The reduction of false positives in Sparse Factorization Machines

In the semiconductor field, which is the primary focus of this study, the increasing demand has led to a supply shortage, necessitating the expansion of production capacity and the reinforcement of the manufacturing infrastructure. Among the various challenges, the issue of defective products is particularly critical, highlighting the importance of feature analysis for identifying defective factors. However, due to the large scale and complexity of semiconductor manufacturing data, feature analysis poses significant challenges. In this study, we focus on Sparse Factorization Machines (SFM) as an interaction modeling approach for high-dimensional data, characterized by high computational efficiency and strong robustness to missing data. Our previous paper proposed an advanced SFM method denoted by SFM1A, which enhances both selections of main factors and interactions by employing a regularization and a new adaptive technique to SFM with Triangle inequality upper boundary. While SFM1A has demonstrated a significant reduction in false positives (FPs) (main: -99%, interaction: -97%), however, it is not yet at a practical level (e.g. target is less than a few hundred selections including FPs when input data dimension is 10000). To address the issue, this study aims to develop an advanced method that minimizes incorrect interaction selections without compromising selection accuracy for true main factors and interactions. The first proposed method, SFM1A_SPC is to combine SPC criteria mathematically proved in the safe pruning method to SFM1A. SFM1A_SPC successfully reduces FPs of interactions. The second proposal, SFM1A_SPC_FP method, further improves the selection accuracy of main factors by applying a sequential selection method (FP) based on the properties of submodular optimization to perform dimensionality reduction. Numerical evaluation of SFM1A_SPC_FP confirms that it maintains the interaction selection accuracy of SFM1A_SPC while further enhancing the categorical main factor selection. Finally, SFM1A_SPC_FP method achieves the target required for the practical application.