  In this paper, we propose persistent spectral based machine learning
(PerSpect ML) models for drug design. Persistent spectral models, including
persistent spectral graph, persistent spectral simplicial complex and
persistent spectral hypergraph, are proposed based on spectral graph theory,
spectral simplicial complex theory and spectral hypergraph theory,
respectively. Different from all previous spectral models, a filtration
process, as proposed in persistent homology, is introduced to generate
multiscale spectral models. More specifically, from the filtration process, a
series of nested topological representations, i,e., graphs, simplicial
complexes, and hypergraphs, can be systematically generated and their spectral
information can be obtained. Persistent spectral variables are defined as the
function of spectral variables over the filtration value. Mathematically,
persistent multiplicity (of zero eigenvalues) is exactly the persistent Betti
number (or Betti curve). We consider 11 persistent spectral variables and use
them as the feature for machine learning models in protein-ligand binding
affinity prediction. We systematically test our models on three most
commonly-used databases, including PDBbind-2007, PDBbind-2013 and PDBbind-2016.
Our results, for all these databases, are better than all existing models, as
far as we know. This demonstrates the great power of our PerSpect ML in
molecular data analysis and drug design.
