A fractal approach for selecting an appropriate bin size for cell-based diversity estimation

Area of Science:

• Computational chemistry
• Cheminformatics
• Data analysis

Background:

• Cell-based diversity assessment is crucial for analyzing molecular descriptor sets.
• Selecting an appropriate bin size is critical for accurate diversity analysis.
• Existing methods may lack robustness in determining optimal bin sizes.

Purpose of the Study:

• To present a novel, robust method for selecting the optimal bin size in cell-based diversity assessment.
• To establish a quantitative approach for measuring the sensitivity of diversity indices to grid resolution.
• To identify the optimal bin size based on the characteristics of molecular descriptor data.

Main Methods:

• Utilized a box-counting algorithm, similar to fractal analysis techniques.
• Measured the sensitivity of diversity indices by varying grid resolution.
• Analyzed the relative variance of diversity scores (sum of squared cell occupancies) for common molecular descriptor sets.

Main Results:

• The relative variance of diversity scores exhibited a characteristic bell-shaped distribution.
• The peak of this distribution reliably indicates the optimal bin size for a given dataset and sample size.
• Optimal bin size is influenced by data distribution, sample size, and feature space dimensionality.

Conclusions:

• The proposed box-counting method provides an effective strategy for optimal bin size selection in diversity assessment.
• The method's performance is dependent on dataset properties and dimensionality.
• Cell-based diversity assessment efficacy diminishes significantly in high-dimensional spaces.