# Shapley Values of Reconstruction Errors of PCA for Explaining Anomaly Detection

arXiv: https://arxiv.org/abs/1909.03495 · HTML: https://mlsanity.com/paper/1909.03495/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2019.

## Built on by (most cited first, 19 of 19)

- [A Survey on Explainable Anomaly Detection](https://mlsanity.com/paper/2210.06959/) (2022)
- [Utilizing XAI technique to improve autoencoder based model for computer network anomaly detection with shapley additive explanation(SHAP)](https://mlsanity.com/paper/2112.08442/) (2021)
- [Using Kernel SHAP XAI Method to optimize the Network Anomaly Detection Model](https://mlsanity.com/paper/2308.00074/) (2023)
- [Explainable Machine Learning for Fraud Detection](https://mlsanity.com/paper/2105.06314/) (2021)
- [Ensembles of Random SHAPs](https://mlsanity.com/paper/2103.03302/) (2021)
- [Unveiling the Unseen: A Comprehensive Survey on Explainable Anomaly Detection in Images and Videos](https://mlsanity.com/paper/2302.06670/) (2023)
- [An Imprecise SHAP as a Tool for Explaining the Class Probability Distributions under Limited Training Data](https://mlsanity.com/paper/2106.09111/) (2021)
- [Control-flow anomaly detection by process mining-based feature extraction and dimensionality reduction](https://mlsanity.com/paper/2502.10211/) (2025)
- [Explaining Anomalies using Denoising Autoencoders for Financial Tabular Data](https://mlsanity.com/paper/2209.10658/) (2022)
- [RESHAPE: Explaining Accounting Anomalies in Financial Statement Audits by enhancing SHapley Additive exPlanations](https://mlsanity.com/paper/2209.09157/) (2022)
- [Interpretable Ensembles of Hyper-Rectangles as Base Models](https://mlsanity.com/paper/2303.08625/) (2023)
- [AcME-AD: Accelerated Model Explanations for Anomaly Detection](https://mlsanity.com/paper/2403.01245/) (2024)
- [Enabling Efficient and Flexible Interpretability of Data-driven Anomaly Detection in Industrial Processes with AcME-AD](https://mlsanity.com/paper/2404.18525/) (2024)
- [Try with Simpler -- An Evaluation of Improved Principal Component Analysis in Log-based Anomaly Detection](https://mlsanity.com/paper/2308.12612/) (2023)
- [On Using the Shapley Value for Anomaly Localization: A Statistical Investigation](https://mlsanity.com/paper/2507.21023/) (2025)
- [RAMSeS: Robust and Adaptive Model Selection for Time-Series Anomaly Detection Algorithms](https://mlsanity.com/paper/2602.21766/) (2026)
- [Disjoint or Overlapping? Inference Windowing for Reconstruction-Based Time Series Anomaly Detection](https://mlsanity.com/paper/2606.09874/) (2026)
- [Statistical Analysis of using the Shapley Value for Sensor Anomaly Localization with Accurate Classifiers](https://mlsanity.com/paper/2606.00867/) (2026)
- [Witnesses Explain Anomalies](https://mlsanity.com/paper/2609.03826/) (2026)

## Abstract (arXiv)

We present a method to compute the Shapley values of reconstruction errors of principal component analysis (PCA), which is particularly useful in explaining the results of anomaly detection based on PCA. Because features are usually correlated when PCA-based anomaly detection is applied, care must be taken in computing a value function for the Shapley values. We utilize the probabilistic view of PCA, particularly its conditional distribution, to exactly compute a value function for the Shapely values. We also present numerical examples, which imply that the Shapley values are advantageous for explaining detected anomalies than raw reconstruction errors of each feature.