Curve prediction and clustering with mixtures of Gaussian process functional regression models |
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Authors: | J Q Shi B Wang |
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Institution: | (1) School of Mathematics and Statistics, University of Newcastle, Newcastle, NE1 7RU, UK;(2) Department of Mathematics, University of York, York, YO10 5DD, UK |
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Abstract: | Shi, Wang, Murray-Smith and Titterington (Biometrics 63:714–723, 2007) proposed a Gaussian process functional regression (GPFR)
model to model functional response curves with a set of functional covariates. Two main problems are addressed by their method:
modelling nonlinear and nonparametric regression relationship and modelling covariance structure and mean structure simultaneously.
The method gives very good results for curve fitting and prediction but side-steps the problem of heterogeneity. In this paper
we present a new method for modelling functional data with ‘spatially’ indexed data, i.e., the heterogeneity is dependent
on factors such as region and individual patient’s information. For data collected from different sources, we assume that
the data corresponding to each curve (or batch) follows a Gaussian process functional regression model as a lower-level model,
and introduce an allocation model for the latent indicator variables as a higher-level model. This higher-level model is dependent
on the information related to each batch. This method takes advantage of both GPFR and mixture models and therefore improves
the accuracy of predictions. The mixture model has also been used for curve clustering, but focusing on the problem of clustering
functional relationships between response curve and covariates, i.e. the clustering is based on the surface shape of the functional
response against the set of functional covariates. The model is examined on simulated data and real data. |
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Keywords: | Curve clustering Curve prediction Functional data analysis Gaussian process Gaussian process functional regression model Allocation model Batch data |
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