Anomaly Detection with Score Functions Based on the Reconstruction Error of the Kernel PCA
Abstract
We propose a novel non-parametric statistical test that allows the detection of anomalies given a set of (possibly high dimensional) sample points drawn from a nominal probability distribution. Our test statistic is the distance of a query point mapped in a feature space to its projection on the eigen-structure of the kernel matrix computed on the sample points. Indeed, the eigenfunction expansion of a Gram matrix is dependent on the input data density f _0. The resulting statistical test is shown to be uniformly most powerful for a given false alarm level α when the alternative density is uniform over the support of the null distribution. The algorithm can be computed in O ( n ^3 + n ^2) and testing a query point only involves matrix vector products. Our method is tested on both artificial and benchmarked real data sets and demonstrates good performances w.r.t. competing methods.
Cite
Text
Chapel and Friguet. "Anomaly Detection with Score Functions Based on the Reconstruction Error of the Kernel PCA." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2014. doi:10.1007/978-3-662-44848-9_15Markdown
[Chapel and Friguet. "Anomaly Detection with Score Functions Based on the Reconstruction Error of the Kernel PCA." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2014.](https://mlanthology.org/ecmlpkdd/2014/chapel2014ecmlpkdd-anomaly/) doi:10.1007/978-3-662-44848-9_15BibTeX
@inproceedings{chapel2014ecmlpkdd-anomaly,
title = {{Anomaly Detection with Score Functions Based on the Reconstruction Error of the Kernel PCA}},
author = {Chapel, Laetitia and Friguet, Chloé},
booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
year = {2014},
pages = {227-241},
doi = {10.1007/978-3-662-44848-9_15},
url = {https://mlanthology.org/ecmlpkdd/2014/chapel2014ecmlpkdd-anomaly/}
}