Recently, multi-scale notions of local homology (a variant of persistent homology) have been used to study the local structure of spaces around a given point from a point cloud sample. Current reconstruction guarantees rely on constructing embedded complexes which become difficult in high dimensions. We show that the persistence diagrams used for estimating local homology, can be approximated u...

Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map from space visual so as preserve some dissimilarity (similarity) measure, such the Euclidean distance example. In fact, although adopting distinct mathematical formulations favor different aspects of data, most multidimensio...