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.