Proposal: Hierarchical Dimensionality Reduction module

[dylanrstewart]

Author of Proposal: Dylan Stewart

Reason or Problem

A common issue with multi-dimensional raster image processing (at the extremes, hyperspectral imagery with hundreds of features) is significant redundancy within the feature space. Some datasets have tens or hundreds of bands when only a handful might be necessary for downstream use (e.g., classification, segmentation, clustering).

Proposal

This module takes high dimensional data and a desired number of output channels or threshold, compares the distributions of the features within the data, and returns the most dissimilar grouping.

Design:

1. Given a dataset containing $N$ pixels and $F$ features, produce a pairwise-distance matrix:
   $$C = F \times F,$$
   where $C$ can be computed using various metrics (e.g., Jensen-Shannon divergence, a symmetric Kullback-Leibler divergence, Mahalanobis Distance Add Mahalanobis Distance Metric #114, Euclidean distance) evaluated over the distribution of pixels within the dataset.
2. Then, select the most similar pair of features (or spectra) by finding the minimum (for a distance/divergence measure) or maximum (similarity measure, e.g., mutual information or cosine similarity) and merge them by a specified aggregation (e.g., mean, median, max, min).
3. Update $C$ based on 2. until stopping criteria is met. Return dataset with reduced dimensionality.

Usage: for reducing the dimensionality of an input by finding correlating features within and removing redundancy.

Value: provide support to high-dimensional raster processing applications (e.g., data fusion, hyperspectral, multispectral)

Additional Notes or Context

Some distance metrics already available to build from:

• cupy KL divergence function
• scipy KL divergence
• Other distance/similarity metrics are easy to implement (Euclidean and cosine)