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Found 10 papers, 4 papers with code
$O(k)$-Equivariant Dimensionality Reduction on Stiefel Manifolds
Then, we define a continuous and $O(k)$-equivariant map $\pi_\alpha$ that acts as a ``closest point operator'' to project the data onto the image of $V_k(\mathbb{R}^n)$ in $V_k(\mathbb{R}^N)$ under the embedding determined by $\alpha$, while minimizing distortion.
Learning on Persistence Diagrams as Radon Measures
Persistence diagrams are common descriptors of the topological structure of data appearing in various classification and regression tasks.
Toroidal Coordinates: Decorrelating Circular Coordinates With Lattice Reduction
The circular coordinates algorithm of de Silva, Morozov, and Vejdemo-Johansson takes as input a dataset together with a cohomology class representing a $1$-dimensional hole in the data; the output is a map from the data into the circle that captures this hole, and that is of minimum energy in a suitable sense.
FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundles
Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms.
Adaptive template systems: Data-driven feature selection for learning with persistence diagrams
The main conclusion of our analysis is that adaptive template systems, as a feature extraction technique, yield competitive and often superior results in the studied examples.
Approximating Continuous Functions on Persistence Diagrams Using Template Functions
Specifically, we begin by characterizing relative compactness with respect to the bottleneck distance, and then provide explicit theoretical methods for constructing compact-open dense subsets of continuous functions on persistence diagrams.
Topological Time Series Analysis
Time series are ubiquitous in our data rich world.
Algebraic Topology Computational Geometry
Twisty Takens: A Geometric Characterization of Good Observations on Dense Trajectories
In nonlinear time series analysis and dynamical systems theory, Takens' embedding theorem states that the sliding window embedding of a generic observation along trajectories in a state space, recovers the region traversed by the dynamics.
Dynamical Systems Computational Geometry Algebraic Topology 37M10, 37M05, 37N99 I.3.5; G.1.m
Chatter Classification in Turning Using Machine Learning and Topological Data Analysis
The features gleaned from the deterministic model are then utilized for characterization of chatter in a stochastic turning model where there are very limited analysis methods.
(Quasi)Periodicity Quantification in Video Data, Using Topology
This work introduces a novel framework for quantifying the presence and strength of recurrent dynamics in video data.
