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

1 LMBA_UBS
LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
2 OBELIX - Environment observation with complex imagery
UBS - Université de Bretagne Sud, IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : 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.
Type de document :
Communication dans un congrès
Computational and Methodological Statistics (CMstatistics), Dec 2015, Londres, United Kingdom. CMStatistics 2015, 2015, <http://cmstatistics.org/CMStatistics2015/index.php>
Domaine :

https://hal.archives-ouvertes.fr/hal-01256506
Contributeur : Chloé Friguet <>
Soumis le : jeudi 14 janvier 2016 - 23:36:35
Dernière modification le : vendredi 17 février 2017 - 16:10:59

### Identifiants

• HAL Id : hal-01256506, version 1

### Citation

Chloé Friguet, Laetitia Chapel. A statistical test for anomaly detection using the reconstruction error of the Kernel PCA. Computational and Methodological Statistics (CMstatistics), Dec 2015, Londres, United Kingdom. CMStatistics 2015, 2015, <http://cmstatistics.org/CMStatistics2015/index.php>. <hal-01256506>

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