Functional clustering as a correction framework for regression models under small-data constraints: predicting...

Area of Science:

• Materials Chemistry
• Computational Chemistry
• Data Science

Background:

• Regression models often perform poorly with limited data in materials science.
• Accurate prediction of material properties is crucial for accelerating discovery.
• Existing methods struggle with small sample sizes and high initial error rates.

Purpose of the Study:

• To develop a method for correcting poorly performing regression models under small-data constraints.
• To improve the accuracy of predicting optical limiting properties in phthalocyanines.
• To establish a quantitative applicability domain and interpretable rules for new compound prediction.

Main Methods:

• Functional clustering that jointly optimizes cluster assignments and local correction functions.
• Bayesian information criterion for determining the optimal number of clusters.
• Leave-one-out cross-validation for assessing generalizability within clusters.
• Decision trees for generating interpretable IF-THEN rules for new compound classification.

Main Results:

• Reduced global prediction error from 32-140% to 10-25% mean absolute percentage error.
• Demonstrated generalizability within well-populated clusters (≥5 compounds) with median errors of 14-36%.
• Identified cluster instability for small clusters (3-4 compounds), defining a quantitative applicability domain.
• Feature importance analysis revealed that cluster assignment relies on descriptors distinct from raw regression inputs, uncovering latent physicochemical structure.

Conclusions:

• Functional clustering is a generalizable and effective method for correcting inaccurate regression models in small-data scenarios within materials chemistry.
• The method provides accurate property predictions and uncovers underlying structure-property relationships.
• Open-source code enables researchers to apply this technique for prescreening compound libraries, accelerating materials discovery.