Computing Gram Matrix for SMILES Strings Using RDKFingerprint and Sinkhorn-Knopp Algorithm

SMILES (Simplified Molecular Input Line Entry System) strings are widely used to represent molecular structures in cheminformatics and drug discovery. However, effectively transforming these string-based representations into meaningful numerical features for machine learning remains a significant challenge due to the complex, non-Euclidean nature of molecular structures. Traditional fingerprint-based and deep learning approaches often struggle with scalability, interpretability, or computational efficiency. Our approach leverages the Morgan Fingerprint to generate molecular feature representations, followed by a pairwise kernel function to compute a structured similarity matrix. We then refine this matrix using the Sinkhorn-Knopp algorithm, ensuring it satisfies probabilistic constraints. To reduce dimensionality, we apply Kernel Principal Component Analysis (PCA), producing compact embeddings suitable for downstream machine learning tasks. We conduct a comprehensive empirical evaluation of the proposed method which is assessed for drug subcategory prediction (classification task) and solubility AlogPS “aqueous solubility and octanol/water partition coefficient” (regression task) using the benchmark SMILES string dataset. The outcomes show the proposed method outperforms baseline methods in supervised analysis and has potential uses in molecular design and drug discovery. By integrating kernel-based learning with probabilistic refinement, our method offers a promising alternative to existing cheminformatics techniques.