Multi-scale local shape analysis and feature selection in machine learning applications

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2015-09-28

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Abstract

© 2015 IEEE.We introduce a method called multi-scale local shape analysis for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of granularity to capture diverse types of local information for subsequent machine learning algorithms operating on the dataset. Using synthetic and real dataset examples, we demonstrate significant performance improvement of classification algorithms constructed for these datasets with correspondingly augmented features.

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10.1109/IJCNN.2015.7280428

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Bendich, P, E Gasparovic, J Harer, R Izmailov and L Ness (2015). Multi-scale local shape analysis and feature selection in machine learning applications. Proceedings of the International Joint Conference on Neural Networks, 2015-September. 10.1109/IJCNN.2015.7280428 Retrieved from https://hdl.handle.net/10161/12014.

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Scholars@Duke

Bendich

Paul L Bendich

Research Professor of Mathematics

I am a mathematician whose main research focus lies in adapting theory from ostensibly pure areas of mathematics, such as topology, geometry, and abstract algebra, into tools that can be broadly used in many data-centered applications.

My initial training was in a recently-emerging field called topological data analysis (TDA). I have been responsible for several essential and widely-used elements of its theoretical toolkit, with a particular focus on building TDA methodology for use on stratified spaces. Some of this work involves the creation of efficient algorithms, but much of it centers around theorem-proof mathematics, using proof techniques not only from algebraic topology, but also from computational geometry, from probability, and from abstract algebra.

Recently, I have done foundational work on TDA applications in several areas, including to neuroscience, to multi-target tracking, to multi-modal data fusion, and to a probabilistic theory of database merging. I am also becoming involved in efforts to integrate TDA within deep learning theory and practice.

I typically teach courses that connect mathematical principles to machine learning, including upper-level undergraduate courses in topological data analysis and more general high-dimensional data analysis, as well as a sophomore level course (joint between pratt and math) that serves as a broad introduction to machine learning and data analysis concepts.

Harer

John Harer

Professor Emeritus of Mathematics

Professor Harer's primary research is in the use of geometric, combinatorial and computational techniques to study a variety of problems in data analysis, shape recognition, image segmentation, tracking, cyber security, ioT, biological networks and gene expression.


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