Simultaneous coherent structure coloring facilitates interpretable clustering of scientific data by amplifying...

Area of Science:

• Computational Physics
• Data Science
• Applied Mathematics

Background:

• Traditional data clustering often necessitates predefined assumptions about the number, size, or shape of data subsets.
• These a priori assumptions can limit the discovery of physically meaningful structures in complex datasets.

Purpose of the Study:

• To introduce a novel unsupervised clustering method, simultaneous coherent structure coloring (sCSC), that bypasses the need for prior structural assumptions.
• To demonstrate sCSC's capability in identifying data clusters and their interrelationships without guidance on subgroup characteristics.

Main Methods:

• sCSC employs a series of binary data splittings, ensuring the most dissimilar points are isolated into distinct clusters.
• It utilizes a generalized eigenvalue problem based on pairwise data dissimilarity to find orthogonal coordinates maximizing data separation.
• The method generates a binary tree representation, naturally revealing cluster numbers and hierarchical relationships.

Main Results:

• The effectiveness of sCSC was demonstrated on three fluid dynamics problems, showcasing its ability to cluster data without prior structural knowledge.
• Application to a high-dimensional protein folding simulation dataset highlighted the method's interpretability and capacity for uncovering complex relationships.

Conclusions:

• sCSC offers a powerful, assumption-free approach to unsupervised data clustering, particularly effective for dynamical physical systems.
• The method's interpretability and adaptability suggest broad applicability in fields like genomics and neuroscience, where data structures are often complex and less accessible.