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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]

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]

Generative adversarial networks are known as being capable of outputting data that can imitate the input well. This characteristic has led the previous research to propose the WGAN_MTD model, which joins the common version of Generative Adversarial Networks and Mega-Trend-Diffusion methods. To prevent the data-driven model from becoming susceptible to small datasets with insufficient information, we introduced a robust Bayesian inference to the process of virtual sample generation based on the previous version and proposed its refined version, WGAN_MTD2. The new version allows users to append subjective information to the contaminated estimation of the unknown population, at a certain level. It helps Mega-Trend-Diffusion methods take into account not only the information from original small datasets but also the user's subjective information when generating virtual samples. The flexible model will not be subject to the information from the present datasets. To verify the performance and confirm whether a robust Bayesian inference benefits the effective generation of virtual samples, we applied the proposed model to the learning task with three open data and conducted corresponding experiments for the significance tests. As the experimental study revealed, the integrated framework based on GAN and RBI, WGAN_MTD2, can perform better and lead to higher learning accuracies than the previous one. The results also confirm that a robust Bayesian inference can improve the information capturing from insufficient datasets. [ABSTRACT FROM AUTHOR]

It is difficult for learning models to achieve high classification performances with imbalanced data sets, because with imbalanced data sets, when one of the classes is much larger than the others, most machine learning and data mining classifiers are overly influenced by the larger classes and ignore the smaller ones. As a result, the classification algorithms often have poor learning performances due to slow convergence in the smaller classes. To balance such data sets, this paper presents a strategy that involves reducing the sizes of the majority data and generating synthetic samples for the minority data. In the reducing operation, we use the box-and-whisker plot approach to exclude outliers and the Mega-Trend-Diffusion method to find representative data from the majority data. To generate the synthetic samples, we propose a counterintuitive hypothesis to find the distributed shape of the minority data, and then produce samples according to this distribution. Four real datasets were used to examine the performance of the proposed approach. We used paired t-tests to compare the Accuracy, G-mean, and F-measure scores of the proposed data pre-processing (PPDP) method merging in the D3C method (PPDP+D3C) with those of the one-sided selection (OSS), the well-known SMOTEBoost (SB) study, and the normal distribution-based oversampling (NDO) approach, and the proposed data pre-processing (PPDP) method. The results indicate that the classification performance of the proposed approach is better than that of above-mentioned methods. [ABSTRACT FROM AUTHOR]

Oversampling is the most popular data preprocessing technique. It makes traditional classifiers available for learning from imbalanced data. Through an overall review of oversampling techniques (oversamplers), we find that some of them can be regarded as danger-information-based oversamplers (DIBOs) that create samples near danger areas to make it possible for these positive examples to be correctly classified, and others are safe-information-based oversamplers (SIBOs) that create samples near safe areas to increase the correct rate of predicted positive values. However, DIBOs cause misclassification of too many negative examples in the overlapped areas, and SIBOs cause incorrect classification of too many borderline positive examples. Based on their advantages and disadvantages, a boundary-information-based oversampler (BIBO) is proposed. First, a concept of boundary information that considers safe information and dangerous information at the same time is proposed that makes created samples near decision boundaries. The experimental results show that DIBOs and BIBO perform better than SIBOs on the basic metrics of recall and negative class precision; SIBOs and BIBO perform better than DIBOs on the basic metrics for specificity and positive class precision, and BIBO is better than both of DIBOs and SIBOs in terms of integrated metrics. [ABSTRACT FROM AUTHOR]

Abstract: Lifetime performance assessment is important in service (or manufacturing) industries. Hence, lifetime performance index is used to measure the potential and performance of a process, where is the lower specification limit. In this paper, assuming the conjugate prior distribution and squared-error loss function, this study constructs a Bayes estimator under the Rayleigh distribution with the progressive type II right censored sample. The Bayes estimator of is then utilized to develop a credible interval in the condition of known . Moreover, we also propose a Bayesian test to assess the lifetime performance of products. Finally, we give two examples and the Monte Carlo simulation to assess the behavior of the lifetime performance index . Moreover, the purchasers can then employ the credible interval and the Bayesian test to determine whether the product performance adheres to the required level. [ABSTRACT FROM AUTHOR]