# An FCM-GABPN Ensemble Approach for Material Feeding Prediction of Printed Circuit Board Template
## 1 Introduction
The experimental results indicated that the attempt of the pre-classifying of inputs and establishing a prediction model for each category can indeed improve the prediction accuracy of material feeding for PCB template production. However, the MSC-ANN considered only one attribute to classify the sample, and the attributes were selected for each category by only one feature selection approach. Meanwhile, a template might be partitioned into multiple categories with different degrees, while the pre-partition based on MSC is a hard clarification. Therefore, it seems to be insufficient to predict the production-feeding panel of each template by using a prediction approach suited to a single category. Besides, MSC-ANN cannot handle a template order belonging to the border of two adjacent categories, because neither of the prediction models for the two categories is suitable for the template. Furthermore, the initialization parameter optimization of ANN benefits accuracy improvement [11; 18; 19] but was not considered. For tackling the aforementioned difficult problems, a fuzzy c-means (FCM) classifier was adopted to handle the fuzzy classification and back-propagation network (BPN) ensemble with an aggregator BPN was employed to tackle the prediction by considering the membership degree of each template. The linear correlation (LC) [20], maximum information coefficient (MIC) [21], recursive feature elimination (RFE) [22], LR [23], lasso regression [24], ridge regression [25], and random forest regression (RFR) [26]seven feature selection approaches were taken to select the critical attributes of each category divided by FCM. The GA was used to optimize the initialization parameters of BPN for each category. The reason for employing an FCM is that it accounts for the flexible classification (a template might be clustered into multiple categories with different membership degrees) and was widely used in many fields [27; 28; 29]. The reason for applying GA is that GA is easy to encode the problem and achieve good optimization results. It was also widely employed to optimize the structure (the number of layers and nodes in each hidden layer) and/or initial weight and bias [18; 19; 30] for the purpose of improving the prediction effectiveness of BPN. An aggregator BPN was adopted to conduct nonlinear aggregation because, theoretically, a BPN can approximate any nonlinear relationship [31]. In the proposed FCM-GABPN approach, input samples were first clustered with FCM, and seven feature selection methods were utilized to select critical attributes related to scrap rate for each category (a cluster is taken as a category) of PCB templates before they were fed into the BPN. Then, samples belonging to different categories were trained with different BPNs, in which the separately selected attributes were taken as their inputs and the initial parameters were optimized with GA. After training, an ensemble predictor formed with all GABPNs was taken to predict the scrap rate. Finally, another BPN was adopted to conduct nonlinear aggregation of the outputs from the component BPNs and determine the predicted feeding panel of the PCB template with a transformation. The proposed FCM-GABPN approach is illustrated in Figure 1.  
The remainder of the paper is organized as follows. In Section 2, variables specification and sample collection are described. The FCM, feature selection methods, GABPN, and the nonlinear aggregation BPN are introduced in Section 3, followed by experimental results and discussion in Section 4. Lastly, conclusions are given in Section 5.