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确定、或选择某种距离度量是模式识别、机器学习和聚类分析的基本问题.图像欧氏距离和广义欧氏距离是重要的两种距离度量,它们可以嵌入到大多数识别算法中去,并且在大量应用中都提升了识别效率.文中揭示了包括IMED和GED在内的一类距离度量与线性平移不变系统的关系.证明了以下结论:输入空间上的平移不变度量等价于对输入信号进行线性滤波再计算传统欧氏度量.这一结果扩展了对距离度量的认识,将在距离度量的选择上起到一定的作用.
Determining, or selecting some kind of distance measure is the basic problem of pattern recognition, machine learning and cluster analysis.The image Euclidean distance and generalized Euclidean distance are two important distance measures which can be embedded in most recognition algorithms, And the recognition efficiency is improved in a large number of applications.The paper reveals the relationship between a class of distance metrics including IMED and GED and linear translational invariant systems.The following conclusions are proved: The translational invariant metric on input space is equivalent to Linear filtering the input signal and then calculating the traditional Euclidean metric, which extends the understanding of distance measurement and will play a role in the choice of distance measurement.