, ChinaSchool of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, ChinaSchool of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, ChinaSchool of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, ChinaThe two-dimensional sample entropy marks a significant advance in evaluating the regularity and predictability of images in the information domain. Unlike the direct computation of sample entropy, which incurs a time complexity of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><msup><mi>N</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula> for the series with <i>N</i> length, the Monte Carlo-based algorithm for computing one-dimensional sample entropy (MCSampEn) markedly reduces computational costs by minimizing the dependence on <i>N</i>. This paper extends MCSampEn to two dimensions, referred to as MCSampEn2D. This new approach substantially accelerates the estimation of two-dimensional sample entropy, outperforming the direct method by more than a thousand fold. Despite these advancements, MCSampEn2D encounters challenges with significant errors and slow convergence rates. To counter these issues, we have incorporated an upper confidence bound (UCB) strategy in MCSampEn2D. This strategy involves assigning varied upper confidence bounds in each Monte Carlo experiment iteration to enhance the algorithm’s speed and accuracy. Our evaluation of this enhanced approach, dubbed UCBMCSampEn2D, involved the use of medical and natural image data sets. The experiments demonstrate that UCBMCSampEn2D achieves a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>40</mn><mo>%</mo></mrow></semantics></math></inline-formula> reduction in computational time compared to MCSampEn2D. Furthermore, the errors with UCBMCSampEn2D are only <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>30</mn><mo>%</mo></mrow></semantics></math></inline-formula> of those observed in MCSampEn2D, highlighting its improved accuracy and efficiency.https://www.mdpi.com/1099-4300/26/2/155sample entropyMonte Carlo algorithmupper confidence bound strategy |
| spellingShingle | Zeheng Zhou Ying Jiang Weifeng Liu Ruifan Wu Zerong Li Wenchao Guan A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo Sampling Entropy sample entropy Monte Carlo algorithm upper confidence bound strategy |
| title | A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo Sampling |
| title_full | A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo Sampling |
| title_fullStr | A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo Sampling |
| title_full_unstemmed | A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo Sampling |
| title_short | A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo Sampling |
| title_sort | fast algorithm for estimating two dimensional sample entropy based on an upper confidence bound and monte carlo sampling |
| topic | sample entropy Monte Carlo algorithm upper confidence bound strategy |
| url | https://www.mdpi.com/1099-4300/26/2/155 |
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