Advanced LLE Method for Dimension Reduction using Nonlinear Manufacturing Data

Abstract

Modern manufacturing processes are often characterized by high dimensionality and nonlinearity; dimension reduction is usually required to identify the critical features and help improve the process yield. Dimension reduction and analysis of data with high nonlinearity has been a challenging task. Many methods have been proposed based on manifold learning, which aims to learn a lower-dimensional manifold from the original high-dimensional space. However, since the mappings are usually implicit, it is difficult to build a connection between the classification results and the original features. Apart from the prediction results, industry data analysis also focus on the features themselves. Therefore, methods that are able to combine feature selection with dimension reduction is often needed. This paper proposed a hybrid method for nonlinear dimension reduction and feature selection based on Locally Linear Embedding (LLE). LLE and many filter feature selection shares a common procedure of neighbor search. By integrating nearest neighbor search for both LLE and ReliefF, and adjusting the distance measure in supervised LLE with results from feature selection, the proposed method could connect the feature selection process with the nonlinear model, extract the critical features for further analysis, and improve the performance of process modelling. Two dataset from real industry processes are also illustrated as case studies.