Development of correlation-based clustering method and its application to software sensing

The individuality of production devices should be taken into account when soft-sensors are designed for parallelized devices. Since it is expressed as differences of the correlation among measured variables, it is useful to cluster samples on the basis of the correlation among variables for adopting a multi-model approach. In addition, changes in process characteristics can be coped with in the same way. In the present work, a new clustering method, referred to as NC-spectral clustering, is proposed by integrating the nearest correlation (NC) method and spectral clustering. Spectral clustering is a graph partitioning method that can be used for sample classification when an affinity matrix of a weighted graph is given. The NC method can detect samples that are similar to the query from the viewpoint of the correlation without a teacher signal. In the proposed method, the NC method is used for constructing the weighted graph that expresses the correlation-based similarities between samples and the constructed graph is partitioned by using spectral clustering. In addition, a new soft-sensor design method is proposed on the basis of the proposed NC-spectral clustering. The usefulness of the proposed methods is demonstrated through a numerical example and a case study of parallelized batch processes. The performance of the proposed correlation-based method is better than that of the conventional distance-based methods.