Feature Extractions from a High-dimension Low-samples Data for Multi-dimension Virtual Metrology

This paper discussed the virtual metrology (VM) modelling of multi-dimensional multi classes to describe the relationship between the variables of a production machine's condition of and the estimated/forecasted product quality soon after finishing the machine processing. Combination of the Principle Component Analysis (PCA) and the LASSO (least absolute shrinkage and selection operator) technique of the sparse modelling were introduced to define the multi-dimensional quality. Because the high accuracy and quick computations are required for the VM modelling, in this study, the PCA-LASSO combination was applied before building the VM models based on the kernel SVM (kSVM), particularly the linear kernel for real-time use. Those usefulness was evaluated by three different data sets; a CVD (Chemical vapor deposition) process in an actual semiconductor factory, an open-data of higher dimension which is measured in a chemical process, and a scalable data which is generated by using a multivariate normal random numbers based on the original CVD data. We will investigate versatility of the proposed method.