Similarity based on extended basis descriptors

We consider the problem of comprehensive characterizations of chemical structures by mathematical invariants. We have illustrated a particular characterization to derive similarities between heptane isomers. Comprehensive characterizations require resolution of the following problems: (1) selection of descriptors that adequately span the structure space; (2) construction of orthogonal basis of descriptors to eliminate bias due to interconnectedness of the descriptors. The latter problem has been resolved recently by a design of a sequential orthogonalization procedure. We proceed here to outline construction of extended bases for the characterization of structures.

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