3 citations · 5 across the 5 of their papers we have counts for
5 papers
Data Analysis using Riemannian Geometry and Applications to Chemical Engineering
Alexander Smith, Benjamin Laubach, Ivan Castillo +1
We explore the use of tools from Riemannian geometry for the analysis of symmetric positive definite matrices (SPD). An SPD matrix is a versatile data representation that is common…
The Euler Characteristic: A General Topological Descriptor for Complex Data
Alexander Smith, Victor Zavala
Datasets are mathematical objects (e.g., point clouds, matrices, graphs, images, fields/functions) that have shape. This shape encodes important knowledge about the system under st…
Reviews: Topological Distances and Losses for Brain Networks
Moo K. Chung, Alexander Smith, Gary Shiu
Almost all statistical and machine learning methods in analyzing brain networks rely on distances and loss functions, which are mostly Euclidean or matrix norms. The Euclidean or m…
Topological Data Analysis: Concepts, Computation, and Applications in Chemical Engineering
Alexander D. Smith, Pawel Dlotko, Victor M. Zavala
A primary hypothesis that drives scientific and engineering studies is that data has structure. The dominant paradigms for describing such structure are statistics (e.g., moments,…
On the Convergence of the Dynamic Inner PCA Algorithm
Sungho Shin, Alex D. Smith, S. Joe Qin +1
Dynamic inner principal component analysis (DiPCA) is a powerful method for the analysis of time-dependent multivariate data. DiPCA extracts dynamic latent variables that capture t…