Generating multi-modality virtual samples with soft DBSCAN for small data set learning

Owing to the factors of cost and time limit, the number of samples is usually small in the early stages of manufacturing systems. When the number of available data is small, traditional statistic techniques have difficulty to obtain robust analyses. Therefore, based on a uni-modality distribution assumption, many researchers have proposed virtual sample generation methods to expand the training sample size to enhance the performance of small data set learning. In practice, small data may be following a multi-modality distribution. Therefore, in order to solve multi-modal small data sets, this study proposes a new approach to create multi-modality Weibull virtual samples, where we use the maximal p-value to estimate parameters of the Weibull distribution. In addition, the soft DBSCAN method is used to identify a suitable number of modalities. One data set is employed to check the performance of the proposed method, and comparisons are made by the prediction on root mean square error. The results using a paired t-test show that the proposed method has a superior prediction performance than that of the mega-trend-diffusion method using a uni-modality triangular membership function.