Entropy-Isomap: Manifold Learning for High-dimensional Dynamic Processes

TL;DR

Entropy-Isomap is a new manifold learning technique designed to effectively reduce high-dimensional, temporally correlated data from complex processes, enabling better understanding and optimization of such systems.

Contribution

The paper introduces Entropy-Isomap, a novel method that overcomes limitations of existing spectral dimensionality reduction techniques for temporally correlated data.

Findings

Successfully applied to organic material fabrication data

Accurately captures process control variables

Enables visualization of material morphology evolution

Abstract

Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates better understanding of the underlying processes, and enables their optimization. In this paper, we first show that off-the-shelf non-linear spectral dimensionality reduction methods, e.g., Isomap, fail for such data, primarily due to the presence of strong temporal correlations. Then, we propose a novel method, Entropy-Isomap, to address the issue. The proposed method is successfully applied to large data describing a fabrication process of organic materials. The resulting low-dimensional representation correctly captures process control variables, allows for low-dimensional visualization of the material morphology evolution, and provides key insights to improve the process.