Automatic binary data classi¯cation using a modi¯ed allen-cahn equation

In this paper, we propose an automatic binary data classi¯cation method using a modi¯ed Allen-Cahn (AC) equation. The modi¯ed AC equation was originally developed for image segmentation. The equation consists of the AC equation with a ¯delity term which enforces the solution to be the given data. In the proposed method, we start from a coarse grid and re¯ne the grid until the accuracy of the data classi¯cation reaches a given tolerance. Therefore, we can avoid a laborious trial and error procedure. For a numerical method for the modi¯ed 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 con¯rm that the proposed algorithm is automatic.