Response prediction based on large data using a local metamodel

Abstract

Even though research on large data application methods has been active in recent years, few papers have presented response prediction methods based on the large data. It is difficult to construct a good metamodel using a whole large data set as samples because existing metamodeling methods require a significant computational burden in the generation process. In this study, we proposed a response prediction method using a metamodel with a local region. First, in order to find data in the nearest clusters to the prediction point, an entire data space was divided into many clusters using a partitioning clustering method. Next, the nearest clusters surrounding a prediction point were identified, and then some of data in the nearest clusters were selected as samples for generating a local metamodel. This was an effort to ensure that the local metamodel could function as an interpolation model from the samples. Then, the response was predicted using the metamodel constructed from the chosen data.

We investigated the proposed technique through a performance test to generate a metamodel for various mathematical problems and calculated the error between the actual values of the examples and the responses from the metamodel. A total of six mathematical problems were tested from low to high dimensions, and the proposed method was compared with other existing metamodeling techniques. We performed test in 2 case. First, the prediction accuracy is compared with the Kriging metamodel when the number of data is 10,000. In the case of more than 10,000 data samples, the Kriging metamodel in the global domain cannot be created on commercial PC owing to the computational burden. Therefore, the second case, when the number of data is 100,000, we compare the prediction performance with the Boosting technique used in industrial engineering. In the first test, out proposed method showed the same level of accuracy as the Kriging model with only a small number of sample data and the efficiency of the metamodel generation was greatly increased. In the second test, In the second test, the prediction error was improved from 11% to 147% as compared with the Boosting techniques, conventional method in large data regression. We confirmed the superior performance of the proposed method and proved its usefulness as a new way of coping with large data.