172 citations · 228 across the 24 of their papers we have counts for
27 papers
ReLU Neural Networks, Polyhedral Decompositions, and Persistent Homolog
Yajing Liu, Christina M Cole, Chris Peterson +1
A ReLU neural network leads to a finite polyhedral decomposition of input space and a corresponding finite dual graph. We show that while this dual graph is a coarse quantization o…
Sparse Linear Centroid-Encoder: A Convex Method for Feature Selection
Tomojit Ghosh, Michael Kirby, Karim Karimov
We present a novel feature selection technique, Sparse Linear Centroid-Encoder (SLCE). The algorithm uses a linear transformation to reconstruct a point as its class centroid and,…
Feature Selection using Sparse Adaptive Bottleneck Centroid-Encoder
Tomojit Ghosh, Michael Kirby
We introduce a novel nonlinear model, Sparse Adaptive Bottleneck Centroid-Encoder (SABCE), for determining the features that discriminate between two or more classes. The algorithm…
Yet Another Algorithm for Supervised Principal Component Analysis: Supervised Linear Centroid-Encoder
Tomojit Ghosh, Michael Kirby
We propose a new supervised dimensionality reduction technique called Supervised Linear Centroid-Encoder (SLCE), a linear counterpart of the nonlinear Centroid-Encoder (CE) \citep{…
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…