We approach the problem of semi-supervised shape classification by exploiting the geometric structure of shape data. We apply manifold regularization to learn a function from shapes to class labels. Central to manifold regularization algorithms is the use of a weighted graph to represent pairwise relationships between training points and capture their geometric structure. Under a regularized least squares formulation, each algorithm only involves solving a linear system of equations. We analyze the classification performance for different features regularization parameters, percentage of labeled data, and noise in the labels. We show that encouraging the smoothness of the classification function on the manifold improves classification performance beyond simply encouraging smoothness in the ambient space. We compare raw pixel features to Signed Distance Function (SDF) features and find that SDF features yield consistently higher accuracy. Finally, we compare manifold regularization to the much simpler k-Nearest-Neighbors and show that manifold regularization is consistently better.
Keywords: shape classification, manifold regularization, semi-supervised learning.