Uncovering interpretable relationships in high-dimensional scientific data through function preserving projections

Liu, Shusen and Anirudh, Rushil and Thiagarajan, Jayaraman J and Bremer, Peer-Timo (2020) Uncovering interpretable relationships in high-dimensional scientific data through function preserving projections. Machine Learning: Science and Technology, 1 (4). 045016. ISSN 2632-2153

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Abstract

In many fields of science and engineering, we frequently encounter experiments or simulations datasets that describe the behavior of complex systems and uncovering human interpretable patterns between their inputs and outputs via exploratory data analysis is essential for building intuition and facilitating discovery. Often, we resort to 2D embeddings for examining these high-dimensional relationships (e.g. dimensionality reduction). However, most existing embedding methods treat the dimensions as coordinates for samples in a high-dimensional space, which fail to capture the potential functional relationships, and the few methods that do take function into consideration either only focus on linear patterns or produce non-linear embeddings that are hard to interpret. To address these challenges, we proposed function preserving projections (FPP), which construct 2D linear embeddings optimized to reveal interpretable yet potentially non-linear patterns between the domain and the range of a high-dimensional function. The intuition here is that humans are good at understanding potentially non-linear patterns in 2D but unable to interpret non-linear mapping from high-dimensional space to 2D. Therefore, we should restrict the projection to linear but not the pattern we are seeking. Using FPP on real-world datasets, one can obtain fundamentally new insights about high-dimensional relationships in extremely large datasets that could not be processed with existing dimension reduction methods.

Item Type: Article
Subjects: Impact Archive > Multidisciplinary
Depositing User: Managing Editor
Date Deposited: 01 Jul 2023 06:50
Last Modified: 31 Oct 2023 04:30
URI: http://research.sdpublishers.net/id/eprint/2628

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