Interaction Modelling of High Dimensional Production Data

Abstract

The final goal of this study is to present a practical interaction modeling methodology for big and complex industrial data in which there are mixed difficulty of high dimension, sparsity, interaction, multicollinearity, series bias, low signal noise ratio, nonlinearity, and so on. Particularly, this paper focuses on the issues of high dimension, sparsity, and interactions. In addition, it is necessary to estimate unknown factors and interactions in order to improve overall efficiency in complex and diverse situations of industry. The main purpose here is to summarize the applicability and challenges of Factorization Machines (FMs) to manufacturing data. FMs has possibility because of the ad-vantage of to identify unknown factors and its robustness to data with more than 95% missing values which has already been reported for recommendation problems. Manufacturing data assumed here incudes the inspected quality of the final products, and a set of various variables (settings, sensing results, etc.) of the series production process which may relate to the quality. Common characteristics of manufacturing data include mixture of numerical and categorical variables, high dimensionality, many missing values, and so on. Therefore, this paper particularly focuses on sparse high-dimensional type-mix data. So far, while interaction modeling of high-dimensional data has been discussed and verified, mainly for screening methods, still there is very few studies to apply FMs to the manufacturing data with many numerical variables. There-fore, we report the evaluation results using some synthesis data and simulation data from actual oracle model to summarize FMs applicability as the first step. The second step is to compare the performance of sparse FMs which has feature selection function, beside our proposal.