172 citations · 228 across the 24 of their papers we have counts for
7 papers · 1 filter
Monitoring the shape of weather, soundscapes, and dynamical systems: a new statistic for dimension-driven data analysis on large data sets
Henry Kvinge, Elin Farnell, Michael Kirby +1
Dimensionality-reduction methods are a fundamental tool in the analysis of large data sets. These algorithms work on the assumption that the "intrinsic dimension" of the data is ge…
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 fractal dimension for measures via persistent homology
Henry Adams, Manuchehr Aminian, Elin Farnell +6
We use persistent homology in order to define a family of fractal dimensions, denoted for each homological dimension , assigned to a proba…
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…
Integral Invariants from Covariance Analysis of Embedded Riemannian Manifolds
Javier Álvarez-Vizoso, Michael Kirby, Chris Peterson
Principal Component Analysis can be performed over small domains of an embedded Riemannian manifold in order to relate the covariance analysis of the underlying point set with the…
Manifold Curvature Descriptors from Hypersurface Integral Invariants
Javier Álvarez-Vizoso, Michael Kirby, Chris Peterson
Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-…