# Distribution-Free Stochastic Analysis and Robust Multilevel Vector Field Anomaly Detection

arXiv: https://arxiv.org/abs/2207.06229 · HTML: https://mlsanity.com/paper/2207.06229/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 43 references that are in the map.
- First posted on arXiv 11 Jul 2022.

## Builds on (most cited first, 5 of 5)

- [Predicting 3D Human Dynamics from Video](https://mlsanity.com/paper/1908.04781/) (2019)
- [Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains](https://mlsanity.com/paper/1509.02029/) (2015)
- [High-dimensional functional time series forecasting: An application to age-specific mortality rates](https://mlsanity.com/paper/1810.01195/) (2018)
- [Stochastic tensor space feature theory with applications to robust machine learning](https://mlsanity.com/paper/2110.01729/) (2021)
- [Distribution-Free Detection of Structured Anomalies: Permutation and Rank-Based Scans](https://mlsanity.com/paper/1508.03002/) (2015)

## Built on by (most cited first, 1 of 1)

- [deFOREST: Fusing Optical and Radar satellite data for Enhanced Sensing of Tree-loss](https://mlsanity.com/paper/2510.14092/) (2025)

## Abstract (arXiv)

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.