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Activity Number: 294 - SPEED: Statistical Learning and Data Science Speed Session 2, Part 1
Type: Contributed
Date/Time: Tuesday, July 30, 2019 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Learning and Data Science
Abstract #304613 Presentation 1 Presentation 2 Presentation 3
Title: Aggregated Pairwise Classification of Statistical Shapes
Author(s): Min Ho Cho*
Companies: The Ohio State University
Keywords: Dimension reduction; LDA; Naive Bayes; Pairwise classification; Projection point; QDA

The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision. While many statistical frameworks have been developed for the classification problem, most are strongly tied to early formulations of the problem - with an object to be classified described as a vector in a relatively low-dimensional Euclidean space. Statistical shape data have two main properties that suggest a need for a novel approach: (i) shapes are inherently infinite dimensional with strong dependence among the positions of nearby points, and (ii) shape space is not Euclidean, but is fundamentally curved. To accommodate these features of the data, we work with the square-root velocity function of the curves to provide a useful formal description of the shape, pass to tangent spaces of the manifold of shapes at different projection points which effectively separate shapes for pairwise classification in the training data, and use principal components within these tangent spaces to reduce dimensionality. We illustrate the impact of the projection point and choice of subspace on the misclassification rate with a novel method of combining pairwise classifiers.

Authors who are presenting talks have a * after their name.

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