Anomaly detection with score functions based on the reconstruction error of the kernel PCA

Laetitia Chapel 1 Chloé Friguet 2
1 OBELIX - Environment observation with complex imagery
UBS - Université de Bretagne Sud, IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
2 LMBA_UBS
LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
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 f0. The resulting 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 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.
Type de document :
Communication dans un congrès
European Conference on Machine Learning (ECML PKDD), Sep 2014, Nancy, France. 8724, pp.227-241, 2014
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https://hal.archives-ouvertes.fr/hal-01061866
Contributeur : Laetitia Chapel <>
Soumis le : lundi 8 septembre 2014 - 16:20:56
Dernière modification le : mercredi 2 août 2017 - 10:09:09

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  • HAL Id : hal-01061866, version 1

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Laetitia Chapel, Chloé Friguet. Anomaly detection with score functions based on the reconstruction error of the kernel PCA. European Conference on Machine Learning (ECML PKDD), Sep 2014, Nancy, France. 8724, pp.227-241, 2014. 〈hal-01061866〉

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