Geometric Multiresolution Analysis in R
Geometric Multiresolution Analysis (Allard, Chen, Maggioni, 2012) is a data science technique for constructing efficient representations of high-dimensional datasets. Essentially, the construction has two stages:
- Cluster, or partition the data into similar groups
- Fit low-dimensional hyperplanes to each data cluster/partition
In this implementation, cover trees are used to produce a subset of the data that "covers" the dataset at a particular scale and the data is partitioned using the Voronoi regions produced by this subset. Fitting of hyperplanes in each Voronoi region is carried out by first computing the local mean and covariance matrix, and identifying the unique hyperplane of dimension d containing the mean and parallel to the top d eigenvectors of the covariance matrix. Strong theoretical justifications for this procedure can be found in Maggioni, Minsker, and Strawn, 2016.
This code is not fully optimized, but should be useful for educational and experimental purposes.
gmRa is released under the MIT license