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Activity Number: 341 - SPEED: Classification and Data Science
Type: Contributed
Date/Time: Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #328853 Presentation
Title: Aggregated Pairwise Classification of Statistical Shapes with Optimal Points of Projection
Author(s): Min Ho Cho* and Sebastian Kurtek and Steve MacEachern
Companies: The Ohio State University and The Ohio State University and The Ohio State University
Keywords: Dimension reduction; Kernel product classifiers; LDA; Naive bayes; QDA; Statistical shapes

The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. 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 position of nearby points; (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 the dimensionality. We illustrate the impact of the projection point and choice of subspace on the misclassification rate with a method of combining pairwise classifiers.

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

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