A nonlinear mixed-effects model for simultaneous smoothing and registration of functional data

Rakêt, Lars Lau; Sommer, Stefan; Markussen, Bo

doi:10.1016/j.patrec.2013.10.018

Cited by 27 publications

(44 citation statements)

References 19 publications

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“…This estimation improves that of Raket et al . (), which used a pointwise estimation based on the inverse warp that ignored the amplitude variance of the curves.…”

Section: Estimationmentioning

confidence: 99%

“…The procedure is a multivariate extension of the estimation procedure that was described in Raket et al . (), however, with an improved estimation of fixed effects.…”

Section: Estimationmentioning

confidence: 99%

“…Instead we propose a maximum likelihood estimation procedure based on iterative local linearization (Lindstrom and Bates, 1990). The procedure is a multivariate extension of the estimation procedure that was described in Raket et al (2014), however, with an improved estimation of fixed effects.…”

Section: Estimationmentioning

confidence: 99%

“…The simultaneous inference in the model enables data-driven regularization of the magnitude of the shifts through the estimated variance parameters. The idea has been extended to more general warping functions that are modelled by polynomials (Gervini and Gasser, 2005;Rønn and Skovgaard, 2009), and lately also to include serially correlated noise within the observations of an individual curve (Raket et al, 2014). In addition to the data-driven regularization of the predicted random effects that is achieved through estimation of variance parameters, the use of likelihood-based inference naturally relates the discrete observation points and the underlying continuous model.…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous Inference for Misaligned Multivariate Functional Data

Olsen

Markussen

Rakêt

2018

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. We introduce a class of generally applicable models where warping effects are modelled through non‐linear transformation of latent Gaussian variables and systematic shape differences are modelled by Gaussian processes. To model cross‐covariance between sample co‐ordinates we propose a class of low dimensional cross‐covariance structures that are suitable for modelling multivariate functional data. We present a method for doing maximum likelihood estimation in the models and apply the method to three data sets. The first data set is from a motion tracking system where the spatial positions of a large number of body markers are tracked in three dimensions over time. The second data set consists of longitudinal height and weight measurements for Danish boys. The third data set consists of three‐dimensional spatial hand paths from a controlled obstacle avoidance experiment. We use the method to estimate the cross‐covariance structure and use a classification set‐up to demonstrate that the method outperforms state of the art methods for handling misaligned curve data.

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“…This estimation improves that of Raket et al . (), which used a pointwise estimation based on the inverse warp that ignored the amplitude variance of the curves.…”

Section: Estimationmentioning

confidence: 99%

“…The procedure is a multivariate extension of the estimation procedure that was described in Raket et al . (), however, with an improved estimation of fixed effects.…”

Section: Estimationmentioning

confidence: 99%

Section: Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simultaneous Inference for Misaligned Multivariate Functional Data

Olsen

Markussen

Rakêt

2018

Journal of the Royal Statistical Society Series C: Applied Statistics

Self Cite

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“…This sequential approach to fitting model (2) seems to work well when the observed data arise from smooth curves possessing a common set of clearly recognizable features. However, as pointed out by Rakêt, Sommer and Markussen (2014), the pre-smoothing step can be problematic for noisy data. In this case an individual curve's data might be overfitted, resulting in a "bumpy" curve with fictitious features being used in the subsequent alignment.…”

Section: Introductionmentioning

confidence: 99%

Model-based curve registration via stochastic approximation EM algorithm

Heckman

2019

Computational Statistics & Data Analysis

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Functional data often exhibit both amplitude and phase variation around a common base shape, with phase variation represented by a so called warping function. The process of removing phase variation by curve alignment and inference of the warping functions is referred to as curve registration. When functional data are observed with substantial noise, model-based methods can be employed for simultaneous smoothing and curve registration. However, the nonlinearity of the model often renders the inference computationally challenging. In this paper, we propose an alternative method for model-based curve registration which is computationally more stable and efficient than existing approaches in the literature. We apply our method to the analysis of elephant seal dive profiles and show that more intuitive groupings can be obtained by clustering on phase variations via the predicted warping functions.; revised 18 December 2017. arXiv:1712.07265v2 [stat.ME]

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Bayesian Registration of Functions

Matuk

Herbei

Kurtek

2021

Wiley StatsRef: Statistics Reference Online

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We present an overview of Bayesian registration of functions. We begin with a general introduction to functional data analysis and the problem of function registration. We then proceed to describe the registration problem in detail mathematically and introduce basic ingredients of a Bayesian model for function registration. These ingredients are then elaborated on for three popular methods in the literature, and their performance is assessed empirically on two simulated and two real datasets.

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A nonlinear mixed-effects model for simultaneous smoothing and registration of functional data

Cited by 27 publications

References 19 publications

Simultaneous Inference for Misaligned Multivariate Functional Data

Simultaneous Inference for Misaligned Multivariate Functional Data

Model-based curve registration via stochastic approximation EM algorithm

Bayesian Registration of Functions

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