A statistical test for anomaly detection using the reconstruction error of the Kernel PCA

Chloé Friguet (1) , Laetitia Chapel (2)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
2 OBELIX - Environment observation with complex imagery

A 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 is presented. Its test statistic is based on the distance between a query point mapped in a feature space and its projection on the eigen-structure of the kernel matrix computed on the sample points. The statistical test is shown to be uniformly most powerful for a given false alarm level $\alpha$ when the alternative density is uniform over the support of the null distribution. The computational performances of the procedure are assessed as 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 regarding both type-I and type-II errors w.r.t. competing methods.

Domaines: Statistiques [stat]; Machine Learning [stat.ML]

Chloé Friguet, Laetitia Chapel. A statistical test for anomaly detection using the reconstruction error of the Kernel PCA. Computational and Methodological Statistics (CMstatistics), ERCIM work group, Dec 2015, Londres, United Kingdom. ⟨hal-01256506⟩