Qualitative Performance Assessment of Adaptive Filtering and Machine Learning Algorithms

信号的形态特征，即对信号的线性、非线性、确定性和随机性的评价，正日益成为多学科研究的重要领域。这些想法出现在20世纪90年代中期的物理学中，然而，在机器学习和信号处理中的应用直到最近才变得明显起来。由于信号性质的变化，例如，从线性到非线性，可以揭示健康危害，因此应该选择信号处理框架以保存这一关键信息。然而，标准的学习算法通常是基于二阶统计量的，并且会自然地将非线性现象线性化。该建议旨在为设计具有更高质量性能的学习算法提供一个新的理论和计算框架。标准的基于二阶统计量的自适应滤波和机器学习算法旨在优化量化性能，但有用的信息往往会丢失。这类问题通常出现在生物医学应用中，例如，脑电记录的性质从线性随机(ARMA)到非线性确定性(混沌)的变化可能表明健康危害。这项工作的基本新颖性是最近提出的一种延迟向量方差(DVV)方法，该方法检查了信号在相空间中的局部可预测性和确定性，并提供了线性、非线性、确定性和随机信号性质的程度的度量。这将作为一个框架，分析信号处理和机器学习对信号性质的改变，并作为开发新的优化标准的基础，该标准将提供所需的量化性能，并将基本信号性质保持到所需的程度。Imperial的团队已经完成了与这一提议相关的概念性工作，但没有对潜在的状态空间特征进行严格的统计评估或相关性分析。拟议的研究将进行全面的测试，以增强对生物医学应用中使用的学习算法的质量性能的理解和洞察。这也将导致新的自适应学习算法的设计，能够在期望的范围内保持信号的性质，这是几个新兴应用中的关键问题。这些问题的解决方案为生物医学工程的进步开辟了新的可能性，这是帝国理工学院与来自德国的领先应用生物医学小组合作的研究提案的基础。

Signal modality characterisation, that is, the assessment of the linear, nonlinear, deterministics and stochastic signal content, is becoming an increasingly important area of multidisciplinary research. These ideas arose in Physics in the mid-1990s, however, the applications in machine learning and signal processing are only recently becoming apparent. As changes in the signal nature from, say, linear to nonlinear, can reveal e.g. health hazard, the signal processing framework should be chosen so as to preserve this critical information. However, standard learning algorithms are typically based on second order statistics, and will linearise naturally nonlinear phenomena.This proposal aims to provide a novel theoretical and computational framework for the design of learning algorithms with enhanced qualitative performance. Standard, second order statistics based adaptive filtering and machine learning algorithms are designed to optimise quantitative performance, and useful information is often lost. This type of problem arises typically in biomedical applications, for example, the change in the nature of brain electrical recordings from linear stochastic (ARMA) to nonlinear deterministic (chaotic) can indicate health hazard. The fundamental novelty of this work is a recently proposed, but not fully tested, delay vector variance (DVV) method which examines the local predictability and determinism of a signal in phase space, and provides a measure for the degree of linear, nonlinear, deterministic, and stochastic signal natures. This will serve as a framework to analyse the changes that signal processing and machine learning make to signal natures, and as a basis for the development of novel optimisation criteria which will both provide the required quantitative performance and preserve the fundamental signal nature to the desired degree. The team at Imperial have performed conceptual work related to this proposal, but no rigorous statistical evaluation or relavance analysis of the underlying state space features. The proposed research will perform comprehensive testing in order to provide enhanced understanding and insight into the qualitative peformance of learning algorithms used in biomedical applications. This will also lead to the design of novel adaptive learning algorithms capable of preserving the signal nature to a desired extent, a critical issue in several emerging applications.Solutions to these problems open new possibilities for advances in biomedical engineering, which underpins this research proposal, based at Imperial College and in collaboration with a leading applied biomedical group from Germany.