Elvira Romano

Clustering Spatio-functional data: a model based approach

In many environmental sciences, such as, in agronomy, in metereology, in oceanography, data analysis has to take into account both spatial and functional components. In this paper we present a strategy for clustering spatio-functional data. The proposed methodology is based on concepts of spatial statistics theory, such as variogram and covariogram when data are curves. Moreover a summarizing spatio-functional model for each cluster is obtained. The assessment of the method is carried out with a study on real data.

Adaptive monitoring of marine disasters with intelligent mobile sensor networks

Accidents and sabotages are kinds of environmental disasters that constitute a growing threat to marine ecosystems. Recent events disclosed to the public audience the importance of developing methodologies and systems that can accurately and continuously monitor such events. Sensor networks have been successfully applied to early warning and environmental monitoring both in terrestrial and marine contexts. In this paper we propose an architecture for continuous monitoring of marine disasters. After the detection of suspect substances in a sea area by means of its concentration in water, the first goal of this approach is to follow the contour of actual affected area by means of reconfigurable sensor networks and a centralized intelligent system. Such systems are able to estimate substance concentrations (functions that variate in space and time) by means of advanced geostatistical techniques, mobile sensor devices and evolutionary computing.

Advances in spatial functional statistics

This is the editorial letter for the special issue dedicated to Spatial Functional Statistics, motivated by the joint VII International Workshop on Spatio-temporal Modelling (METMAVII) and the 2014 meeting of the research group for Statistical Applications to Environmental Problems (GRASPA14), which took place in Turin (Italy) from 10 to 12 September 2014. This special issue summarises and discusses peer-reviewed contributions related to the analysis of functional data showing complex characteristics such as spatial dependence structures. The selection of papers comprises both new methodological proposals and a wide range of applications. In particular, we cover a wide range of statistical aspects, comprising prediction of functional data with spatial dependence, optimal sampling designs using functional covariates, non-parametric clustering methods for dependent functional data, and depth measures for spatially dependent functional data.

A Regionalization Method for Spatial Functional Data Based on Variogram Models: An Application on Environmental Data

This chapter proposes a Dynamic Clustering Algorithm (DCA) as a new regionalization method for spatial functional data. The method looks for the best partition optimizing a criterion of spatial association among functional data. Furthermore it is such that a summary of the variability structure of each cluster is discovered. The performance of the proposal is checked through an application on real data.

Spatial functional normal mixed effect approach for curve classification

This paper proposes a spatial functional formulation of the normal mixed effect model for the statistical classification of spatially dependent Gaussian curves, in both parametric and state space model frameworks. Fixed effect parameters are represented in terms of a functional multiple regression model whose regression operators can change in space. Local spatial homogeneity of these operators is measured in terms of their Hilbert–Schmidt distances, leading to the classification of fixed effect curves in different groups. Assuming that the Gaussian random effect curves obey a spatial autoregressive dynamics of order one [SARH(1) dynamics], a second functional classification criterion is proposed in order to detect local spatially homogeneous patterns in the mean quadratic functional variation of Gaussian random effect curve increments. Finally, the two criteria are combined to detect local spatially homogeneous patterns in the regression operators and in the functional mean quadratic variation, under a state space approach. A real data example in the financial context is analyzed as an illustration.

Modified half-region depth for spatially dependent functional data

In this paper, we address the problem of getting order statistics for georeferenced functional data by means of depth functions. To reach this aim, we introduce the concept of spatial dispersion function for functional data in a specific location of the geographic space. Then we generalize the notion of modified half-region depth to spatial dispersion functions. Through the use of spatial dispersion functions we show how the data ordering criterion depends not only on the functional but also on the spatial component. The proposal is applied to two wide simulation studies and to real data coming from sensors.

Spatial variability clustering for spatially dependent functional data

This paper introduces a method for clustering spatially dependent functional data. The idea is to consider the contribution of each curve to the spatial variability. Thus, we define a spatial dispersion function associated to each curve and perform a k-means like clustering algorithm. The algorithm is based on the optimization of a fitting criterion between the spatial dispersion functions associated to each curve and the representative of the clusters. The performance of the proposed method is illustrated by an application on real data and a simulation study.

Clustering Geostatistical Functional Data

In this paper, we among functional data. A first strategy aims to classify curves spatially dependent and to obtain a spatio-functional model prototype for each cluster. It is based on a Dynamic Clustering Algorithm with on an optimization problem that minimizes the spatial variability among the curves in each cluster. A second one looks simultaneously for an optimal partition of spatial functional data set and a set of bivariate functional regression models associated to each cluster. These models take into account both the interactions among different functional variables and the spatial relations among the observations.

Outlier Detection for Geostatistical Functional Data: An Application to Sensor Data

In this paper we propose an outlier detection method for geostatistical functional data. Our approach generalizes the functional proposal of Febrero et al. (Comput 5 Stat 22(3):411–427, 2007; Environmetrics 19(4):331–345, 2008) in the spatial framework. It is based on the concept of the kernelized functional modal depth that we have opportunely defined extending the functional modal depth. As an illustration, the methodology is applied to sensor data corresponding to long-term daily climatic time series from meteorological stations.

Clustering Spatially Correlated Functional Data

In this paper we discuss and compare two clustering strategies: a hierarchical clustering and a dynamic clustering method for spatially correlated functional data. Both the approaches aim to obtain clusters which are internally homogeneous in terms of their spatial correlation structure. With this scope they incorporate the spatial information into the clustering process by considering, in a different manner, a measure of spatial association ables to emphasize the average spatial dependence among curves: the trace-variogram function.