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Found 23 papers, 3 papers with code
ReLU Neural Networks, Polyhedral Decompositions, and Persistent Homolog
A ReLU neural network leads to a finite polyhedral decomposition of input space and a corresponding finite dual graph.
Sparse Linear Centroid-Encoder: A Convex Method for Feature Selection
In the first step, we solve the linear Centroid-Encoder, a convex optimization problem over a matrix $A$.
Feature Selection using Sparse Adaptive Bottleneck Centroid-Encoder
During training, we update class centroids by taking the Hadamard product of the centroids and weights of the sparse layer, thus ignoring the irrelevant features from the target.
Yet Another Algorithm for Supervised Principal Component Analysis: Supervised Linear Centroid-Encoder
SLCE works by mapping the samples of a class to its class centroid using a linear transformation.
Hamming Similarity and Graph Laplacians for Class Partitioning and Adversarial Image Detection
Here, we investigate the potential for ReLU activation patterns (encoded as bit vectors) to aid in understanding and interpreting the behavior of neural networks.
Dual Graphs of Polyhedral Decompositions for the Detection of Adversarial Attacks
This paper illustrates how one can utilize the dual graph to detect and analyze adversarial attacks in the context of digital images.
The Flag Median and FlagIRLS
We provide evidence that the flag median is robust to outliers and can be used effectively in algorithms like Linde-Buzo-Grey (LBG) to produce improved clusterings on Grassmannians.
Sparse Centroid-Encoder: A Nonlinear Model for Feature Selection
The resulting algorithm, Sparse Centroid-Encoder (SCE), extracts discriminatory features in groups using a sparsity inducing $\ell_1$-norm while mapping a point to its class centroid.
Robust Feature Selection using Sparse Centroid-Encoder
We develop a sparse optimization problem for the determination of the total set of features that discriminate two or more classes.
Locally Linear Attributes of ReLU Neural Networks
The weights in the neural network determine a decomposition of the input space into convex polytopes and on each of these polytopes the network can be described by a single affine mapping.
The flag manifold as a tool for analyzing and comparing data sets
Subspace methods, utilizing Grassmann manifolds, have been a great aid in dealing with such variability.
Supervised Dimensionality Reduction and Visualization using Centroid-encoder
The Centroid-Encoder (CE) method is similar to the autoencoder but incorporates label information to keep objects of a class close together in the reduced visualization space.
More chemical detection through less sampling: amplifying chemical signals in hyperspectral data cubes through compressive sensing
In this paper we explore a phenomenon in which bandwise CS sampling of a hyperspectral data cube followed by reconstruction can actually result in amplification of chemical signals contained in the cube.
A data-driven approach to sampling matrix selection for compressive sensing
We propose a method for defining an order for a sampling basis that is optimal with respect to capturing variance in data, thus allowing for meaningful sensing at any desired level of compression.
Monitoring the shape of weather, soundscapes, and dynamical systems: a new statistic for dimension-driven data analysis on large data sets
In this paper, we propose a new statistic that we call the $\kappa$-profile for analysis of large data sets.
Too many secants: a hierarchical approach to secant-based dimensionality reduction on large data sets
Intuitively, the SAP algorithm seeks to determine a projection which best preserves the lengths of all secants between points in a data set; by applying the algorithm to find the best projections to vector spaces of various dimensions, one may infer the dimension of the manifold of origination.
A GPU-Oriented Algorithm Design for Secant-Based Dimensionality Reduction
Dimensionality-reduction techniques are a fundamental tool for extracting useful information from high-dimensional data sets.
Endmember Extraction on the Grassmannian
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 feature.
A Roadmap for HEP Software and Computing R&D for the 2020s
Particle physics has an ambitious and broad experimental programme for the coming decades.
Computational Physics High Energy Physics - Experiment
Persistent Homology on Grassmann Manifolds for Analysis of Hyperspectral Movies
This realization has motivated the development of new tools such as persistent homology for exploring topological invariants, or features, in large data sets.
Persistence Images: A Stable Vector Representation of Persistent Homology
We convert a PD to a finite-dimensional vector representation which we call a persistence image (PI), and prove the stability of this transformation with respect to small perturbations in the inputs.
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Classification of Hyperspectral Imagery on Embedded Grassmannians
The resulting points on the Grassmannian have representations as orthonormal matrices and as such do not reside in Euclidean space in the usual sense.
Finding the Subspace Mean or Median to Fit Your Need
The extrinsic manifold mean, the L2-median, and the flag mean are alternative averages that can be substituted directly for the Karcher mean in many applications.
