Mahalanobis distance is a classical tool in multivariate analysis. We suggest here an extension of this concept to the case of functional data. More precisely, the proposed definition concerns those statistical problems where the sample data are real functions defined on a compact interval of the real line. The obvious difficulty for such a functional extension is the non-invertibility of the covariance operator in infinite-dimensional cases. Unlike other recent proposals, our definition is suggested and motivated in terms of the Reproducing Kernel Hilbert Space (RKHS) associated with the stochastic process that generates the data. The proposed distance is a true metric; it depends on a unique real smoothing parameter which is fully motivated in RKHS terms. Moreover, it shares some properties of its finite dimensional counterpart: it is invariant under isometries, it can be consistently estimated from the data and its sampling distribution is known under Gaussian models. An empirical study for two statistical applications, outliers detection and binary classification, is included. The results are quite competitive when compared to other recent proposals in the literature.

Network Management tasks are currently characterized by their diversity both in terms of the situations that must be faced and the data used to reach conclusions. This complex and changing context imposes diverse needs and restrictions that must be covered by management tools in order for them to be useful. In order to face current challenges, we propose the application of Functional Data Analysis (FDA) techniques in the different functional areas of Network Management. FDA can be applied to network data compression, definition of baselines, anomaly detection, or traffic classification as well as forecasting for network dimensioning.