This thesis will focus on applying smoothing splines to magnetic resonance
image (MRI) analysis. Some additional work on support vector machine with
a hybrid loss function will be discussed.
We apply smoothing splines to both the structural MRI and functional MRI.
For the structural MRI, we t thin plate splines to overlapping blocks of the image
with different configurations of knots. The optimal configurations are found
by the generalized cross validation with a constant factor (Luo and Wahba,
1997). The tted splines with the optimal con gurations are then blended to
get a smoothed image of the brain. Thresholds are found along the way with
k-means algorithm and are blended as well. By thresholding the blended image
we obtained, we get the boundaries between gray matter, white matter, cerebrospinal uid, and others. The combination of smoothing and thresholding gives us very good results in terms of segmentation. 数据挖掘研究院
For the functional magnetic resonance image analysis, we propose a partial
spline model for the model fitting and hypothesis testing. Simulation are done
to test the theoretical properties of the model. It appears that the partial spline
model can compete with the commonly used smoothing+GLM paradigm.
A support vector machine with a new hybrid loss is studied in the thesis.
We propose a loss function that is a hybrid of the hinge loss and the logistic loss, with the aim to achieve the nice properties of these two loss functions, i.e.,
giving sparse solutions and being able to estimate the conditional probabilities
at the same time. Our results and theoretical derivation show that the new loss
function has the properties we expected and serves as a nice loss function for
classi cation as well.
