FibeRed:
Fiberwise Dimensionality Reduction with vector bundles and characteristic classes
FibeRed is a dimensionality reduction algorithm for topologically complex data. It takes as input an initial map —e.g. a projection — from the data to a manifold embedded in a low-dimensional Euclidean space (computed with DREiMac, PCA, Isomap, Laplacian eigenmaps, etc). FibeRed applies dimensionality reduction to the fibers of this map, and assembles them in the normal bundle of the embedded manifold. Applications include the parametrization of molecular conformation spaces and energy landscapes.
DREiMac:
Dimensionality Reduction with Eilenberg-MacLane Coordinates
DREiMac is a topological dimensionality reduction algorithm. It transforms persistent cohomology classes of a data set, into maps to appropriate (classifying) Eilenberg-MacLane spaces (i.e. the circle, the n-torus, real/complex projective spaces and Lens spaces). These maps are designed to preserve the selected cohomology classes, and can be used to interpret persistent cohomology computations, parametrize the state space of dynamical systems and perform data visualization.
Adaptive Templates:
Machine learning with persistence diagrams
Templates Implements the tools developed in Approximating Continuous Functions on Persistence Diagrams Using Template Functions. The main goal is to extract machine learning features for persistence diagrams in a data-driven and adaptive manner.
Video SW1PerS uses sliding window embeddings and persistent homology to detect recurrence (i.e. periodicity and quasiperiodicity) in videos. This is done automatically, without the need for tracking or surrogate 1-dimensional signals. Applications include laryngeal high-speed videoendoscopy and the synthesis of slow-motion videos from periodic low frame-rate recordings.
Video-SW1PerS:
(Quasi)Periodicity detection in recurrent videos
SW1PerS:
Sliding Windows and 1-Persistence Scoring
SW1PerS is a Topological Data Analysis method for quantifying periodicity in time series data. This is done in a shape-agnostic manner and with resistance to damping. Applications include identification of periodic genes in biological organisms, detection of chatter in machining and manufacturing applications, as well as action classification from motion capture sensors.