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的研究（1,2,3）表明，局部线性模型比基于神经网络的非线性PCA计算速度更快，并且提供更准确的编码。这项工作的一个主要推力是适应和应用我们的模型来检测问题，并快速优化转换编码。故障检测部分建立在该领域最近使用的三层自关联神经网络（4,5）。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）是由于无法准确地对新数据建模而引起的。然而，三层自关联网络提供了一个非常粗糙的数据模型，本质上是一个PCA子空间模型。实际数据可以更准确地用一般的曲线流形表示，非线性主成分分析将基于非线性主成分分析的模型应用于基准数据集的检测问题。这个项目也将应用非线性PCA转换编码。这是对非线性和局部线性变换的自然推广。在上面讨论的检测范例中，使用PCA进行转换编码是次优的，因为真实数据没有被二阶统计量或子空间几何模型充分建模。非线性PCA能够检测和减少数据组件之间的高阶冗余，从而提供更紧凑的表示。将非线性PCA算法用于变换编码（例如图像）将提供优于DCT或PCA变换编码获得的速率失真曲线。

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.