Entropy-Isomap: Manifold Learning for High-dimensional Dynamic Processes
This addresses the challenge of analyzing and optimizing complex scientific and engineering processes with high-dimensional data, though it appears incremental as it builds on Isomap with a specific fix for temporal issues.
The authors tackled the problem of manifold learning for high-dimensional dynamic processes, showing that existing methods like Isomap fail due to temporal correlations, and proposed Entropy-Isomap, which successfully captured process control variables and enabled visualization of material morphology evolution in an organic materials fabrication case.
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.