Fast Non-Linear Transforms for Coding and Detection

该项目将开发局部线性和网络模型，用于检测问题和转换编码。重点是主成分分析(PCA)的非线性扩展在这些领域的发展和适应。我们之前对非线性PCA(1，2，3)的研究表明，局部线性模型的计算速度更快，并且提供了比基于神经网络的非线性PCA更准确的编码。这项工作的一个主要目的是使我们的模型适应并应用于检测问题，以及快速最优变换编码。这项工作是故障检测在一定程度上建立在该领域最近使用的三层自联想神经网络(4，5)的基础上。在工作中，网络用于提供与正常系统行为相对应的数据模型。异常行为(故障)是指未能准确地对新数据建模。然而，三层自关联网络提供了一个非常原始的数据模型，本质上是一个PCA子空间模型。实际数据可以用一般的曲线流形更准确地表示，正如非线性主元分析所提供的那样，非线性主元分析将基于非线性主元分析的模型应用于基准数据集中的检测问题。本项目还将把非线性主元分析应用于变换编码。这是关于非线性和局部线性变换的工作的自然扩展。在上面讨论的检测范例中，使用PCA进行变换编码是次优的，因为真实数据没有被二阶统计量或子空间几何模型充分地建模。非线性主元分析能够检测和减少数据分量之间的高阶冗余，从而提供更紧凑的表示。对用于变换编码(例如，图像的)的非线性PCA算法的适应将提供优于从DCT或PCA变换编码获得的率失真曲线。

This project will develop local linear and network models for application to detection problems, and to transform coding. The focus is on the development and adaptation of nonlinear extensions of principal component analysis (PCA) to these domains. Our previous work on nonlinear PCA (1,2,3) showed that local linear models are faster to compute, and provide more accurate encodings that neural network-based nonlinear PCA. A major thrust of this work is adapting and applying our models to detection problems, and to fast optimal transform coding. The work is fault detection builds in part on the recent use of three-layer autoassociative neural networks in this realm (4,5). In work, networks are used to provide a model of data corresponding to normal system behavior. Abnormal behavior (faults) are the indicated by the failure to accurately model the new data. However three-layer autoassociateve networks provide a very crude model of data, essentially a PCA subspace model. Real data can be more accurately represented by generally curved manifolds, as provided by nonlinear PCA will apply models based on nonlinear PCA to detection problems form benchmark datasets. This project will also apply nonlinear PCA to transform coding. This a natural extension of the work on nonlinear, and local linear transforms. As in the detection paradigms discussed above, the use of PCA for transform coding is suboptimal because real data is not adequately modeled by second order statistics, or by subspace geometric models. Nonlinear PCA is able to detect and reduce higher-order redundancies between data components, thus providing more compact representations. Adaptation of nonlinear PCA algorithms for transform coding (e.g. of images) will provide rate distortion curves superior to those obtained form DCT or PCA transform codes.