Fitness Functions for Forward Selection: Application in Seven Data Sets

Introduction

Quantitative structure-activity/property relationship (QSAR/ QSPR) is a computational methodology for discerning the linkage between chemical structures of investigated compounds with their respective biological activity/chemical property. This is achieved by learning the inherent patterns hidden within the data set of interest by employing traditional and machine learning techniques. Predictive QSAR/QSPR modelling has been successfully employed to investigate a myriad of biological activities (Nantasenamat, Worachartcheewan, Prachayasittikul, Isarankuranaayudhya, & Prachayasittikul, 2013; Worachartcheewan, Nantasenamat, Isarankura-Na-Ayudhya, & Prachayasittikul, 2013) and chemical properties (Chanin, Thanakorn, & Virapong, 2007; Lapins et al., 2013; Nantasenamat, Isarankura-Na-Ayudhya, Tansila, Naenna, & Prachayasittikul, 2010; Nantasenamat, Naenna, & Prachayasittikul, 2005; Nantasenamat, Srungboonmee, Jamsak, Tansila, & Prachayasittikul, 2013). A more in-depth coverage on the concepts of QSAR/QSPR can be found in previous review article (Chanin & Virapong, 2010).

The progress in the quantitative structure-activity relationship (QSAR) approaches has been increasing in the recent years due to the fast-developing field of chemometrics (Neely, Madihally, & Gasem, 2010). As an example, utilization of feature (descriptor) selection (FS) has become a necessity in many QSAR studies (Martin, Ulf, Scott, & Lars, 2014; Shukla et al., 2014). FS removes such calculated descriptors that are redundant, noisy, or irrelevant to the target property at hand without loss of important information (Goodarzi, Dejaegher, & Vander, 2012; Shahlaei, 2013). FS helps in constructing robust and reliable QSPR models that are free from overfitting, a major QSAR model flaw taking place due to the use of a large number of descriptors relative to the training set data points. In this case, the model becomes tailored to fit the training set data and with low predictive ability on the unseen data points (test set).

FS has drawn the attention of researchers since the 1970s (Toussaint, 2006) and has been an important sub-area in data mining (Dietterich, 1997; Guyon, 2003). At present, FS has been widely applied to QSAR modelling (Goodarzi et al., 2012). Liu and Yu (Liu & Yu, 2005) defined the FS as a process of selecting a subset from a set of original features, and the subset’s optimality is measured by an evaluation strategy. The literature (Hocking & R., 1976) reviewed the problems of FS and variable analysis in linear regression. FS includes two aspects, which are fitness function and FS method. In the field of FS, the current research focuses on FS methods (Moghadam, Rahgozar, & Gharaghani, 2016; Ponzoni et al., 2017; Xia et al., 2018), but seldom on fitness function.

Which fitness function should be used depends on the purpose of the research. The three common roles of regression models are structural analysis, control and prediction. If the researchers want to do structural analysis through a regression model, the fitness function of adjusted-r² (r²_adj) can be considered in feature selection, so that the regression equation retains more independent variables. If the purpose of the regression equation is to be used for control, the fitness function of Bayesian Information Criterion (BIC) (Posada & Buckley, 2004) should be used, which can reduce the estimation standard error of regression parameters by simplifying the model.