Small Sample Size Problem Research Articles

Novel Discriminant Locality Preserving Projection Integrated With Monte Carlo Sampling for Fault Diagnosis

In complex industrial processes, the technique of fault diagnosis has been playing an increasingly considerable role in ensuring the safety of life and property. Unfortunately, the process data of complex industrial processes have the features of high dimension. Feature extraction from high-dimensional data is promising to coping with the fault data with high dimension. Recently, one of manifold learning methods named discriminant locality preserving projection achieves excellent performance in feature extraction. However, the performance of discriminant locality preserving projection (DLPP) is subject to the problem of matrix decomposition in the denominator of the objection function caused by the small sample size (SSS) issue. To overcome this limitation, novel DLPP integrated with Monte Carlo sampling is proposed to enhance the performance of feature extraction through dimensionality reduction. In the proposed MC-DLPP, Monte Carlo sampling is first utilized to generate fault samples for each fault type. With the aid of the virtually generated fault samples, the rank of the matrix in the denominator of the objection function of DLPP increases, thus well addressing the SSS problem. The Softmax classifier is used for fault diagnosis. To test the performance of the improved DLPP-based fault diagnosis, case studies using the Tennessee Eastman process are carried out. Simulation results confirm the presented MC-DLPP achieves superior accuracy in fault diagnosis.

Machine Learning Models for Predicting Adverse Pregnancy Outcomes in Pregnant Women with Systemic Lupus Erythematosus

Predicting adverse outcomes is essential for pregnant women with systemic lupus erythematosus (SLE) to minimize risks. Applying statistical analysis may be limited for the small sample size of childbearing patients, while the informative medical records could be provided. This study aimed to develop predictive models applying machine learning (ML) techniques to explore more information. We performed a retrospective analysis of 51 pregnant women exhibiting SLE, including 288 variables. After correlation analysis and feature selection, six ML models were applied to the filtered dataset. The efficiency of these overall models was evaluated by the Receiver Operating Characteristic Curve. Meanwhile, real-time models with different timespans based on gestation were also explored. Eighteen variables demonstrated statistical differences between the two groups; more than forty variables were screened out by ML variable selection strategies as contributing predictors, while the overlap of variables were the influential indicators testified by the two selection strategies. The Random Forest (RF) algorithm demonstrated the best discrimination ability under the current dataset for overall predictive models regardless of the data missing rate, while Multi-Layer Perceptron models ranked second. Meanwhile, RF achieved best performance when assessing the real-time predictive accuracy of models. ML models could compensate the limitation of statistical methods when the small sample size problem happens along with numerous variables acquired, while RF classifier performed relatively best when applied to such structured medical records.

An Adaptive Multipath Linear Interpolation Method for Sample Optimization

When using machine learning methods to make predictions, the problem of small sample sizes or highly noisy observation samples is common. Current mainstream sample expansion methods cannot handle the data noise problem well. We propose a multipath sample expansion method (AMLI) based on the idea of linear interpolation, which mainly solves the problem of insufficient prediction sample size or large error between the observed sample and the actual distribution. The rationale of the AMLI method is to divide the original feature space into several subspaces with equal samples, randomly extract a sample from each subspace as a class, and then perform linear interpolation on the samples in the same class (i.e., K-path linear interpolation). After the AMLI processing, valid samples are greatly expanded, the sample structure is adjusted, and the average noise of the samples is reduced so that the prediction effect of the machine learning model is improved. The hyperparameters of this method have an intuitive explanation and usually require little calibration. We compared the proposed method with a variety of machine learning prediction methods and demonstrated that the AMLI method can significantly improve the prediction result. We also propose an AMLI plus method based on the linear interpolation between classes by combining the idea of AMLI with the clustering method and present theoretical proofs of the effectiveness of the AMLI and AMLI plus methods.

Discriminant Feature Extraction by Generalized Difference Subspace.

In this paper, we reveal the discriminant capacity of orthogonal data projection onto the generalized difference subspace (GDS), both theoretically and experimentally. In our previous work, we demonstrated that the GDS projection works as a quasi-orthogonalization of class subspaces, which is an effective feature extraction for subspace based classifiers. Here, we further show that GDS projection also works as a discriminant feature extraction through a similar mechanism to the Fisher discriminant analysis (FDA). A direct proof of the connection between GDS projection and FDA is difficult due to the significant difference in their formulations. To circumvent the complication, we first introduce geometrical Fisher discriminant analysis (gFDA) based on a simplified Fisher criterion. It is derived from a heuristic yet practically plausible assumption: the direction of the sample mean vector of a class is largely aligned to the first principal component vector of the class, given that the principal component analysis (PCA) is applied without data centering. gFDA works stably even under few samples, bypassing the small sample size (SSS) problem of FDA. We then prove that gFDA is equivalent to GDS projection with a small correction term. This equivalence ensures GDS projection to inherit the discriminant ability from FDA via gFDA. Furthermore, we discuss two useful extensions of these methods, 1) a nonlinear extension by kernel trick, 2) a combination with CNN features. The equivalence and the effectiveness of the extensions have been verified through extensive experiments on the extended Yale B+, CMU face database, ALOI, ETH80, MNIST, and CIFAR10, mainly focusing on image recognition under small samples.

SeqTrans: Automatic Vulnerability Fix Via Sequence to Sequence Learning

Software vulnerabilities are now reported unprecedentedly due to the recent development of automated vulnerability hunting tools. However, fixing vulnerabilities still mainly depends on programmers’ manual efforts. Developers need to deeply understand the vulnerability and affect the system’s functions as little as possible. In this paper, with the advancement of Neural Machine Translation (NMT) techniques, we provide a novel approach called SeqTrans to exploit historical vulnerability fixes to provide suggestions and automatically fix the source code. To capture the contextual information around the vulnerable code, we propose to leverage data-flow dependencies to construct code sequences and feed them into the state-of-the-art transformer model. The fine-tuning strategy has been introduced to overcome the small sample size problem. We evaluate SeqTrans on a dataset containing 1,282 commits that fix 624 CVEs in 205 Java projects. Results show that the accuracy of SeqTrans outperforms the latest techniques and achieves 23.3% in statement-level fix and 25.3% in CVE-level fix. In the meantime, we look deep inside the result and observe that the NMT model performs very well in certain kinds of vulnerabilities like CWE-287 (Improper Authentication) and CWE-863 (Incorrect Authorization).

FedFV: A Personalized Federated Learning Framework for Finger Vein Authentication

Most finger vein authentication systems suffer from the problem of small sample size. However, the data augmentation can alleviate this problem to a certain extent but did not fundamentally solve the problem of category diversity. So the researchers resort to pre-training or multi-source data joint training methods, but these methods will lead to the problem of user privacy leakage. In view of the above issues, this paper proposes a federated learning-based finger vein authentication framework (FedFV) to solve the problem of small sample size and category diversity while protecting user privacy. Through training under FedFV, each client can share the knowledge learned from its user’s finger vein data with the federated client without causing template leaks. In addition, we further propose an efficient personalized federated aggregation algorithm, named federated weighted proportion reduction (FedWPR), to tackle the problem of non-independent identically distribution caused by client diversity, thus achieving the best performance for each client. To thoroughly evaluate the effectiveness of FedFV, comprehensive experiments are conducted on nine publicly available finger vein datasets. Experimental results show that FedFV can improve the performance of the finger vein authentication system without directly using other client data. To the best of our knowledge, FedFV is the first personalized federated finger vein authentication framework, which has some reference value for subsequent biometric privacy protection research.

Disease Classification Model Based on Multi-Modal Feature Fusion

Aiming at the application of classification tasks in deep learning in disease classification, this paper proposes a disease classification model based on multi-modal feature fusion. In this model, chest X-ray images of patients are used as image modal data, and corresponding disease descriptions are used as text modal data. By innovatively pro-posing an adaptive multi-modal attention mechanism, the feature vectors extracted from the two modal data are fused for classification by classifier. In order to verify the effectiveness of the proposed model in disease classification, this paper uses Chest X-ray dataset in open I database. In order to solve the problem of small sample size and unbalanced sample categories in this dataset, SMOTE algorithm is used to expand the samples and ablation study is designed to compare the model effects. The results show that the model based on both image and text modes and sample expansion by SMOTE algorithm can solve the problems of overfitting, low recall and F1 value due to small samples and unbalanced samples. In addition, the classification accuracy of multi-modal model using image and text is improved by about 0.55% and 2.69% respectively compared with single-modal model using only image or text. Similarly, the addition of adaptive multi-modal attention mechanism also improves the classification effect of the model by about 0.41% compared with the feature fusion method using vector concatenation simply.

A Sample Enhancement Method Based on Simple Linear Iterative Clustering Superpixel Segmentation Applied to Multibeam Seabed Classification

Full-coverage and high-efficiency seabed sediment detection and identification are critical elements of digital marine construction that support the three-dimensional and thematic development of maritime spatial geographic information systems. With the development of multibeam echo sounder (MBES), the use of MBES backscatter intensity and bathymetry data to extract backscatter angular response (AR) features has increased. Using backscatter intensity features and seabed terrain features for classification is an effective way to achieve large-scale seabed sediment classification. However, it was still limited by small sample size problems and the poor stability of the classification model due to the complexity of performing seabed sediment sampling. In response to the above issues, this paper proposes a sample enhancement method based on simple linear iterative clustering (SLIC) superpixel segmentation to address the problems. First, a superpixel-based sample homogeneity expansion method is combined with multibeam backscatter intensity images to achieve adaptive sample range selection. Then, a Random Forest (RF)-based model is constructed using MBES backscatter intensity and seabed terrain features. To assess the model’s validity, the experiment uses data from an extensive MBES survey and field sampling information from the Celtic Sea, UK. It achieves accurate predictions for the area’s eight sediment types. The experimental results show that the proposed method expands 60 groups of original sample points to 9293 groups of valid sample points, and achieves an overall classification accuracy and kappa coefficient of 84.05% and 0.81 for the seabed sediment, respectively. In addition, the classification accuracy is significantly better compared to the traditional methods.

Block Division Convolutional Network With Implicit Deep Features Augmentation for Micro-Expression Recognition

Despite the development of computer vision techniques, the micro-expression (ME) recognition task still remains a great challenge because MEs have very low intensity and short duration. However, the ME recognition is of great significance since it provides important clues for real affective states detection. This paper proposes a novel Block Division Convolutional Network (BDCNN) with the implicit deep features augmentation. In detail, BDCNN learns from four optical flow features computed by the onset and apex frames of each video. It innovatively divides each image into a set of small blocks in the deep learning model, then the convolution and pooling operations are performed on these small blocks in sequence. To handle the small sample size problem in the micro-expression data, this study uses the improved implicit semantic data augmentation algorithm in the deep features space. Experiments are conducted on three publicly available databases, viz, CASME II, SMIC, and SAMM. Experimental results show that our model outperforms the state-of-the-art methods by attaining the accuracy of 84.32% and F1-score of 82.13% on the 3-class datasets, and the accuracy of 81.82% and F1-score of 75.46% on the 5-class datasets, respectively. Our source code is publicly available for non-commercial or research use at https://github.com/MLDMXM2017/BDCNN.

Swallow Detection with Acoustics and Accelerometric-Based Wearable Technology: A Scoping Review.

Swallowing disorders, especially dysphagia, might lead to malnutrition and dehydration and could potentially lead to fatal aspiration. Benchmark swallowing assessments, such as videofluoroscopy or endoscopy, are expensive and invasive. Wearable technologies using acoustics and accelerometric sensors could offer opportunities for accessible and home-based long-term assessment. Identifying valid swallow events is the first step before enabling the technology for clinical applications. The objective of this review is to summarize the evidence of using acoustics-based and accelerometric-based wearable technology for swallow detection, in addition to their configurations, modeling, and assessment protocols. Two authors independently searched electronic databases, including PubMed, Web of Science, and CINAHL. Eleven (n = 11) articles were eligible for review. In addition to swallowing events, non-swallowing events were also recognized by dry (saliva) swallowing, reading, yawning, etc., while some attempted to classify the types of swallowed foods. Only about half of the studies reported that the device attained an accuracy level of >90%, while a few studies reported poor performance with an accuracy of <60%. The reviewed articles were at high risk of bias because of the small sample size and imbalanced class size problem. There was high heterogeneity in assessment protocol that calls for standardization for swallowing, dry-swallowing and non-swallowing tasks. There is a need to improve the current wearable technology and the credibility of relevant research for accurate swallowing detection before translating into clinical screening for dysphagia and other swallowing disorders.

Designing a multi-objective mathematical model of a perishable supply chain (PSC) in a state of uncertainty

PurposeThe pharmaceutical industry is one of the most essential areas of health in any country. It is defined as a system of processes, operations and organizations involved in discovering, developing and producing drugs. The supply chain in the pharmaceutical field is one of the most important strategic issues in the pharmaceutical and health-care industries. The purpose of this study is to reduce the total cost of the supply chain network and reduce the amount of distribution scheduling.Design/methodology/approachIn this study, the authors designed a drug supply chain network with uncertainty-related corruption. The optimal number and location of potential facilities, the optimal allocation of flow between facilities, the optimal routing of vehicles and the optimal amount of inventory in production and distribution center warehouses were determined to achieve these two objective functions.FindingsIn evaluating the small sample size problem, it was found that the comprehensive benchmarking method was more efficient than the other methods in obtaining the mean index of the first objective function. The utility function method has also proved its efficiency in obtaining the mean of the second objective function indices, the spacing index and the computational time. Because of the inefficiency of GAMS software in resolving size issues, the modified NSGA II and MOPSO algorithms with modified priority-based encryption have been used. First, using the Taguchi method, the initial parameters of the metaheuristic algorithms are adjusted, and then, 15 sample problems are designed in larger sizes. To avoid generating random data, five problems were equally designed, and the averages of objective functions and metrics of met heuristic algorithms (number of efficient solutions, maximum expansion index, spacing index and computational time) were analyzed as the basis of evaluation and comparison. Therefore, using all the indicators and results of the NSGA II algorithm is recommended.Originality/valueIn this research, a biobjective modeling approach is proposed to minimize the total costs of the supply chain network (construction costs, storage costs and product transportation costs between centers) and advertising costs and to minimize distribution and transportation scheduling across each level of the supply chain network.

Multimodal data fusion based on IGERNNC algorithm for detecting pathogenic brain regions and genes in Alzheimer's disease.

At present, the study on the pathogenesis of Alzheimer's disease (AD) by multimodal data fusion analysis has been attracted wide attention. It often has the problems of small sample size and high dimension with the multimodal medical data. In view of the characteristics of multimodal medical data, the existing genetic evolution random neural network cluster (GERNNC) model combine genetic evolution algorithm and neural network for the classification of AD patients and the extraction of pathogenic factors. However, the model does not take into account the non-linear relationship between brain regions and genes and the problem that the genetic evolution algorithm can fall into local optimal solutions, which leads to the overall performance of the model is not satisfactory. In order to solve the above two problems, this paper made some improvements on the construction of fusion features and genetic evolution algorithm in GERNNC model, and proposed an improved genetic evolution random neural network cluster (IGERNNC) model. The IGERNNC model uses mutual information correlation analysis method to combine resting-state functional magnetic resonance imaging data with single nucleotide polymorphism data for the construction of fusion features. Based on the traditional genetic evolution algorithm, elite retention strategy and large variation genetic algorithm are added to avoid the model falling into the local optimal solution. Through multiple independent experimental comparisons, the IGERNNC model can more effectively identify AD patients and extract relevant pathogenic factors, which is expected to become an effective tool in the field of AD research.

Exponential Graph Regularized Non-Negative Low-Rank Factorization for Robust Latent Representation

Non-negative matrix factorization (NMF) is a fundamental theory that has received much attention and is widely used in image engineering, pattern recognition and other fields. However, the classical NMF has limitations such as only focusing on local information, sensitivity to noise and small sample size (SSS) problems. Therefore, how to develop the NMF to improve the performance and robustness of the algorithm is a worthy challenge. Based on the bottlenecks above, we propose an exponential graph regularization non-negative low-rank factorization algorithm (EGNLRF) combining sparseness, low rank and matrix exponential. Firstly, based on the assumption that the data is corroded, we decompose a given raw data item with a data error fitting noise matrix, applying a low-rank constraint to the denoising data. Then, we perform a non-negative factorization on the resulting low-rank matrix, from which we derive the low-dimensional representation of the original matrix. Finally, we use the low-dimensional representation for graph embedding to maintain the geometry between samples. The graph embedding terms are matrix exponentiated to cope with SSS problems and nearest neighbor sensitivity. The above three steps will be incorporated into a joint framework to validate and optimize each other; therefore, we can learn latent data representations that are undisturbed by noise and preserve the local structure of known samples. We conducted simulation experiments on different datasets and verified the effectiveness of the algorithm by comparing the proposed with the lasting ones related to NMF, low rank and graph embedding.

Quality prediction and sensitivity analysis of fine chemical products based on support matrix machine

Real-time detection of product quality in the chemical production process is essential for quality control and process adjustment. At present, in the chemical production process, product quality is sometimes difficult to be tested online, which is mainly obtained through laboratory sampling and testing. Due to the low sampling frequency of products and the large proportion of qualified products, there are problems of small sample size and imbalance between positive and negative samples. In addition, the chemical production process is complex, and there is coupling relationship among process variables. The soft quality prediction model based on the multiclass support matrix machine (MSMM) combined with bagging-SMOTE(BAG-SMOTE) and a sensitivity analysis method based on the change of curve shape is proposed in this paper. First, the time series process data is intercepted over a period of time based on the product sampling time to accurately correspond to the quality data from the laboratory. Second, the MSMM is used to build quality prediction model, which using the structural information between the ranks of the matrix samples consisted of time series process data. Besides, the imbalance problem between positive and negative samples is effectively solved by BAG-SMOTE ensemble sampling method. Then, the ensemble classification method is applied to the Tennessee Eastman (TE) and a fine chemical process. The classification evaluation index G-mean are 93% and F-score are 92%, respectively. The superiority of the proposed ensemble classification method is verified. Finally, in order to analyze the key factors of quality fluctuation, a sensitivity analysis method based on curve shape change is proposed via integrated classification metamodel. The method can effectively find out the main factors affecting the quality fluctuation, and the results are consistent with the actual situation.

Small-sample size problems solving based on incremental learning: an adaptive Bayesian quadrature approach

Small-sample size problems solving based on incremental learning: an adaptive Bayesian quadrature approach

Spatial Modeling of COVID-19 Prevalence Using Adaptive Neuro-Fuzzy Inference System

This study is dedicated to modeling the spatial variation in COVID-19 prevalence using the adaptive neuro-fuzzy inference system (ANFIS) when dealing with nonlinear relationships, especially useful for small areas or small sample size problems. We compiled a broad range of socio-demographic, environmental, and climatic factors along with potentially related urban land uses to predict COVID-19 prevalence in rural districts of the Golestan province northeast of Iran with a very high-case fatality ratio (9.06%) during the first year of the pandemic (2020–2021). We also compared the ANFIS and principal component analysis (PCA)-ANFIS methods for modeling COVID-19 prevalence in a geographical information system framework. Our results showed that combined with the PCA, the ANFIS accuracy significantly increased. The PCA-ANFIS model showed a superior performance (R2 (determination coefficient) = 0.615, MAE (mean absolute error) = 0.104, MSE (mean square error) = 0.020, and RMSE (root mean square error) = 0.139) than the ANFIS model (R2 = 0.543, MAE = 0.137, MSE = 0.034, and RMSE = 0.185). The sensitivity analysis of the ANFIS model indicated that migration rate, employment rate, the number of days with rainfall, and residential apartment units were the most contributing factors in predicting COVID-19 prevalence in the Golestan province. Our findings indicated the ability of the ANFIS model in dealing with nonlinear parameters, particularly for small sample sizes. Identifying the main factors in the spread of COVID-19 may provide useful insights for health policymakers to effectively mitigate the high prevalence of the disease.

Comparing Some Methods of Kernel Discriminant Analysis Under Fuzzy Environment

One of the most widely used statistical methods in the field of data analysis is the method of discriminant analysis, and the use of discriminant analysis requires the availability of a number of assumptions, the most important of which is that the data of explanatory variables have a multivariate normal distribution. The discriminant analysis often suffers from the problem of small sample size, especially when it is applied to classify several dimensions; we deal with this problem through the use of the Kernel Discriminant Analysis method (KDAM). But in many situations in real world suffuref from inaccuracy in measurements that is leads to inaccuracy in conducting the required statistical analyzes, so it is necessary to get out of the traditional pattern of data to that fuzzy pattern by finding a fuzzy information system based on the principle of cutting in the fuzzy group to find measurements of data that represent the phenomenon with certainty and which represent the group of important elements that represent those phenomenon. In this paper, we form the estimation function of the kernel density with an application in discriminant analysis to be a comparison in estimation density function depends on the choice of bandwidth, which controls the smoothing of the estimate and on the choice of the kernel function., some methods were used to estimate the bandwidth parameter, which is least square Cross validation, Biased cross validation and Bayes discriminant rule Method under fuzzy measurements. The estimation of Kernel density is important in multivariate data analysis, and it depends heavily on the appropriate selection of the bandwidth matrix (H) that reduces the mean integration square error (MISE) and the error rate (𝑀𝑅̂) through the common rule of sets which is KDR kernel discrimination. Finally, it was based on real data from the disease (general leukemia) and the 6 factors (variables) that affect the disease. We note that (KDA-Bay) method is better than (KDA-SCV) and (KDA-BCV) because it gives the lowest classification error rate from the results, and we note that all methods under fuzzy data better than the methods under traditional data.

Measuring and Mapping Micro Level Earning Inequality towards Addressing the Sustainable Development Goals – A Multivariate Small Area Modelling Approach

Abstract The earning inequality in India has unfavorably obstructed underprivileged in accessing elementary needs like health and education. Periodic labour force survey conducted by National Statistical Office of India generates estimates on earning status at national and state level for both rural and urban sectors separately. However, due to small sample size problem, these surveys cannot generate reliable estimates at micro-level viz. district or block. Thus, owing to unavailability of district-level estimates, analysis of earning inequality is restricted to the national and the state level. Therefore, the existing variability in disaggregate-level earning distribution often goes unnoticed. This article describes multivariate small area estimation method to generate precise and representative district-wise estimate of earning distribution in rural and urban areas of the Indian State of Bihar by linking Periodic labour force survey data of 2018–2019 and 2011 Population Census data of India. These disaggregate-level estimates and spatial mapping of earning distribution are essential for measuring and monitoring the goal of reduced inequalities related to the sustainable development of 2030 agenda. They expected to offer insightful information to decision-makers and policy experts for identifying the areas demanding more attention.

Co-training based virtual sample generation for solving the small sample size problem in process industry

With the development of industrialization, the production scale and complexity of process industries are getting larger and larger. But, limited by the small amounts of samples and the uneven sample distribution in the process industry, it is difficult to establish accurate and efficient data-driven soft sensor models to predict some variables. To further develop the application of soft sensor models, generating new virtual samples based on the original sample distribution to extend the sample set is an ideal approach to solve this problem. In this paper, a novel virtual sample generation method based on the co-training of two K-Nearest Neighbor (KNN) models is proposed. First, according to the sparse parameter, sparse regions in each dimension of the feature space are identified. Second, the input features of virtual samples are generated in these sparse regions by performing interpolation operations. Third, the outputs of virtual samples are predicted by double KNN regressors based on co-training. The qualified virtual samples are screened and the model is updated using these virtual samples to improve the prediction accuracy of the double KNN models. To verify the effectiveness and superiority of the proposed virtual sample generation method based on the co-training (CTVSG), case studies are conducted using two standard functions and a Purified Terephthalic Acid (PTA) industrial dataset, where the effectiveness of CTVSG is confirmed.

The application of support vector regression and virtual sample generation technique in the optimization design of transonic compressor

With the development of artificial intelligence, machine learning technique has been applied in turbomachinery optimization. However, the performance of a classic machine learning method largely depends on the quantity and quality of data samples. Due to the high cost of computational fluid dynamics models, a small sample size may restrict the reliability of machine learning models and optimization results. To tackle the small sample size problem in the turbomachinery optimization, this study uses support vector regression as a surrogate model. As a development of statistic learning theory, it performs well in the case of small samples. In order to expand the sample set, a mega-trend diffusion technique is adopted to generate virtual samples. The virtual samples generated from real samples can fill in the information gaps in the sparse domain. Then the support vector regression model is updated iteratively by virtual samples instead of real samples during optimization. In this way the calls of time-consuming numerical models are reduced and the optimization process is accelerated. The proposed method is validated by a high-dimensional aerodynamic optimization on the transonic compressor NASA Rotor 37. Firstly, a multi-objective optimization based on Free-form Deformation parameterization, support vector regression and NSGA-II algorithm is carried out. The optimized isentropic efficiency and total pressure ratio are increased by 1.7% and 12%, respectively. The choked mass flow rate is also raised. Then the virtual samples are generated using mega-trend diffusion and the surrogate model is updated. Finally, the optimization with virtual sample generation increases the efficiency by 2.3% compared to the baseline. Consequently, the proposed method can improve optimization results and relieve computational burden.