An Overview of Data-Mining Methods in Catalysis

The simplest form of regression is multiple linear regression (MLR), Y = XB + E. Here, X contains the descriptors, [di... dn] B contains the regression coefficients, Y contains the figures of merit and E contains the residuals. One well known example of MLR is the relationship shown in Equation (6.9). This model requires a few well-characterized parameters d. .. dn, which are usually derived from experimental measurements or from QM calculations. There are several applications of MLR in catalysis, eg., the quantitative analysis of ligand effects (QALE) model developed by Fernandez et al. [90]. 

The trouble is that you often have too many descriptors, and/or insufficient information on the reaction mechanism. This creates two problems building a regression model requires the calculation of the inverse ofXTX, which cannot be done for a matrix X that contains more variables than experiments. Moreover, if you 

Selecting the right variables often improves the models and makes interpretation easier. When there are too many descriptors, and especially when these descriptors do not have a clear physico-chemical meaning (e.g., connectivity indices and other 2D descriptors), stochastic methods such as genetic algorithms and evolutionary strategies can be used for finding an optimal subset of descriptors [91,92]. 

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