Selecting High-Dimensional Representations of Physical Systems by Reweighted Diffusion Maps.

Area of Science:

• Physical Chemistry
• Computational Chemistry
• Machine Learning

Background:

• Dimensionality reduction is crucial for analyzing high-dimensional systems in physical chemistry.
• Unsupervised machine learning methods are commonly used for this task.
• The choice of the initial high-dimensional representation is often overlooked but critical.

Purpose of the Study:

• To address the problem of selecting appropriate high-dimensional representations for dimensionality reduction.
• To introduce and demonstrate a quantitative method for this selection process.

Main Methods:

• Utilized a recently developed method: reweighted diffusion maps.
• Employed spectral decomposition of Markov transition matrices.
• Data was obtained from standard or enhanced sampling atomistic simulations.

Main Results:

• Developed a quantitative approach for selecting high-dimensional representations.
• Demonstrated the method's effectiveness on several high-dimensional examples.
• Showcased the link between spectral properties of transition matrices and representation quality.

Conclusions:

• The proposed method provides a systematic way to choose descriptive high-dimensional representations.
• This approach enhances the reliability and interpretability of dimensionality reduction in physical chemistry.
• The reweighted diffusion map method offers a powerful tool for computational chemistry applications.