Biomedical Engineering Reference
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Fig. 5.8 Cross-sectional regression of shapes. Each patient is associated to a point in time (patient
age for instance). A regression model is derived from the temporal data
from that we can revert the problem to the desired form as a function of the shape
using canonical correlation analysis (CCA) to give a generative growth model of the
heart.
For this example we use body surface area (BSA) as the index of growth rather
than patient age to better represent the growth given the variable age at which
children enter puberty. We use the Dubois formula [ 5 ] to compute the BSA for
each patient:
BSA ( m 2 )=0 . 007184 × weight ( kg ) 0 . 425 × height ( cm ) 0 . 725 .
(5.7)
The pipeline we have just described for computing a generative growth model is
shown in Fig. 5.7 (bottom row).
5.3.3.1
Model Reduction Using Partial Least Squares Regression
As introduced in the previous section, regression using the partial least squares
regression (PLS) method is based on finding an optimal basis of the predictor
variables X that maximizes the variances of X and Y as well as their covariances.
The method can be considered as the optimal estimation of two weight vectors r
and s that satisfy
) 2 var
max
|r| = |s| =1
cov
(
Xr,Ys
)= max
|r| = |s| =1
var
(
Xr
)
corr
(
Xr,Y s
(
Ys
)
,
(5.8)
under the constraint that the regression between X and Y is optimal. Mathemati-
cally, the generative model is
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