Stochastic Functional Analysis and Multilevel Vector Field Anomaly Detection
This work addresses anomaly detection in complex vector field data for applications like environmental monitoring, though it appears incremental as it builds on existing stochastic analysis techniques.
The paper tackles the problem of detecting anomalies in massive vector field datasets, such as deforestation in the Amazon, by developing a stochastic functional analysis method that uses a multilevel orthogonal basis derived from a Karhunen-Loeve expansion, resulting in improved detection beyond scalar-based methods.
Massive vector field datasets are common in multi-spectral optical and radar sensors, among many other emerging areas of application. In this paper 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. In addition, reliable hypothesis tests are formed that do not require prior assumptions on probability distributions of the data. The method is applied to the important problem of deforestation and degradation in the Amazon forest. This is a complex non-monotonic process, as forests can degrade and recover. Using multi-spectral satellite data from Sentinel-2, the multilevel filter is constructed and anomalies are treated as deviations from the initial state of the forest. Forest anomalies are quantified with robust hypothesis tests. Our approach shows the advantage of using multiple bands of data in a vectorized complex, leading to better anomaly detection beyond the capabilities of scalar-based methods.