Optimal Transforms of Random Vectors

这一建议侧重于发展最优变换，以便在只知道统计信息的情况下描述和模拟非线性现象。最优转换是一种数学过程，它使我们能够以最适合手头任务的方式处理信息。这些变换已成功地应用于逼近、信息论、通信、控制理论以及信号和图像处理等领域。应用包括物理、化学和生物系统的建模、信号的过滤和压缩以及数据分类和聚类。在一般的结构框架下，我们提出了两个新的混合模型，用于现实变换。

This proposal focusses on development of optimal transforms to describe and model nonlinear phenomena when only statistical information is known. An optimal transform is a mathematical procedure that enables us to process information in a way that is most suited to the task in hand. These transforms have been successfully used in approximation, information theory, communications, control theory and signal and image processing. Applications include modelling of physical, chemical and biological systems, filtering and compression of signals and data classification and clustering. We propose two new hybrid models for realistic transforms in a general structural framework.