To measure the quality of a set of vector quantization points a means of measuring the distance between a random point and its quantization is required. Common metrics such as the {\em Hamming} and {\em Euclidean} metrics, while mathematically simple, are inappropriate for comparing natural signals such as speech or images. In this paper it is shown how an {\em environment} of functions on an input space $X$ induces a {\em canonical distortion measure} (CDM) on X. The depiction 'canonical" is justified because it is shown that optimizing the reconstruction error of X with respect to the CDM gives rise to optimal piecewise constant approximations of the functions in the environment. The CDM is calculated in closed form for several different function classes. An algorithm for training neural networks to implement the CDM is presented along with some encouraging experimental results.
翻译:测量一组矢量量化点的质量需要一种测量随机点与其量化之间的距离的方法。 通用指标,如 ~em Hamming} 和 ~em Euclidean} 等,虽然数学简单,但不适合比较语言或图像等自然信号。 本文显示,输入空间$X美元上函数的 ~em 环境} 如何在 X. 上诱发 ~em Canical 扭曲 } (CDM) 。 描述“ canonical”是有道理的, 因为它表明在清洁发展机制方面优化 X 的重建错误可以对环境功能产生最佳的片状常态近似值。 清洁发展机制以封闭的形式为若干不同的功能类别计算。 用于执行清洁发展机制的神经网络的培训算法与一些令人鼓舞的实验结果一起提出。