# Label-Free Multivariate Time Series Anomaly Detection

arXiv: https://arxiv.org/abs/2312.11549 · HTML: https://mlsanity.com/paper/2312.11549/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 71 references that are in the map.
- First posted on arXiv 17 Dec 2023.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12571/) (2021)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [AnomalyCLIP: Object-agnostic Prompt Learning for Zero-shot Anomaly Detection](https://mlsanity.com/paper/2310.18961/) (2023)
- [LSTM-based Encoder-Decoder for Multi-sensor Anomaly Detection](https://mlsanity.com/paper/1607.00148/) (2016)
- [TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2201.07284/) (2022)
- [Same Same But DifferNet: Semi-Supervised Defect Detection with Normalizing Flows](https://mlsanity.com/paper/2008.12577/) (2020)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data](https://mlsanity.com/paper/1811.08055/) (2018)
- [Current Time Series Anomaly Detection Benchmarks are Flawed and are Creating the Illusion of Progress](https://mlsanity.com/paper/2009.13807/) (2020)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [DROCC: Deep Robust One-Class Classification](https://mlsanity.com/paper/2002.12718/) (2020)
- [Semi-Supervised Learning with Normalizing Flows](https://mlsanity.com/paper/1912.13025/) (2019)
- [Latent Outlier Exposure for Anomaly Detection with Contaminated Data](https://mlsanity.com/paper/2202.08088/) (2022)
- [LUNAR: Unifying Local Outlier Detection Methods via Graph Neural Networks](https://mlsanity.com/paper/2112.05355/) (2021)
- [Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series](https://mlsanity.com/paper/2202.07857/) (2022)

## Built on by (most cited first, 14 of 14)

- [Large Language Model Guided Knowledge Distillation for Time Series Anomaly Detection](https://mlsanity.com/paper/2401.15123/) (2024)
- [Deep Learning Advancements in Anomaly Detection: A Comprehensive Survey](https://mlsanity.com/paper/2503.13195/) (2025)
- [FreCT: Frequency-augmented Convolutional Transformer for Robust Time Series Anomaly Detection](https://mlsanity.com/paper/2505.00941/) (2025)
- [DACAD: Domain Adaptation Contrastive Learning for Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2404.11269/) (2024)
- [Deep Multi-Manifold Transformation Based Multivariate Time Series Fault Detection](https://mlsanity.com/paper/2405.16258/) (2024)
- [iADCPS: Time Series Anomaly Detection for Evolving Cyber-physical Systems via Incremental Meta-learning](https://mlsanity.com/paper/2504.04374/) (2025)
- [CAPMix: Robust KPI Anomaly Detection for AIOps in Noisy and Dynamic Environments](https://mlsanity.com/paper/2509.06419/) (2025)
- [Causal Disentanglement Learning for Accurate Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2510.11084/) (2025)
- [Multivariate Time Series Forecasting with Hybrid Euclidean-SPD Manifold Graph Neural Networks](https://mlsanity.com/paper/2512.14023/) (2025)
- [CGSTA: Cross-Scale Graph Contrast with Stability-Aware Alignment for Multivariate Time-Series Anomaly Detection](https://mlsanity.com/paper/2602.20468/) (2026)
- [Temporal-Conditioned Normalizing Flows for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2603.09490/) (2026)
- [VAN-AD: Visual Masked Autoencoder with Normalizing Flow For Time Series Anomaly Detection](https://mlsanity.com/paper/2603.26842/) (2026)
- [RagGAD: Rationale-Aware Conditional Gaussian Mixture Normalizing Flow for Unsupervised Graph Anomaly Detection](https://mlsanity.com/paper/2608.16018/) (2026)
- [Towards Robust Time Series Learning via Capacity-Centric Modulation](https://mlsanity.com/paper/2609.39489/) (2026)

## Abstract (arXiv)

Anomaly detection in multivariate time series (MTS) has been widely studied in one-class classification (OCC) setting. The training samples in OCC are assumed to be normal, which is difficult to guarantee in practical situations. Such a case may degrade the performance of OCC-based anomaly detection methods which fit the training distribution as the normal distribution. In this paper, we propose MTGFlow, an unsupervised anomaly detection approach for MTS anomaly detection via dynamic Graph and entity-aware normalizing Flow. MTGFlow first estimates the density of the entire training samples and then identifies anomalous instances based on the density of the test samples within the fitted distribution. This relies on a widely accepted assumption that anomalous instances exhibit more sparse densities than normal ones, with no reliance on the clean training dataset. However, it is intractable to directly estimate the density due to complex dependencies among entities and their diverse inherent characteristics. To mitigate this, we utilize the graph structure learning model to learn interdependent and evolving relations among entities, which effectively captures complex and accurate distribution patterns of MTS. In addition, our approach incorporates the unique characteristics of individual entities by employing an entity-aware normalizing flow. This enables us to represent each entity as a parameterized normal distribution. Furthermore, considering that some entities present similar characteristics, we propose a cluster strategy that capitalizes on the commonalities of entities with similar characteristics, resulting in more precise and detailed density estimation. We refer to this cluster-aware extension as MTGFlow_cluster. Extensive experiments are conducted on six widely used benchmark datasets, in which MTGFlow and MTGFlow cluster demonstrate their superior detection performance.