Nonlinear dimensionality reduction (NLDR) algorithms such as Isomap, LLE and Laplacian
Eigenmaps address the problem of representing high-dimensional nonlinear data in terms …

''Topological''is an unlikely adjective to be associated with signal processing, which is
dominated by results flowing from geometric rigidity. However, heterogeneous sensors and …

We consider problems of localization, disambiguation, and mapping in a domain filled with
signals-of-opportunity generated by transmitters. One or more (static or mobile) receivers …

1.1. Javaplex. Javaplex is a Java software package for computing the persistent homology of
filtered simplicial complexes (or more generally, filtered chain complexes), with special …

We show how a Hopfield network with modifiable recurrent connections undergoing slow
Hebbian learning can extract the underlying geometry of an input space. First, we use a slow …

1.1. JPlex. JPlex is a Java software package for computing the persistent homology of
filtered simplicial complexes, often generated from point cloud data. The authors are Harlan …

Persistent homology is a relatively new tool from topological data analysis that has
transformed, for many, the way data sets (and the information contained in those sets) are …

1.1. JPlex. JPlex is a Java software package for computing the persistent homology of
filtered simplicial complexes, often generated from point cloud data. The authors are Harlan …

Signals are a collection of related measurements. Of course, all measurements contain
errors, so error tolerance is a desirable feature of any signal processing system. At first sight …

The main goal of this paper is to describe a natural procedure for constructing circular
coordinates on a nonlinear data set using techniques from algebraic topology and persistent …