We propose a modified Gray–Scott (GS) model for binary data classification. We assign the corresponding initial values to the concentrations of reactants U and V in the GS model, and discretize them on a grid. In each simulation iteration, we retain the initial value of V for calculation to determine the fuzzy boundary so that the concentration of the reactants remains within a certain range near the boundary during diffusion. This ultimately stabilizes the diffusion process and forms a nonlinear interface or hyperplane. We conduct various computational tests to verify the efficiency and robustness of the proposed algorithm. In addition, classification problems in real-world applications, such as those involving Electroencephalogram (EEG) signals, are also considered. Some statistical metrics such as Shannon entropy (SNE), Higuchi’s Hurst exponent (HHE), Kolmogorov complexity (KC), and Hurst exponents <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11520_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">$H(-10)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mo stretchy="false">(</mo> <mo>-</mo> <mn>10</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, H(0), and H(10), which are extracted from <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11520_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="101" /> </InlineMediaObject> <EquationSource Format="TEX">$q=-10, 0, 10$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>=</mo> <mo>-</mo> <mn>10</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>10</mn> </mrow> </math></EquationSource> </InlineEquation> by Multiple Fractal Detrending Fluctuation Analysis (MF-DFA) were used to characterize the EEG signals. The advantage of this method compared to traditional machine learning classification methods is that it can construct a nonlinear interface or hyperplane, which can significantly improve classification accuracy, recall and precision.

A novel binary data classification system based on the modified Gray–Scott model

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发表日期：

2025年7月1日

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Jian Wang,
Shanshan Ge,
Heming Xu,
Wenjing Jiang,
Junseok Kim

摘要

We propose a modified Gray–Scott (GS) model for binary data classification. We assign the corresponding initial values to the concentrations of reactants U and V in the GS model, and discretize them on a grid. In each simulation iteration, we retain the initial value of V for calculation to determine the fuzzy boundary so that the concentration of the reactants remains within a certain range near the boundary during diffusion. This ultimately stabilizes the diffusion process and forms a nonlinear interface or hyperplane. We conduct various computational tests to verify the efficiency and robustness of the proposed algorithm. In addition, classification problems in real-world applications, such as those involving Electroencephalogram (EEG) signals, are also considered. Some statistical metrics such as Shannon entropy (SNE), Higuchi’s Hurst exponent (HHE), Kolmogorov complexity (KC), and Hurst exponents $H(-10)$ $H (- 10)$ , H(0), and H(10), which are extracted from $q=-10, 0, 10$ $q = - 10, 0, 10$ by Multiple Fractal Detrending Fluctuation Analysis (MF-DFA) were used to characterize the EEG signals. The advantage of this method compared to traditional machine learning classification methods is that it can construct a nonlinear interface or hyperplane, which can significantly improve classification accuracy, recall and precision.