Manifold Kernelization of Molecular Surface to Encode Quantum Information of Electronic Attributes for Machine Learning

A novel concept of encoding electronic quantities on a molecular surface is developed by unsupervised kernel learning. Through optimization of the hyperparameters of Spectral Mixture (SM) kernel functions in conducting Sparse Gaussian Process (SGP) regression of electronic attributes on a surface manifold, the resultant covariance matrix, or kernel, captures the mutual relationships among the electronic quantities as well as the topology of the molecular surface. As such, a kernel, coined MKMS (Manifold Kernelization of Molecular Surface), can be treated as a symmetric positive definite (SPD) matrix to represent a molecule for machine learning. A proper neural network model was implemented to utilize SPD matrices and preserve their collected Riemannian topology for predicting the molecular properties. The prediction results of two solubility data sets support promising potentials of using MKMS to encode quantum information on a molecule and enable machine learning applications.