Smoothing spatio-temporal data with complex missing data patterns

Arnone, Eleonora; Sangalli, Laura M.; Vicini, Andrea

doi:10.1177/1471082x211057959

Cited by 6 publications

(3 citation statements)

References 63 publications

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“…This avoids removing much of the data variability in the mean, and bypasses the problem raised by spatio-temporal locations (p i , t j ) for which there is no observation available, for any statistical units. To compute a smooth estimate of the mean spatio-temporal temperature field, we use the smoothing method described in (Arnone et al 2022) and implemented in the R package fdaPDE ). The estimate is obtained using the triangulation shown in the left panel of Fig.…”

Section: Discussionmentioning

confidence: 99%

“…The L functions are evaluated on a regular grid of 15 × 15 points over the spatial domain [0, 1] 2 and at 15 equidistant time points over the temporal domain [0, 1]. Finally, data are obtained adding to each x l (p i , t j ) uncorrelated Gaussian errors two different missing data settings: an independent censoring in space and time, obtained as in the censoring scheme (a) of Arnone et al (2022); a dependent censoring in space and time, in which data might be missing for large regions of the spatiotemporal domain, obtained as in the censoring scheme (d) of Arnone et al (2022). Figure 3 shows the profile of a sparsely observed space-time signal, resulting from an independent censoring in space and time.…”

Section: Data Generationmentioning

confidence: 99%

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Functional principal component analysis for incomplete space–time data

Palummo,

Arnone,

Formaggia

et al. 2024

Environ Ecol Stat

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Environmental signals, acquired, e.g., by remote sensing, often present large gaps of missing observations in space and time. In this work, we present an innovative approach to identify the main variability patterns, in space–time data, when data may be affected by complex missing data structures. We formalize the problem in the framework of functional data analysis, proposing an innovative method of functional principal component analysis (fPCA) for incomplete space–time data. The functional nature of the proposed method permits to borrow information from measurements observed at nearby spatio-temporal locations. The resulting functional principal components are smooth fields over the considered spatio-temporal domain, and can lead to interesting insights in the spatio-temporal dynamic of the phenomenon under study. Moreover, they can be used to provide a reconstruction of the missing entries, also under severe missing data patterns. The proposed model combines a weighted rank-one approximation of the data matrix with a roughness penalty. We show that the estimation problem can be solved using a majorize–minimization approach, and provide a numerically efficient algorithm for its solution. Thanks to a discretization based on finite elements in space and B-splines in time, the proposed method can handle multidimensional spatial domains with complex shapes, such as water bodies with complicated shorelines, or curved spatial regions with complex orography. As shown by simulation studies, the proposed space–time fPCA is superior to alternative techniques for Principal Component Analysis with missing data. We further highlight the potentiality of the proposed method for environmental problems, by applying space–time fPCA to the study of the lake water surface temperature (LWST) of Lake Victoria, in Central Africa, starting from satellite measurements with large gaps. LWST is considered one of the fundamental indicators of how climate change is affecting the environment, and is recognized as an essential climate variable.

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Section: Discussionmentioning

confidence: 99%

Section: Data Generationmentioning

confidence: 99%

Functional principal component analysis for incomplete space–time data

Palummo,

Arnone,

Formaggia

et al. 2024

Environ Ecol Stat

Self Cite

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“…(2017), and Arnone et al. (2021), in the case of 2D planar domains, or a single penalty involving a time‐dependent PDE, as done for 2D planar domains by Arnone et al. (2019).…”

Section: Discussionmentioning

confidence: 99%

Analyzing Data in Complicated 3D Domains: Smoothing, Semiparametric Regression, and Functional Principal Component Analysis

et al. 2023

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In this work, we introduce a family of methods for the analysis of data observed at locations scattered in three‐dimensional (3D) domains, with possibly complicated shapes. The proposed family of methods includes smoothing, regression, and functional principal component analysis for functional signals defined over (possibly nonconvex) 3D domains, appropriately complying with the nontrivial shape of the domain. This constitutes an important advance with respect to the literature, because the available methods to analyze data observed in 3D domains rely on Euclidean distances, which are inappropriate when the shape of the domain influences the phenomenon under study. The common building block of the proposed methods is a nonparametric regression model with differential regularization. We derive the asymptotic properties of the methods and show, through simulation studies, that they are superior to the available alternatives for the analysis of data in 3D domains, even when considering domains with simple shapes. We finally illustrate an application to a neurosciences study, with neuroimaging signals from functional magnetic resonance imaging, measuring neural activity in the gray matter, a nonconvex volume with a highly complicated structure.

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Generalized Spatio-Temporal Regression with PDE Penalization

Arnone,

Cunial,

Sangalli

2023

Studies in Classification, Data Analysis, and Knowledge Organization

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We develop a novel generalised linear model for the analysis of data distributed over space and time. The model involves a nonparametric term 5, a smooth function over space and time. The estimation is carried out by the minimization of an appropriate penalized negative log-likelihood functional, with a roughness penalty on 5 that involves space and time differential operators, in a separable fashion, or an evolution partial differential equation. The model can include covariate information in a semi-parametric setting. The functional is discretized by means of finite elements in space, and B-splines or finite differences in time. Thanks to the use of finite elements, the proposed method is able to efficiently model data sampled over irregularly shaped spatial domains, with complicated boundaries. To illustrate the proposed model we present an application to study the criminality in the city of Portland, from 2015 to 2020.

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Smoothing spatio-temporal data with complex missing data patterns

Cited by 6 publications

References 63 publications

Functional principal component analysis for incomplete space–time data

Functional principal component analysis for incomplete space–time data

Analyzing Data in Complicated 3D Domains: Smoothing, Semiparametric Regression, and Functional Principal Component Analysis

Generalized Spatio-Temporal Regression with PDE Penalization

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