## 5 Case Study
### Experimental Results and Comparison  
We run all the methods by missing rate ranging from 10% to 50%. In the following section, we first demonstrate that the methods using the proposed framework are better than single methods. Then, the performance of KNN-SVM is significantly better than the reference methods. Finally, we discuss the influences of cold- and warm-start scenarios in prediction. The single methods, KNN, GRNN, SVD, BPCA, BBPCA, are commonly used for continuous variables. For the mixed data type, they put the categories as the continuous numbers instead of labels. The predict values tend to be wildly inaccurate due to rounding errors. As shown in Figure 5a, the performance of all single methods predicting with categorical variables is negative. Compared with continuous variables, RMSE of categorical variables triples. By comparing the performance of different single methods, KNN outperforms other methods in terms of \(\text{RMSE}_{1}\) (Figure 5b) and has reasonable computation time in real-world applications (Figure 5c). GRNN has poor performance in not only the accuracy but also the computation time. For the shortest computation time of SVD (<0.01 s), there is a fatal flaw that when the missing rate is large, SVD is trapped into a loop without solution. For BPCA, the predicted values of the same requirement are identical, which cannot be applied to predict missing values of FR in product customization. Although BBPCA repairs the gap in BPCA, the performance is still unsatisfactory. KNN seems to be the best method for regression in the first layer of the proposed framework. Then, we compare the composite methods strengthened by the proposed framework. As shown in Table 2, handling the continuous and categorical variables of FR separately (in the proposed framework) is beneficial. The significant benefit of KNN-GRNN is the shorter computation time than GRNN. After KNN finishes the continuous variable prediction, there are fewer missing values for GRNN to classify; thus, the training time of GRNN is shortened and the total computation time is also shortened. For KNN-SVD, the problem of no solution in high missing rate is solved. As parts of missing values have been predicted, SVD can be operated even with high missing rate. The performance of KNN-BBPCA is a bit better than BBPCA. However, the improvement is not significant for these methods, with average reduction in RMSE of only 3.7% against single methods. It is found that SVD and BBPCA are not feasible for categorical variable prediction. Meanwhile, GRNN costs too long computation time. Thus, we search for other classification methods for predicting the missing categorical variables in the proposed framework. The selected methods include the naive Bayes classifier, decision trees model, and SVM, which are all classic and popular methods in data classification. Some classic binary classifiers are advanced with DAG for multi-class classification (Section 4.2.1). As shown in Figure 6, all three new classifiers are better than the original three composite methods. In detail, with the same method (KNN) predicting the continuous variables, KNN-SVM outperforms other methods in terms of RMSE as well as Ang, Len, and FSN. KNN-SVD and KNN-Tree are better than KNN-SVM in terms of computation time