Sliding Windows and 1-Persistence Scoring

SW1PerS is a Topological Data Analysis method for quantifying periodicity in time series, in a shape-agnostic manner and with resistance to damping. The measurement is performed directly, without presupposing a particular pattern, by evaluating the circularity of a high-dimensional representation of the signal.


Dimensionality Reduction with Eilenberg-MacLane Coordinates

DREiMac leverages the underlying topology of the data — measured with persistent cohomology — and constructs classifying maps to the appropriate (classifying) Eilenberg-MacLane spaces (i.e. the circle, real and complex projective spaces and Lens spaces).


Topological Alignment of Locally Euclidean models

TALLEM assembles a collection of local Euclidean coordinates, and leverages ideas from the theory of fiber bundles to yield a globally consistent map reflecting the underlying topology of the data.

Video SW1PerS uses sliding window embeddings and persistent homology to detect recurrence (i.e. periodicity and quasiperiodicity) in videos, without the need for tracking or surrogate 1-dimensional signals.


(Quasi)Periodicity detection in recurrent videos