Regression Methods Based on Nearest Neighbors with Adaptive Distance Metrics Applied to a Polymerization Process

Abstract

Empirical models based on sampled data can be useful for complex chemical engineering processes such as the free radical polymerization of methyl methacrylate achieved in a batch bulk process. In this case, the goal is to predict the monomer conversion, the numerical average molecular weight and the gravimetrical average molecular weight. This process is characterized by non-linear gel and glass effects caused by the sharp increase in the viscosity as the reaction progresses. To increase accuracy, one needs more samples in the areas with higher variation and this is achieved with adaptive sampling. An extensive comparative study is performed between three regression algorithms for this chemical process. The first two are based on the concept of a large margin, typical of support vector machines, but used for regression, in conjunction with an instance-based method. The learning of problem-specific distance metrics can be performed by means of either an evolutionary algorithm or an approximate differential approach. Having a set of prototypes with different distance metrics is especially useful when a large number of instances should be handled. Another original regression method is based on the idea of denoising autoencoders, i.e., the prototype weights and positions are set in such a way as to minimize the mean square error on a slightly corrupted version of the training set, where the instances inputs are slightly changed with a small random quantity. Several combinations of parameters and ways of splitting the data into training and testing sets are used in order to assess the performance of the algorithms in different scenarios.