In the process of chemical engineering

multiple manifold structures has different optimal number of nearest neighborhood under various operating modes. Locally linear embedding (LLE) algorithm based on clustering to select the nearest neighborhood is proposed for nonlinear monitoring. LLE algorithm was performed for dimensionality reduction and extract the available information in high-dimensional data. The mapping matrix from data space to feature space was obtained by local linear regression. The Silhouette index was selected as the clustering validity index to estimate the similarity between the embedded sample information

and further determine the optimal number of neighbors. Process monitoring statistics and its control limits were built based on the mapping matrix. Finally

the feasibility and efficiency of the proposed method were illustrated through the Tennessee Eastman process.