Fast Global Sparse Principal Component Analysis for Sensor Reduction in Virtual Metrology

In semiconductor manufacturing, virtual metrology (VM) leverages high-dimensional sensor data for real-time quality estimation. However, excessive sensor deployment leads to increased operational costs, data redundancy, and system complexity due to substantial infrastructure, installation, and maintenance requirements. To address these manufacturing challenges, we propose a Fast Global Sparse Principal Component Analysis (FGS-PCA) framework for systematic sensor reduction in VM applications. FGS-PCA efficiently constructs sparse principal components that capture dominant variance while strictly enforcing a global constraint on the total number of sensors used across components, a critical requirement for cost-effective industrial deployment. Unlike existing sparse PCA methods that impose sparsity on each principal component independently, FGS-PCA explicitly controls the total sensor count across all components, enabling structured dimensionality reduction aligned with real-world manufacturing constraints. The framework combines a computationally efficient sparse loading identification approach with an optional anchor-based refinement step to achieve near-optimal variance retention while significantly reducing sensor requirements. The proposed method offers a scalable, interpretable, and practically deployable solution that enables substantial cost savings while maintaining process control effectiveness in modern semiconductor manufacturing systems.