Structural interpretation of a topological index. 1. External factor variable connectivity index (EFVCI)

The external factor variable connectivity index (EFVCI) is interpreted by mining out the structural features hidden in the space spanned by the EFVCI indices through projection pursuit combining with number-theory net (NT-net) on the unit sphere U(Us). Projection pursuit is concerned with "interesting" projections of high-dimensional data sets to machine-pick "interesting" low-dimensional projections of a high-dimensional point cloud by numerically maximizing a certain objective function or projection index. At first, the optimal EFVCI index reaches to -0.80 in the correlation with a retention index of 207 hydrocarbons produced by insects. The EFVCI indices, with regression results of R = 0.99998, s = 3.49, RMSECV = 3.90, and F = 7.9560e+005, obtain high regression quality. The model is proven valid by leave-one-out cross validation. Second, the EFVCI index is interpreted by the structure information, that is, size, branch number, graph center, and branching position of topological structures, which is searched out on the unit sphere U(Us) by projection pursuit. Finally, the interpretation information is used to discover some chemical knowledge concerning the variation of the retention index with the change in chemical structures.