Molecular Similarity from Manifold Learning on D2-Property Images

This section will cover tagging of book web only. The development of quantitative structure activity relationships (QSAR) is based upon the observation that similar molecules will have similar properties. Therefore, one can predict the properties of an uncharacterized molecule by computing its similarity to the three-dimensional structures of the molecules in a database of reference compounds. The alignment free method we propose is based on the D2-shape similarity descriptor, enriched by the values of properties on the molecular surface in a way analogous to methods based on the property encoded surface translator (PEST). Molecular similarity can be computed from the Euclidean distance in the reduced dimensional space. This manifold will generally be a curved hypersurface in the high-dimensional space, if the manifold is smooth then the local distances are well approximated by a Euclidean distance formula. One of the simplest manifold-learning methods is Laplacian eigenmaps. To provide an intuitive explanation, suppose that are given a two-dimensional surface embedded in a three-dimensional space.