Abstract
Small sample problems indicate that the lack of sufficient training data leads to poor prediction performance and erroneous conclusions as well. For that matter, collecting more data is the simplest and most direct choice. However, in some cases it is difficult, even impossible, to pursue additional data for analysis. For example, ever since the product life cycle became shorter and shorter, it has become more and more difficult to collect sufficient data for acquiring management knowledge in the early stages in manufacturing systems. It indeed has been an awkward situation for managers. Also, there are some circumstances, namely rare events, to infrequently occur in the real world, e.g. severe earthquakes, tsunamis, tornados, terrorist attacks, and periodic psychotic episodes of individual schizophrenics. In analyzing such events, their available data are rare in nature, and what is more, they often go along with high socio-economic cost. Thus, how to bring out the information from a small sample as more as possible remains a critical issue.To serve the needs above, we have advanced a heuristic measure termed as Data Construction Method (DCM) based on the multiset division. The DCM can not only generate addition data within the domain value of the given sample for revealing the data’s patterns, but also creates the membership function from the generated data for further applications. In this way, the DCM is taken to filling up the information gaps caused by small-sample-sets.To demonstrate the effectiveness of DCM, after presenting the DCM’s theoretic background, properties, and algorithm, we compared the DCM with several existing approaches in estimating the population mean and improving the supervised neural network learning performance. The results show that the DCM performs better in a comparative manner. Then, we applied the membership function derived from the DCM data to the studies of predicting the severe earthquakes in Taiwan and forecasting the psychotic episode of individual schizophrenics. The results show that the DCM can provide an appropriate reference for prediction.