Fast Multi-Scale Clustering and Manifold Identification in 2D and 3D
Dan Kushnir,
Weizmann Institute
A multiscale approach for solving the clustering problem in 2D and 3D
data is demonstrated. Our
main motivation is to find partitions that are consistent with
predefined features such as shape, dimensionality,
and density. Starting from a graph representation, the algorithm
constructs, through a
bottom-up process, a hierarchy of data clusters. Similarity measures
based on the multiscale features
conduct this process of hierarchy construction. In addition, each
cluster is described by its dimensionality,
and approximated by a simplified manifold. As a feedback the simplified
manifolds are used to
improve the clustering. A top-down process is applied for resolving
intersections of clusters and for
detecting dense patterns inside noise. Our algorithm complexity is
linear in the amount of data. It has
been tested on 2D and 3D astrophysical and fluid turbulence data, and on
representative 2D and 3D examples.
This is a joint work with Dr. Meirav Galun and Prof. Achi Brandt from
the Weizmann Institute of Science, Rehovot, Israel.