# Robust Projection based Anomaly Extraction (RPE) in Univariate Time-Series

arXiv: https://arxiv.org/abs/2205.15548 · HTML: https://mlsanity.com/paper/2205.15548/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 11 of 11)

- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Unsupervised Anomaly Detection via Variational Auto-Encoder for Seasonal KPIs in Web Applications](https://mlsanity.com/paper/1802.03903/) (2018)
- [Multivariate Time-series Anomaly Detection via Graph Attention Network](https://mlsanity.com/paper/2009.02040/) (2020)
- [Time-Series Anomaly Detection Service at Microsoft](https://mlsanity.com/paper/1906.03821/) (2019)
- [Anomaly Detection in Univariate Time-series: A Survey on the State-of-the-Art](https://mlsanity.com/paper/2004.00433/) (2020)
- [Fast, Robust and Non-convex Subspace Recovery](https://mlsanity.com/paper/1406.6145/) (2014)
- [Deep Generative model with Hierarchical Latent Factors for Time Series Anomaly Detection](https://mlsanity.com/paper/2202.07586/) (2022)
- [Coherence Pursuit: Fast, Simple, and Robust Principal Component Analysis](https://mlsanity.com/paper/1609.04789/) (2016)
- [Structured low-rank matrix completion for forecasting in time series analysis](https://mlsanity.com/paper/1802.08242/) (2018)
- [Online Matrix Completion and Online Robust PCA](https://mlsanity.com/paper/1503.03525/) (2015)
- [High Dimensional Low Rank plus Sparse Matrix Decomposition](https://mlsanity.com/paper/1502.00182/) (2015)

## Abstract (arXiv)

This paper presents a novel, closed-form, and data/computation efficient online anomaly detection algorithm for time-series data. The proposed method, dubbed RPE, is a window-based method and in sharp contrast to the existing window-based methods, it is robust to the presence of anomalies in its window and it can distinguish the anomalies in time-stamp level. RPE leverages the linear structure of the trajectory matrix of the time-series and employs a robust projection step which makes the algorithm able to handle the presence of multiple arbitrarily large anomalies in its window. A closed-form/non-iterative algorithm for the robust projection step is provided and it is proved that it can identify the corrupted time-stamps. RPE is a great candidate for the applications where a large training data is not available which is the common scenario in the area of time-series. An extensive set of numerical experiments show that RPE can outperform the existing approaches with a notable margin.