A spatio-temporal model based on the SVD to analyze large spatio-temporal datasets

Rossella Onorati

Risultato della ricerca: Other

Abstract

A common problem in the analysis of space-time data is to compress a large dataset in order to extract the underlying trends. Empirical orthogonal function (EOF) analysis is a useful tool for examining both the temporal and the spatial variation in atmospherical and physical process and a convenient method of performing this is the Singular Value Decomposition (SVD). Many spatio-temporal models for measurements Z(s; t) at location s at time t, can be written as a sum of a systematic component and a residual component: Z = M+E, where Z, M and E are all T x N matrices. Our approach permits modeling ofincomplete data matrices using an "EM-like" iterative algorithm for the SVD. We model the trend, M, by linear combinations of smooth temporal basis functions derived from left (temporal) singular vectors of the SDV of Z with dimension of the model chosen by cross-validation. We further decompose by SVD the spatio-temporal residual matrix E computed as residuals from regressions at each site (column) of the observations on the smoothed temporal basis functions. Finally we fit an autoregressive model to the columns (time series) of residuals from the SVD of E. Our aim is to illustrate a simple model to characterize trends and model the variability in large spatio-temporal data matrices. The methodology is demostrated with a spatiotemporal dataset.
Lingua originaleEnglish
Numero di pagine1
Stato di pubblicazionePublished - 2009
Pubblicato esternamenteYes

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decomposition
matrix
spatial variation
time series
methodology
modeling
trend

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A spatio-temporal model based on the SVD to analyze large spatio-temporal datasets. / Onorati, Rossella.

2009.

Risultato della ricerca: Other

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abstract = "A common problem in the analysis of space-time data is to compress a large dataset in order to extract the underlying trends. Empirical orthogonal function (EOF) analysis is a useful tool for examining both the temporal and the spatial variation in atmospherical and physical process and a convenient method of performing this is the Singular Value Decomposition (SVD). Many spatio-temporal models for measurements Z(s; t) at location s at time t, can be written as a sum of a systematic component and a residual component: Z = M+E, where Z, M and E are all T x N matrices. Our approach permits modeling ofincomplete data matrices using an {"}EM-like{"} iterative algorithm for the SVD. We model the trend, M, by linear combinations of smooth temporal basis functions derived from left (temporal) singular vectors of the SDV of Z with dimension of the model chosen by cross-validation. We further decompose by SVD the spatio-temporal residual matrix E computed as residuals from regressions at each site (column) of the observations on the smoothed temporal basis functions. Finally we fit an autoregressive model to the columns (time series) of residuals from the SVD of E. Our aim is to illustrate a simple model to characterize trends and model the variability in large spatio-temporal data matrices. The methodology is demostrated with a spatiotemporal dataset.",
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N2 - A common problem in the analysis of space-time data is to compress a large dataset in order to extract the underlying trends. Empirical orthogonal function (EOF) analysis is a useful tool for examining both the temporal and the spatial variation in atmospherical and physical process and a convenient method of performing this is the Singular Value Decomposition (SVD). Many spatio-temporal models for measurements Z(s; t) at location s at time t, can be written as a sum of a systematic component and a residual component: Z = M+E, where Z, M and E are all T x N matrices. Our approach permits modeling ofincomplete data matrices using an "EM-like" iterative algorithm for the SVD. We model the trend, M, by linear combinations of smooth temporal basis functions derived from left (temporal) singular vectors of the SDV of Z with dimension of the model chosen by cross-validation. We further decompose by SVD the spatio-temporal residual matrix E computed as residuals from regressions at each site (column) of the observations on the smoothed temporal basis functions. Finally we fit an autoregressive model to the columns (time series) of residuals from the SVD of E. Our aim is to illustrate a simple model to characterize trends and model the variability in large spatio-temporal data matrices. The methodology is demostrated with a spatiotemporal dataset.

AB - A common problem in the analysis of space-time data is to compress a large dataset in order to extract the underlying trends. Empirical orthogonal function (EOF) analysis is a useful tool for examining both the temporal and the spatial variation in atmospherical and physical process and a convenient method of performing this is the Singular Value Decomposition (SVD). Many spatio-temporal models for measurements Z(s; t) at location s at time t, can be written as a sum of a systematic component and a residual component: Z = M+E, where Z, M and E are all T x N matrices. Our approach permits modeling ofincomplete data matrices using an "EM-like" iterative algorithm for the SVD. We model the trend, M, by linear combinations of smooth temporal basis functions derived from left (temporal) singular vectors of the SDV of Z with dimension of the model chosen by cross-validation. We further decompose by SVD the spatio-temporal residual matrix E computed as residuals from regressions at each site (column) of the observations on the smoothed temporal basis functions. Finally we fit an autoregressive model to the columns (time series) of residuals from the SVD of E. Our aim is to illustrate a simple model to characterize trends and model the variability in large spatio-temporal data matrices. The methodology is demostrated with a spatiotemporal dataset.

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UR - http://hdl.handle.net/10447/52889

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