论文标题
使用Riemannian几何形状和化学工程应用的数据分析
Data Analysis using Riemannian Geometry and Applications to Chemical Engineering
论文作者
论文摘要
我们探索了Riemannian几何形状中的工具用于分析对称阳性矩阵（SPD）的分析。 SPD矩阵是一种多功能数据表示，通常用于化学工程（例如协方差/相关/Hessian矩阵和图像），并且有强大的技术可用于其分析（例如，主要成分分析）。激励这项工作的关键观察是，SPD矩阵生活在Riemannian歧管上，实施利用此基本属性的技术可以在以数据为中心的任务中产生重大好处，例如分类和降低维度。我们通过几个案例研究在过程监测和图像分析的背景下进行异常检测来证明这一点。
We explore the use of tools from Riemannian geometry for the analysis of symmetric positive definite matrices (SPD). An SPD matrix is a versatile data representation that is commonly used in chemical engineering (e.g., covariance/correlation/Hessian matrices and images) and powerful techniques are available for its analysis (e.g., principal component analysis). A key observation that motivates this work is that SPD matrices live on a Riemannian manifold and that implementing techniques that exploit this basic property can yield significant benefits in data-centric tasks such classification and dimensionality reduction. We demonstrate this via a couple of case studies that conduct anomaly detection in the context of process monitoring and image analysis.
