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06/20/2023
Topological Parallax: A Geometric Specification for Deep Perception Models
For safety and robustness of AI systems, we introduce topological parall...
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08/03/2022
A Convolutional Persistence Transform
We consider a new topological feauturization of d-dimensional images, ob...
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05/25/2022
Topological Simplification of Signals for Inference and Approximate Reconstruction
As Internet of Things (IoT) devices become both cheaper and more powerfu...
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06/14/2021
Improving Metric Dimensionality Reduction with Distributed Topology
We propose a novel approach to dimensionality reduction combining techni...
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01/28/2021
From Geometry to Topology: Inverse Theorems for Distributed Persistence
What is the "right" topological invariant of a large point cloud X? Prio...
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09/17/2020
A Fast and Robust Method for Global Topological Functional Optimization
Topological statistics, in the form of persistence diagrams, are a class...
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02/25/2020
Geometric Fusion via Joint Delay Embeddings
We introduce geometric and topological methods to develop a new framewor...
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10/10/2019
Graph Spectral Embedding for Parsimonious Transmission of Multivariate Time Series
We propose a graph spectral representation of time series data that 1) i...
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10/13/2018
Multi-scale Geometric Summaries for Similarity-based Sensor Fusion
In this work, we address fusion of heterogeneous sensor data using wavel...
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11/23/2017
Geometric Cross-Modal Comparison of Heterogeneous Sensor Data
In this work, we address the problem of cross-modal comparison of aerial...
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02/26/2017
Supervised Learning of Labeled Pointcloud Differences via Cover-Tree Entropy Reduction
We introduce a new algorithm, called CDER, for supervised machine learni...
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10/13/2014
Multi-Scale Local Shape Analysis and Feature Selection in Machine Learning Applications
We introduce a method called multi-scale local shape analysis, or MLSA, ...
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08/20/2010