2021
DOI: 10.1016/j.neuroimage.2021.117891
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Beyond linearity in neuroimaging: Capturing nonlinear relationships with application to longitudinal studies

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Cited by 9 publications
(9 citation statements)
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“…As the second derivative of a function is associated with its curvature or concavity, a positive second derivative corresponds to an upwardly concave, while a negative second derivative represents downward concavity. Thus, we control the smoothness or curvature of the HRF h ( t ) by tuning the following penalty term on the integrated square of its second derivative (Wood, 2017; Chen et al, 2021), The metric (4) is considered a natural measure of function smoothness (Wood, 2017), which can be expressed as a regularization process among all the spline weights excluding the first two (corresponding to baseline and linear trend, whose second derivatives are zero): ( β 2 , β 3 , …, β P ) . An example of the impact of this regularization on the original data (Fig.…”
Section: Estimating Population-level Hrf Through Smoothing Splinesmentioning
confidence: 99%
See 1 more Smart Citation
“…As the second derivative of a function is associated with its curvature or concavity, a positive second derivative corresponds to an upwardly concave, while a negative second derivative represents downward concavity. Thus, we control the smoothness or curvature of the HRF h ( t ) by tuning the following penalty term on the integrated square of its second derivative (Wood, 2017; Chen et al, 2021), The metric (4) is considered a natural measure of function smoothness (Wood, 2017), which can be expressed as a regularization process among all the spline weights excluding the first two (corresponding to baseline and linear trend, whose second derivatives are zero): ( β 2 , β 3 , …, β P ) . An example of the impact of this regularization on the original data (Fig.…”
Section: Estimating Population-level Hrf Through Smoothing Splinesmentioning
confidence: 99%
“…First, as the first two splines among the thin plates are overall mean and linearity (Fig. 2B), the penalty (4) on β is essentially an L 2 regularization imposed on those spline weights other than the first two elements, β 0 and β 1 (Wood, 2017; Chen et al, 2021). That is, the information is regularized across the nonlinear elements ( β 2 , β 3 , …, β P ) ′ .…”
Section: Estimating Population-level Hrf Through Smoothing Splinesmentioning
confidence: 99%
“…Therefore, domain adaptation should be well-suited to MRI data harmonization by creating features that are indiscriminate with respect to the scanner, but correctly discriminate with respect to the data features of interest such as case-control status, age, etc. (Chen et al, 2020b). Convolutional neural networks (CNN), which are popular and well-adapted to vision problems, have also been deployed for data harmonization with demonstrated success at age prediction, although CNN performance can be susceptible to registration related artifacts (Dinsdale et al, 2021).…”
Section: Discussionmentioning
confidence: 99%
“…6b ). Specifically, we adopted thin plate splines as basis functions in a multilevel model to adaptively accommodate the nonlinearity of each cross-layer profile 107 . The measurement uncertainty (standard error) of the VASO response was incorporated as part of the input in the model, which was numerically solved through the R package mgcv 108 to obtain the estimated cross-layer VASO profiles and their uncertainty bands.…”
Section: Methodsmentioning
confidence: 99%