iSIM-Sigma: Efficient Standard Deviation Calculation for Molecular Similarity.

Area of Science:

• Computational Chemistry
• Cheminformatics
• Data Science

Background:

• Molecular similarity metrics are vital for cheminformatics tasks like chemical space exploration and subset selection.
• Calculating the variance of a complete similarity matrix has quadratic complexity (O(N^2)), making it infeasible for large molecular libraries.
• Efficient methods are needed to compute similarity variance for increasingly large datasets.

Purpose of the Study:

• To develop a computationally efficient method for calculating the exact standard deviation of molecular similarities.
• To create a highly accurate, linear complexity approximation for estimating molecular similarity standard deviation.
• To enable scalable cheminformatics analyses on large molecular datasets.

Main Methods:

• Developed an O(NM^2) exact calculation method for Russell-Rao (RR) and Sokal-Michener (SM) similarity indices.
• Proposed a linear complexity O(N) approximation based on sampling representative molecules.
• Extended the approximation method to other similarity indices, including Jaccard-Tanimoto (JT).

Main Results:

• The exact calculation method significantly reduces complexity compared to pairwise approaches.
• The sampling-based approximation achieves an RMSE < 0.01 for up to 50,000 molecules with only 50 samples.
• Random sampling proved insufficient for accurate approximation compared to the proposed method.

Conclusions:

• The developed methods provide efficient and accurate ways to compute molecular similarity variance.
• The linear approximation method enables scalable and reliable cheminformatics analyses on large molecular libraries.
• This approach enhances the feasibility of tasks like chemical space exploration and subset selection.