An adaptive Hamiltonian circuit of virtual sample generation for a small dataset

Small datasets often lead to poor performance of data-driven prediction models due to uneven data distribution and large data spacing. One popular approach to address this issue is to use virtual samples during machine learning (ML) model training. This study proposes a Hamiltonian Circuit Virtual Sample Generation (HCVSG) method to distribute virtual samples generated using interpolation techniques while integrating the K-Nearest Neighbors (KNN) algorithm in model development. The Hamiltonian circuit is chosen because it doesn’t depend on the distribution assumption and provides multiple circuits that allow adaptive sample distribution, allowing the selection of circuits that produce minimum errors. This method supports improving feature-target correlation, reducing the risk of overfitting, and stabilizing error values as model complexity increases. Applying this method to three datasets in material research (MLCC, PSH, and EFD) shows that HCVSG significantly improves prediction accuracy compared to conventional KNN and eight MTD-based methods. The distribution of virtual samples along the Hamiltonian circuit helps fill the information gap and makes the data distribution more even, ultimately improving the predictive model's performance.