# Multi-Source Heterogeneous Kernel Mapping in Software Defect Prediction
## 2 Related Works
### Heterogeneous Defect Prediction
The kernel matrix is then used to align the source and target domains by maximizing the correlation between them. After that, in [16], they presented a novel two-stage ensemble learning (TSEL) method for HDP. In the first stage, the EMKCA method is employed. In the second stage, the RESample with replacement (RES) technique is adopted to train multiple EMKCA predictors with diversity, which are then aggregated using the average ensemble method. [PERSON] et al. [17] suggested an innovative approach for HDP, called the kernel spectral embedding transfer ensemble (KSETE). Their approach entails tackling the class imbalance issue within the source data set initially, then combining kernel spectral embedding, transfer learning, and ensemble learning, to identify potential common kernel feature subspaces. Finally, classifiers are built on every common feature space to make predictions for the target. [PERSON] et al. [18] proposed a new heterogeneous domain adaptation (HDA) method for HDP. HDA is a subfield of domain adaptation. It is utilized to embed cross-project data into a low-dimensional comparable feature space, followed by the measurement of the dissimilarity between the mapped domains based on dictionary learning techniques. Subsequently, in [19], they proposed a novel Multiple-View Spectral Embedding (MVSE) approach for HDP. MVSE combines multiple views of the data into a unified low-dimensional depiction that aptly captures the underlying structure of the data. In terms of HDP, MVSE utilizes a spectral embedding technique to transform the heterogeneous feature set into a coherent space, maximizing the similarity between the two mapped feature sets. The key idea is to perform spectral embedding on each view of the data. [PERSON] et al. [20] proposed an unsupervised deep domain adaptation method for HDP. Specifically, they first adopt the unified metric representation (UMR) of the source and target project data. Next, a deep autoencoder is employed to acquire feature representations for both source and target projects. Finally, the maximum mean difference (MMD) is introduced, as a measure to characterize the disparity between the projects, and an adversarial loss function is utilized to minimize the distance between these feature representations. [PERSON] et al. [22] presented a few-shot learning-based balanced distribution adaptation (FSLBDA), which requires little labeled data to fit the distribution of the target domain. Specifically, first, extreme gradient boosting is employed to eliminate redundant metrics of the data sets. Then, balanced distribution adaptation is utilized to alleviate the difference between the source and target domains. Finally, the influence of a small training data set can be reduced by adaptive boosting. [PERSON] et al. [23] recently introduced optimal transport (OT) theory, and proposed two prediction algorithms for HDP using optimal transport: one algorithm is based on the entropic Gromov-Wasserstein (EGW) discrepancy, while the other is the EGW+ transport algorithm. Specifically, the method first computes a transportation plan that minimizes the discrepancy between the source and target distributions. Subsequently, a weighted transfer learning approach is used to transfer knowledge from the source domain to the target domain, based on the transportation plan. The above HDP methods all use single-source project data as training data. However, in order to obtain good model performance, the data quality of the source project needs to be high. Once the data does not meet the requirements, it will lead to negative transfers. In this scenario, these methods cannot achieve satisfactory model performance.