A Metric-Learning-Based Nonlinear Modeling Algorithm and Its Application in Key-Performance-Indicator Prediction

Abstract

For the purpose of improving economic benefits, manufacturers pay more attention on key-performance-indicator prediction, since it plays a central role in process monitoring, quality control, and operational optimization. However, the existing methods only develop prediction models under Euclidean distance, which is not flexible enough for different problems. In addition, few methods are able to extract useful features through supervised learning. In this article, a novel metric-learning-based algorithm is proposed, named as metric-learning-based least-squares support vector machine (MLSSVM). The MLSSVM learns a task-dependent metric through optimizing the metric matrix of the Mahalanobis distance employed in the kernel function of the least-squares support vector machine. Locality preserving projection is employed to preserve the local structure of data. Besides, by enforcing the low-rank property of the metric matrix, the MLSSVM is able to explore the low-dimensional representation of features in a supervised and effective way. An accelerated proximal method is employed to solve the constructed nonsmooth constrained optimization problem. The effectiveness of the MLSSVM is illustrated through the tests on several problems, including a practical one from the glass production process.