# Unsupervised Anomaly and Change Detection with Multivariate Gaussianization

arXiv: https://arxiv.org/abs/2204.05699 · HTML: https://mlsanity.com/paper/2204.05699/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 12 Apr 2022.

## Builds on (most cited first, 8 of 8)

- [An Evaluation of Change Point Detection Algorithms](https://mlsanity.com/paper/2003.06222/) (2020)
- [Advances in Hyperspectral Image Classification: Earth monitoring with statistical learning methods](https://mlsanity.com/paper/1310.5107/) (2013)
- [Iterative Gaussianization: from ICA to Random Rotations](https://mlsanity.com/paper/1602.00229/) (2016)
- [Information Theory Measures via Multidimensional Gaussianization](https://mlsanity.com/paper/2010.03807/) (2020)
- [Gaussianizing the Earth: Multidimensional Information Measures for Earth Data Analysis](https://mlsanity.com/paper/2010.06476/) (2020)
- [Kernel Anomalous Change Detection for Remote Sensing Imagery](https://mlsanity.com/paper/2012.04920/) (2020)
- [Efficient Nonlinear RX Anomaly Detectors](https://mlsanity.com/paper/2012.05799/) (2020)
- [Information Theory in Density Destructors](https://mlsanity.com/paper/2012.01012/) (2020)

## Built on by (most cited first, 2 of 2)

- [Orthonormal Convolutions for the Rotation Based Iterative Gaussianization](https://mlsanity.com/paper/2206.03860/) (2022)
- [A Two-Stage Cascade for Near-Real-Time Forest Anomaly Detection from Sentinel-1 SAR Time Series](https://mlsanity.com/paper/2610.02763/) (2026)

## Abstract (arXiv)

Anomaly detection is a field of intense research. Identifying low probability events in data/images is a challenging problem given the high-dimensionality of the data, especially when no (or little) information about the anomaly is available a priori. While plenty of methods are available, the vast majority of them do not scale well to large datasets and require the choice of some (very often critical) hyperparameters. Therefore, unsupervised and computationally efficient detection methods become strictly necessary. We propose an unsupervised method for detecting anomalies and changes in remote sensing images by means of a multivariate Gaussianization methodology that allows to estimate multivariate densities accurately, a long-standing problem in statistics and machine learning. The methodology transforms arbitrarily complex multivariate data into a multivariate Gaussian distribution. Since the transformation is differentiable, by applying the change of variables formula one can estimate the probability at any point of the original domain. The assumption is straightforward: pixels with low estimated probability are considered anomalies. Our method can describe any multivariate distribution, makes an efficient use of memory and computational resources, and is parameter-free. We show the efficiency of the method in experiments involving both anomaly detection and change detection in different remote sensing image sets. Results show that our approach outperforms other linear and nonlinear methods in terms of detection power in both anomaly and change detection scenarios, showing robustness and scalability to dimensionality and sample sizes.