Kernel Methods for Chemical Compounds: From Classification to Design

In this paper, we briefly review kernel methods for analysis of chemical compounds with focusing on the authors' works. We begin with a brief review of existing kernel functions that are used for classification of chemical compounds and prediction of their activities. Then, we focus on the pre-image problem for chemical compounds, which is to infer a chemical structure that is mapped to a given feature vector, and has a potential application to design of novel chemical compounds. In particular, we consider the pre-image problem for feature vectors consisting of frequencies of labeled paths of length at most K. We present several time complexity results that include: NP-hardness result for a general case, polynomial time algorithm for tree structured compounds with fixed K, and polynomial time algorithm for K=1 based on graph detachment. Then we review practical algorithms for the pre-image problem, which are based on enumeration of chemical structures satisfying given constraints. We also briefly review related results which include efficient enumeration of stereoisomers of tree-like chemical compounds and efficient enumeration of outerplanar graphs.

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