Maseeh Mathematics + Statistics Colloquium Series presents: Separable Shape Tensors: Emerging Methods in Pattern Recognition

Speaker: Dr. Zachary Grey, NIST Information Technology Laboratory

Title: Separable Shape Tensors: Emerging Methods in Pattern Recognition

Abstract: Scientists often leverage image segmentation to extract shape ensembles containing thousands of curves representing patterns in measurements. Shape ensembles facilitate inferences about important changes when comparing and contrasting images---e.g., examining material microstructures. We introduce novel pattern recognition formalisms combined with inference methods over ensembles containing thousands of segmented curves. This is accomplished by accurately approximating eigenspaces of composite integral operators to motivate discrete, dual representations collocated at quadrature nodes. Approximations are projected onto underlying matrix manifolds and the resulting separable shape tensors constitute rigid-invariant decompositions of curves into generalized (linear) scale variations and complementary (nonlinear) undulations. With thousands of curves segmented from pairs of images, we demonstrate how data-driven features of separable shape tensors inform explainable binary classification utilizing a product maximum mean discrepancy; absent labeled data, building interpretable feature spaces in seconds without high performance computation, and detecting discrepancies below cursory visual inspections.

Biography: Zach is a staff applied mathematician in the Applied and Computational Mathematics Division within the Information Technology Laboratory at NIST - Boulder, CO. His research involves model-based dimension reduction and manifold learning for facilitating novel explanations and interpretations related to artificial intelligence and machine learning. Specifically, he often works with data-driven applications involving imaging/signal processing, geometry, and optimization.