Detecting ambiguities in regression using TSK models

Regression problems occur in many data analysis applications. The aim of regression is to approximate a function from which measurements were taken. When considering a regression problem, we have to take a number of aspects into account: how noisy the data are, whether they cover the domain sufficiently in which we want to find the regression function and what kind of regression function we should choose. However, the underlying assumption is always that the data actually are (noisy) samples of a function. In some cases, this might not be true. For instance, when we consider data from a technical process that is controlled by human operators, these operators might use different strategies to reach a particular goal. Even a single operator might not stick to the same strategy all the time. Thus, a dataset, containing a mixture of samples from different strategies, does not represent (noisy) samples from a single function. Therefore, there exists an ambiguity of selecting data from a large dataset for regression problems (RP) to fit a single model. To tackle this problem, an approach is proposed here to detect ambiguities in RP by selecting a subset of data form the total dataset using two TSK models, which work in parallel by sharing the data with each other in every step. The proposed approach is verified with artificial data, and finally utilised to real data of grinding, a manufacturing process used to generate a smooth surfaces on workpieces.