Hessian Semisupervised Scatter Regularized Classification Model With Geometric and Discriminative Information for Nonlinear Process

The integration of semisupervised modeling and discriminative information has been sporadically discussed in the research literature of traditional classification modeling, while the former one would make full use of the collected data and the latter one would further improve the classification performance. In this article, the Hessian semisupervised scatter regularized classification model is proposed as a coherent framework for the nonlinear process classification upon both labeled and unlabeled data. It is innovatively designed with a loss function to evaluate the classification accuracy and three regularization terms, respectively, corresponding to the geometry information, discriminative information, and model complexity. Both cases of the coherent framework, respectively, casted to the reproducing kernel Hilbert space and linear space, enjoy a theoretically guaranteed analytical solution. Experiments on process classification tasks on a benchmark dataset and a real industrial polyethylene process illustrate the merits of the proposed method in a sense that the class information of novel collected data is accurately predicted.