56 citations · 135 across the 12 of their papers we have counts for
14 papers
Persistent Obstruction Theory for a Model Category of Measures with Applications to Data Merging
Abraham D. Smith, Paul Bendich, John Harer
Collections of measures on compact metric spaces form a model category ("data complexes"), whose morphisms are marginalization integrals. The fibrant objects in this category repre…
Multi-scale Geometric Summaries for Similarity-based Sensor Fusion
Christopher J. Tralie, Paul Bendich, John Harer
In this work, we address fusion of heterogeneous sensor data using wavelet-based summaries of fused self-similarity information from each sensor. The technique we develop is quite…
Geometric Cross-Modal Comparison of Heterogeneous Sensor Data
Christopher J. Tralie, Abraham Smith, Nathan Borggren +4
In this work, we address the problem of cross-modal comparison of aerial data streams. A variety of simulated automobile trajectories are sensed using two different modalities: ful…
Supervised Learning of Labeled Pointcloud Differences via Cover-Tree Entropy Reduction
Abraham Smith, Paul Bendich, John Harer +2
We introduce a new algorithm, called CDER, for supervised machine learning that merges the multi-scale geometric properties of Cover Trees with the information-theoretic properties…
Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology
Paul Bendich, Ellen Gasparovic, Christopher J. Tralie +1
We propose a flexible and multi-scale method for organizing, visualizing, and understanding datasets sampled from or near stratified spaces. The first part of the algorithm produce…
Multi-Scale Local Shape Analysis and Feature Selection in Machine Learning Applications
Paul Bendich, Ellen Gasparovic, John Harer +2
We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both g…