多类数据分类的扩散方法
Diffusive method for multiple class data classification
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中文总结 AI 辅助
研究多类数据分类问题，基于热方程无限传播速度和强极大值原理提出算法，考虑热方程特定初始数据解，通过解的差值符号分类，给出高维离散数据数值算法及手写数字库分类结果。
中文摘要 AI 辅助
提出了一种基于热方程无限传播速度和强极大值原理的多类数据分类简单算法。该方法考虑以训练数据集特征函数为初始数据的热方程解，通过在极短时间间隔内两个解的差值符号进行分类。还提出了高维特征空间中离散训练数据的数值算法，并给出了手写数字数据库分类的数值结果。
英文摘要
A simple algorithm for multiple class data classification is proposed, which is based on the infinit speed of propagation and the strong maximum principle for the heat equation. In this method, solutions of the heat equation whose initial data are the characteristic function of the training dataset are considered. The classification is established by the sign of the difference of two solutions in a very short time interval. A numerical algorithm for discrete training data in high-dimensional feature space is proposed. As an application of the proposed method, numerical results on the classification of handwritten digits database are presented in this paper.
