Similarity and sparsity collaborative embedding and its application to robust process monitoring

Multivariate measurements in complex industrial processes are commonly contaminated by a number of outliers. In this context, robustness to the corrupted data is an important problem in process monitoring tasks. This paper proposed a novel approach called similarity and sparsity collaborative embedding (SSCE) for efficient robust process monitoring. The proposed SSCE can learn a sparse coefficient matrix by a ℓ1-norm regularization as the sparse constraint on the reconstruction errors, making it robust to the data contaminated by outliers. The similarity preserving matrix is proposed to capture the local structure of the given data, and then the local information is transferred to the sparse coefficients such that the similarity among data points can be preserved. In this way, the reduced-dimensional representations extracted is capable of containing more informative and discriminating characteristics of the original data, which is beneficial to enhance monitoring performance. Meanwhile, projection learning is integrated into the proposed objective function to learn an explicit projection matrix in an overall optimum way, which enables the SSCE to circumvent the out-of-sample problem and facilitate subsequent process monitoring tasks. Two case studies on a simulated typical chemical process and a practical fractionation process demonstrate the effectiveness of the proposed approach.