无需分布的随机分析与鲁棒多级向量场异常检测
Distribution-Free Stochastic Analysis and Robust Multilevel Vector Field Anomaly Detection
AI总结：
本文提出一种基于随机行为协方差结构的新型随机函数分析方法，用于多级向量场异常检测，通过多级正交函数子空间实现可靠假设检验，适用于复杂高维数据集。
摘要：
大规模向量场数据集在多光谱光学和雷达传感器等新兴领域中普遍存在。本文开发了一种新的随机函数（数据）分析方法，用于基于域内名义随机行为的协方差结构检测异常。最优向量场Karhunen-Loeve展开被应用于此类随机场数据。从域的几何结构构造了一系列多级正交函数子空间，借鉴了KL展开。通过检查随机场在多级基上的投影实现检测。该方法的关键特征是能够形成可靠的假设检验，而无需对数据的概率分布做出先验假设。该方法应用于亚马逊森林退化问题。由于卫星影像的复杂性和高维性，无法假设已知分布或估计它们。除了提供可靠的假设检验外，本文方法还展示了在向量化的复杂多波段数据中使用多个波段的优势，从而实现更好的异常检测。此外，通过模拟数据，本文方法能够检测到PCA方法无法检测到的细微异常。
英文摘要：
Massive vector field datasets are common in multi-spectral optical and radar sensors, among many other emerging areas of application. We develop a novel stochastic functional (data) analysis approach for detecting anomalies based on the covariance structure of nominal stochastic behavior across a domain. An optimal vector field Karhunen-Loeve expansion is applied to such random field data. A series of multilevel orthogonal functional subspaces is constructed from the geometry of the domain, adapted from the KL expansion. Detection is achieved by examining the projection of the random field on the multilevel basis. A critical feature of this approach is that reliable hypothesis tests are formed, which do not require prior assumptions on probability distributions of the data. The method is applied to the important problem of degradation in the Amazon forest. Due to the complexity and high dimensionality of satellite imagery, it is not feasible to assume known distributions, nor to estimate them. In addition to providing reliable hypothesis tests, our approach shows the advantage of using multiple bands of data in a vectorized complex, leading to better anomaly detection. Furthermore, using simulated data, our approach is capable of detecting subtle anomalies that are impossible to detect with PCA-based methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
