Topological data analysis and, more specifically, persistent homology have received
significant attention as a method of describing the shape of complex data. Persistent …

Persistence diagrams (PD) s play a central role in topological data analysis. This analysis
requires computing distances among such diagrams such as the 1-Wasserstein distance …

The space of persistence diagrams under bottleneck distance is known to have infinite
doubling dimension. Because many metric search algorithms and data structures have …

Persistence diagrams have been widely used to quantify the underlying features of filtered
topological spaces in data visualization. In many applications, computing distances between …

We present a topological audio fingerprinting approach for robustly identifying duplicate
audio tracks. Our method applies persistent homology on local spectral decompositions of …

Given a persistence diagram with $ n $ points, we give an algorithm that produces a
sequence of $ n $ persistence diagrams converging in bottleneck distance to the input …

Since its introduction in the mid-1990s, DBSCAN has become one of the most widely used
clustering algorithms. However, one of the steps in DBSCAN is to perform a range query, a …

Given a set of persistence diagrams P 1,..., P m, for the data reduction purpose, one way to
summarize their topological features is to compute the center C of them first under the …

Persistence diagrams have been widely used to quantify the underlying features of filtered
topological spaces in data visualization. In many applications, computing distances between …

The space of persistence diagrams under bottleneck distance is known to be
highdimensional. Because many metric search algorithms and data structures have bounds …