In this paper, we propose an automatic binary data classification method using a modified Allen–Cahn (AC) equation. The modified AC equation was originally developed for image segmentation. The equation consists of the AC equation with a fidelity term which enforces the solution to be the given data. In the proposed method, we start from a coarse grid and refine the grid until the accuracy of the data classification reaches a given tolerance. Therefore, we can avoid a laborious trial and error procedure. For a numerical method for the modified AC equation, we use a recently developed explicit hybrid scheme. We perform several 2D and 3D computational tests to demonstrate the performance of the proposed method. The computational results confirm that the proposed algorithm is automatic.

中文翻译：

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使用修正的 Allen-Cahn 方程的自动二进制数据分类

在本文中，我们提出了一种使用改进的 Allen-Cahn (AC) 方程的自动二进制数据分类方法。修改后的 AC 方程最初是为图像分割而开发的。该方程由具有保真度项的 AC 方程组成，该保真度项将解强制为给定数据。在所提出的方法中，我们从粗网格开始并细化网格，直到数据分类的准确性达到给定的容差。因此，我们可以避免费力的试错过程。对于修改后的 AC 方程的数值方法，我们使用最近开发的显式混合方案。我们执行了几个 2D 和 3D 计算测试来证明所提出方法的性能。计算结果证实了所提出的算法是自动的。