Probabilistic Models for Nonlinear PCA, Transform Coding, and Fusion

9976452leen本项目扩展了以前在非线性主成分分析（PCA）的局部线性模型和全局非线性模型（如神经网络）混合方面的工作。涉及的应用领域包括转换编码、数据可视化和传感器融合，最初的重点是图像处理。理论重点是在生成（概率）模型方面确保算法的基础。有待探索的应用包括传感器融合，以提高机场无线电的质量，以及视频数据压缩，以提高互联网视频通信等系统的性能。一类包含潜在的、未观察到的变量和概率映射到观测数据空间的约束混合模型具有合适的性质；它们自然地表达非线性主成分，并在适当的范围内包含混合或局部线性主成分（以及标准主成分）。因此，这些模型可以作为与非线性PCA相关的编码、可视化和融合算法背后的组织焦点。这个项目将发展这些模型，它们的理论属性，拟合和正则化它们的艺术，以及它们在编码和可视化中的应用。该模型能够表达数据的簇结构和曲面模型，因此非常适合于可视化。这种概率模型有助于阐明非线性主成分分析与独立成分分析（ICA）之间的其他关系

9976452LeenThis project extends previous work on mixtures of local linear models, and global nonlinear models (e.g. neural networks) for nonlinear principal component analysis (PCA). The application domains addressed include transform coding, data visualization, and sensor fusion, with initial focus on image processing. Theoretical focus is on securing a foundation for the algorithms in terms of generative (probabilistic) models. Applications to be explored include sensor fusion to improve the quality of airport radio, and video data compression to improve the performance at systems like Internet video communications.A class of constrained mixture models that incorporate latent, unobserved variables together with probabilistic maps int0 observed data space has suitable properties; they naturally express nonlinear PCA, and they contain mixture, or local linear PCA (as well as standard PCA) in appropriate limits. Hence these models can serve as an organizing focus behind algorithms for coding, visualization, and fusion that are related to nonlinear PCA.This project will develop these models, their theoretical properties, the art of fitting and regularizing them, and their application to coding and visualization. The models are capable of expressing, both cluster structure, and curved surface models of data, and are thus well suited for visualization. Such probabilistic models can help illuminate other relation between nonlinear PCA and independent component analysis (ICA).***