172 citations · 228 across the 24 of their papers we have counts for
8 papers · 1 filter
Hamming Similarity and Graph Laplacians for Class Partitioning and Adversarial Image Detection
Huma Jamil, Yajing Liu, Turgay Caglar +4
Researchers typically investigate neural network representations by examining activation outputs for one or more layers of a network. Here, we investigate the potential for ReLU ac…
Dual Graphs of Polyhedral Decompositions for the Detection of Adversarial Attacks
Huma Jamil, Yajing Liu, Christina M. Cole +4
Previous work has shown that a neural network with the rectified linear unit (ReLU) activation function leads to a convex polyhedral decomposition of the input space. These decompo…
The flag manifold as a tool for analyzing and comparing data sets
Xiaofeng Ma, Michael Kirby, Chris Peterson
The shape and orientation of data clouds reflect variability in observations that can confound pattern recognition systems. Subspace methods, utilizing Grassmann manifolds, have be…
Too many secants: a hierarchical approach to secant-based dimensionality reduction on large data sets
Henry Kvinge, Elin Farnell, Michael Kirby +1
A fundamental question in many data analysis settings is the problem of discerning the "natural" dimension of a data set. That is, when a data set is drawn from a manifold (possibl…
A GPU-Oriented Algorithm Design for Secant-Based Dimensionality Reduction
Henry Kvinge, Elin Farnell, Michael Kirby +1
Dimensionality-reduction techniques are a fundamental tool for extracting useful information from high-dimensional data sets. Because secant sets encode manifold geometry, they are…
Endmember Extraction on the Grassmannian
Elin Farnell, Henry Kvinge, Michael Kirby +1
Endmember extraction plays a prominent role in a variety of data analysis problems as endmembers often correspond to data representing the purest or best representative of some fea…
Persistent Homology on Grassmann Manifolds for Analysis of Hyperspectral Movies
Sofya Chepushtanova, Michael Kirby, Chris Peterson +1
The existence of characteristic structure, or shape, in complex data sets has been recognized as increasingly important for mathematical data analysis. This realization has motivat…
Classification of Hyperspectral Imagery on Embedded Grassmannians
Sofya Chepushtanova, Michael Kirby
We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and u…