# Multi-Source Heterogeneous Kernel Mapping in Software Defect Prediction
## 2 Related Works  
### Heterogeneous Defect Prediction  
There have been several studies on HDP. [PERSON] et al. [9] introduced a method for HDP, utilizing metric matching as its foundation. First, feature selection is carried out on the source data to eliminate irrelevant or redundant features. Second, a metric match analyzer is used to calculate the matching scores between source and target data. Finally, a conventional machine learning method is used to facilitate the model training process and predict the defect tendency. [PERSON] et al. [10] introduced the statistical canonical correlation analysis (CCA) method into CPDP, and proposed a new method called CCA+. The core idea is to take the canonical correlation coefficient as the measurement standard of disparity in the distribution between the datasets, minimizing the canonical correlation coefficient to diminish the distribution discrepancy between the source and target data sets. The specific principles are as follows: First, the source and target data are pre-processed to construct a unified metric representation (UMR). Then, on the basis of UMR, canonical correlation analysis is carried out to calculate the projection vector and the mapping outcomes of both source and target data under the projection vector. Finally, the defect tendency within the target data set is forecast using the nearest neighbor classification in the new projection space, based on CCA+. [PERSON] et al. [11] introduced an innovative support vector machine algorithm for HDP, called the cost-sensitive correlation transfer support vector machine (CCT-SVM). They stated that the key emphasis of the software defect prediction process is placed on risk costs. By endeavoring to classify a module as defective, CCT-SVM offers an effective solution for reducing the negative impact of data imbalance. The specific method is as follows: First, the UMR technique is employed to enable the comparison of heterogeneous data. Subsequently, drawing upon the UMR result for heterogeneous data, the CCA technique is utilized to identify a common representation for features extracted from both source and target projects. Finally, they construct a novel SVM model for heterogeneous defect prediction by introducing a correlation regularizer and specific misclassification costs. [PERSON] et al. [12] put forward a new methodology, KCCA+, by combining a kernel function with CCA+, considering that CCA is essentially a linear transformation, and that there are often complex non-linear relationships between metric elements of different data sets. [PERSON] et al. [13] applied the technique of cost-sensitive learning and combined it with kernel learning technology to suggest a novel analysis approach for HDP, called cost-sensitive transfer kernel canonical correlation analysis (CTKCCA), which aims to address the problem of linear inseparability and alleviate issues related to class imbalance in the software defect prediction process. [PERSON] et al. [14] presented a heterogeneous cross-project defect tendency prediction algorithm on the basis of feature matching, called feature match transfer (FMT). The principle is as follows: First, the features of source data are selected, and the distribution curves of the features are calculated. Simultaneously, the method employed to calculate the distribution curves of features in the target data remains consistent. Then, according to a defined feature distance formula, feature matching between the source data and target data is completed. Finally, the model is trained, and the defects in the target data are predicted on the matched feature space. [PERSON] et al. [15] incorporated the concept of ensemble learning, and proposed a novel HDP method, known as ensemble multi-kernel correlation alignment (EMKCA). EMKCA constructs multiple kernels, based on different types of features extracted from the source and target domains. These kernels are then combined into a single kernel matrix, using an ensemble approach.