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Recently, a great deal of research work has been devoted to the development of algorithms to estimate the intrinsic dimensionality (id) of a given dataset, that is the minimum number of parameters needed to represent the data without information loss. id estimation is important for the following reasons: the capacity and the generalization capability of discriminant methods depend on it; id is a necessary information for any dimensionality reduction technique; in neural network design the number of hidden units in the encoding middle layer should be chosen according to the id of data; the id value is strongly related to the model order in a time series, that is crucial to obtain reliable time series predictions.Although many estimation techniques have been proposed in the literature, most of them fail on noisy data, or compute underestimated values when the id is sufficiently high. In this paper, after reviewing some of the most important id estimators related to our work, we provide a theoretical motivation of the bias that causes the underestimation effect, and we present two id estimators based on the statistical properties of manifold neighborhoods, which have been developed in order to reduce this effect. We exhaustively evaluate the proposed techniques on synthetic and real datasets, by employing an objective evaluation measure to compare their performance with those achieved by state of the art algorithms; the results show that the proposed methods are promising, and produce reliable estimates also in the difficult case of datasets drawn from non-linearly embedded manifolds, characterized by high id.

Abstract. Most of the machine learning techniques suffer the "curse of dimensionality" effect when applied to high dimensional data. To face this limitation, a common preprocessing step consists in employing a dimensionality reduction technique. In literature, a great deal of research work has been devoted to the development of algorithms performing this task. Often, these techniques require as parameter the number of dimensions to be retained; to this aim, they need to estimate the "intrinsic dimensionality" of the given dataset, which refers to the minimum number of degrees of freedom needed to capture all the information carried by the data. Although many estimation techniques have been proposed, most of them fail in case of noisy data or when the intrinsic dimensionality is too high. In this paper we present a family of estimators based on the probability density function of the normalized nearest neighbor distance. We evaluate the proposed techniques on both synthetic and real datasets comparing their performances with those obtained by state of the art algorithms; the achieved results prove that the proposed methods are promising.

Analysis of ensemble forecasting strategies, which can provide a tangible backing for flood early warning procedures and mitigation measures over the Mediterranean region, is one of the fundamental motivations of the international HyMeX programme. Here, we examine two severe hydrometeorological episodes that affected the Milano urban area and for which the complex flood protection system of the city did not completely succeed. Indeed, flood damage have exponentially increased during the last 60 years, due to industrial and urban developments. Thus, the improvement of the Milano flood control system needs a synergism between structural and non-structural approaches. First, we examine how land-use changes due to urban development have altered the hydrological response to intense rainfalls. Second, we test a flood forecasting system which comprises the Flash-flood Event-based Spatially distributed rainfall-runoff Transformation, including Water Balance (FEST-WB) and the Weather Research and Forecasting (WRF) models. Accurate forecasts of deep moist convection and extreme precipitation are difficult to be predicted due to uncertainties arising from the numeric weather prediction (NWP) physical parameterizations and high sensitivity to misrepresentation of the atmospheric state; however, two hydrological ensemble prediction systems (HEPS) have been designed to explicitly cope with uncertainties in the initial and lateral boundary conditions (IC/LBCs) and physical parameterizations of the NWP model. No substantial differences in skill have been found between both ensemble strategies when considering an enhanced diversity of IC/LBCs for the perturbed initial conditions ensemble. Furthermore, no additional benefits have been found by considering more frequent LBCs in a mixed physics ensemble, as ensemble spread seems to be reduced. These findings could help to design the most appropriate ensemble strategies before these hydrometeorological extremes, given the computational cost of running such advanced HEPSs for operational purposes

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