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

Alexander Yu Tolbin1

  • 1FSBIS Institute of Physiologically Active Compounds of the Russian Academy of Sciences, Russian Academy of Sciences, 1, Severny proezd, Chernogolovka 142432, Moscow Region, Russian Federation. tolbin@ipac.ac.ru.

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Summary

Functional clustering improves inaccurate regression models for materials science, reducing prediction errors from over 30% to under 25%. This method enhances accuracy for small datasets, aiding in property prediction.

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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.