Search

A small dataset that contains very few samples, a maximum of thirty as defined in traditional normal distribution statistics, often makes it difficult for learning algorithms to make precise predictions. In past studies, many virtual sample generation (VSG) approaches have been shown to be effective in overcoming this issue by adding virtual samples to training sets, with some methods creating samples based on their estimated sample distributions and directly treating the distributions as unimodal without considering that small data may actually present multimodal distributions. Accordingly, before estimating sample distributions, this paper employs density-based spatial clustering of applications with noise to cluster small data and applies the AICc (the corrected version of the Akaike information criterion for small datasets) to assess clustering results as an essential procedure in data pre-processing. Once the AICc shows that the clusters are appropriate to present the data dispersion of small datasets, each of their sample distributions is estimated by using the maximal p value (MPV) method to present multimodal distributions; otherwise, all of the data is inferred as having unimodal distributions. We call the proposed method multimodal MPV (MMPV). Based on the estimated distributions, virtual samples are created with a mechanism to evaluate suitable sample sizes. In the experiments, one real and two public datasets are examined, and the bagging (bootstrap aggregating) procedure is employed to build the models, where the models are support vector regressions with three kernel functions: linear, polynomial, and radial basis. The results show that the forecasting accuracies of the MMPV are significantly better than those of MPV, a VSG method developed based on fuzzy C-means, and REAL (using original training sets), based on most of the statistical results of the paired t test. [ABSTRACT FROM AUTHOR]

[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]