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[Display omitted] • The small dataset problem is an important issue in manufacturing and academia. • A new Newton-VSG approach generates virtual samples with non-linear distributions. • The suggested method's efficacy is verified using two real datasets. • Paired Wilcoxon test elucidates the significance of differences among four VSG methods. In today's highly competitive environment, modeling the relationship between inputs and outputs using limited data for a management system at the early stages is important, but difficult. The virtual sample generation (VSG) method has been proposed in many studies to explore potential information to improve prediction performance of learning models for small datasets. However, those studies in general must assume an underlying distribution such as a linear triangular membership function or a Gaussian distribution to generate virtual samples. Thus, previous VSG methods may not effectively upgrade learning performance when the assumed distribution is not elastic enough for small datasets. To address this issue, in this paper, we proposed a novel VSG method called Newton-VSG method to generate virtual samples for small datasets with non-linear and asymmetric distributions. In the suggested method, we used Newton's method to estimate the minimum value of data range and the shape of data distribution. Further, we developed two deep learning models including Siamese network (SN) model for screening virtual sample input values and bagging auto-encoder (AE) model for predicting virtual sample output to ensure the quality of virtual samples. One real dataset for solidification cracking susceptibility test data and an other real dataset obtained from TFT-LCD process of a leading company in Taiwan were used to demonstrate the efficacy of the proposed method. On the partial least square regression (PLSR) and the back propagation neural network (BPNN) predictive models, we compared the proposed method with three state-of-the-art VSG methods in items of the mean absolute error (MAE) and the root mean squared error (RMSE). The experimental results demonstrated that the proposed method outperforms the other three VSG methods in prediction accuracy for small datasets. [ABSTRACT FROM AUTHOR]

A small dataset often makes it difficult to build a reliable learning model, and thus some researchers have proposed virtual sample generation (VSG) methods to add artificial samples into small datasets to extend the data size. However, for some datasets the assumption of the distribution of data in the VSG methods may be vague, and when data only has a few attributes, such approaches may not work effectively. Other researchers thus proposed attribute extension methods to generate attributes to convert data into a higher dimensional space. Unfortunately, the resulting dataset may become a sparse dataset with many null or zero values in extended attributes, and then a large quantity of such attributes will reduce the representativeness of instances for the learning model. Therefore, based on fuzzy theories, this paper proposes a novel sample attribute extending (SEA) method to extend a suitable quantity of attributes to improve small dataset learning. In order to verify the validity of the SEA method, using SVR and BPNN, this paper adopts two real cases and two public datasets to conduct the learning of the predictive model, and uses the paired t -test to statistically examine the significance of improvement. The experimental results show that the proposed SEA method can effectively improve the learning accuracy of small datasets. [ABSTRACT FROM AUTHOR]