Classification of data with missing elements and outliers

Missing elements and outliers can often occur in experimental data. The presence of outliers makes the evaluation of any least squares model parameters difficult, while the missing values influence the adequate identification of outliers. Therefore, approaches that can handle incomplete data containing outliers are highly valued. In this paper, we present the expectation-maximization robust soft independent modeling of class analogy approach (EM-S-SIMCA) based on the recently introduced spherical SIMCA method. Several important issues like the possibility of choosing the complexity of the model with the leverage correction procedure, the selection of training and test sets using methods of uniform design for incomplete data and prediction of new samples containing missing elements are discussed. The results of a comparison study showed that EM-S-SIMCA outperforms the classic expectation-maximization SIMCA method. The performance of the method was illustrated on simulated and real data sets and led to satisfactory results.