Methods of variable selection and their applications in quantitative structure-property relationship (QSPR)

Quantitative structure-activity/property relationships (QSAR/QSPR) has become an important branch of modern chemistry in past decades. A fundamental goal of QSAR/QSPR studies is to predict complex physical, chemical; biological, and technological properties of chemicals from simpler descriptors, preferably those calculated solely from molecular structure. Topological indices (TIs) are numerical descriptors derived from the molecular graphs. They provide a convenient and inexpensive means of quantifying molecular structure, measuring molecular characters such as branching, shape and size. However, with the development of the topological indices, a large number of such descriptors have been proposed and their definition become more and more complex. They bring new problems to QSAR/QSPR studies. Based on the problems we met, this thesis includes two parts, one is the generalization and structural interpretation of topological indices, and the other is the applications of variable selection methods in QSPR.; In the first part of this thesis, we investigate a large amount of famous topological indices and decompose them into sets of topological character bases, different sets of character bases indicate different information of molecular structures, such as bond, atom, etc. Using the topological character bases of connectivity index chi, we illustrate the great success of the connectivity index on many QSAR or QSPR researches in a new point of view-the impersonality of chi's bond weighting formula. Then, it is suggested to recompose some topological indices by adjusting the weights upon character bases according to different properties/activities. Using the method of orthogonal block variables, the character base sets are blocked to extract the most useful information from different information subspaces (constructed by different character bases). The regression of only a few new orthogonal block variables shows large improvements both in fitting and prediction ability of the model.; The second part of my thesis is about the variable selection methods and their applications in QSPR. A new variable selection approach based on smoothly clipped absolute deviation (SCAD) penalized least squares is employed for interpretation and prediction of boiling points (BPs) of 530 alkanes. All the saturated hydrocarbons with carbon numbers from 2 to 10 and 128 common topological indices are taken into account. As a result, only 12 topological indices are selected from 95 pretreated ones but they still present a satisfying fitting and prediction effects. On the other hand, the proposed variable selection method is based on linear models. However, most of the existing relationships in QSPR cannot be described well by simple linear models. In such cases, some non-linear models should be taken into account. In the following part of the thesis, the Kriging method is considered to construct a non-linear model on variables selected by SCAD. The sequential combination of the two methods shows large improvement on the prediction ability when compared with the simple linear regression on the selected variables and the Kriging model on randomly chosen variables.