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06/30/2023
ReLU Neural Networks, Polyhedral Decompositions, and Persistent Homolog
A ReLU neural network leads to a finite polyhedral decomposition of inpu...
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06/07/2023
Sparse Linear Centroid-Encoder: A Convex Method for Feature Selection
We present a novel feature selection technique, Sparse Linear Centroid-E...
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06/07/2023
Feature Selection using Sparse Adaptive Bottleneck Centroid-Encoder
We introduce a novel nonlinear model, Sparse Adaptive Bottleneck Centroi...
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06/07/2023
Yet Another Algorithm for Supervised Principal Component Analysis: Supervised Linear Centroid-Encoder
We propose a new supervised dimensionality reduction technique called Su...
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05/02/2023
Hamming Similarity and Graph Laplacians for Class Partitioning and Adversarial Image Detection
Researchers typically investigate neural network representations by exam...
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11/23/2022
Dual Graphs of Polyhedral Decompositions for the Detection of Adversarial Attacks
Previous work has shown that a neural network with the rectified linear ...
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03/08/2022
The Flag Median and FlagIRLS
Finding prototypes (e.g., mean and median) for a dataset is central to a...
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01/30/2022
Sparse Centroid-Encoder: A Nonlinear Model for Feature Selection
We develop a sparse optimization problem for the determination of the to...
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11/30/2020
Locally Linear Attributes of ReLU Neural Networks
A ReLU neural network determines/is a continuous piecewise linear map fr...
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06/24/2020
The flag manifold as a tool for analyzing and comparing data sets
The shape and orientation of data clouds reflect variability in observat...
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02/27/2020
Supervised Dimensionality Reduction and Visualization using Centroid-encoder
Visualizing high-dimensional data is an essential task in Data Science a...
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06/27/2019
More chemical detection through less sampling: amplifying chemical signals in hyperspectral data cubes through compressive sensing
Compressive sensing (CS) is a method of sampling which permits some clas...
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06/20/2019
A data-driven approach to sampling matrix selection for compressive sensing
Sampling is a fundamental aspect of any implementation of compressive se...
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10/27/2018
Monitoring the shape of weather, soundscapes, and dynamical systems: a new statistic for dimension-driven data analysis on large data sets
Dimensionality-reduction methods are a fundamental tool in the analysis ...
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08/05/2018
Too many secants: a hierarchical approach to secant-based dimensionality reduction on large data sets
A fundamental question in many data analysis settings is the problem of ...
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07/10/2018
A GPU-Oriented Algorithm Design for Secant-Based Dimensionality Reduction
Dimensionality-reduction techniques are a fundamental tool for extractin...
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07/03/2018
Endmember Extraction on the Grassmannian
Endmember extraction plays a prominent role in a variety of data analysi...
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07/07/2016
Persistent Homology on Grassmann Manifolds for Analysis of Hyperspectral Movies
The existence of characteristic structure, or shape, in complex data set...
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02/03/2015
