# Multi-Criteria Spare Parts Classification Using the Deep Convolutional Neural Network Method
## 2 Preliminaries
### AlexNet Structure  
For original AlexNet structure, as shown in Figure 1, there are a total of eight layers including five convolutions and three fully connected layers in this network. It is obvious that the AlexNet structure proceeds in both the upper and the down layer with 2 GPUs at the same time, which improves the computing efficiency greatly [32].  
The first layer is the input layer wherein RGB images with pixels of 224 \(\times\) 224 \(\times\) 3 are preprocessed into 227 \(\times\) 227 \(\times\) 3. In this layer, 96 convolution kernels \(11*11*3\) in size are used to extract the features. With the stride movement of four pixels, FeatureMap generates \(55\times 55\times 96\). FeatureMap is input into the first ReLu activation function and then processed via max-pooling with a pooling unit of size \(3*3\) to obtain pixel sets of 27 \(\times\) 27 \(\times\) 96. Local response normalization is adopted in this layer with the output 27 \(\times\) 27 \(\times\) 96, and the data is divided into two groups as 27 \(\times\) 27 \(\times\) 48 because of two GPUs.  
Next, for the second layer, the input has been two sets of 27 \(\times\) 27 \(\times\) 48. For each set, 128 convolution kernels \(5*5*48\) bring about the output of 27 \(\times\) 27 \(\times\) 128. There are the same calculation processes in this layer as the first layer, including ReLu function and local response normalization, finally with the output of two sets 13 \(\times\) 13 \(\times\) 128.  
The third layer is fully connected to the two GPUs in second layer. However, only convolution and ReLu are processed in this layer with 384 convolution kernels \(3*3*256\), with the FeatureMap of 13 \(\times\) 13 \(\times\) 384 and 13 \(\times\) 13 \(\times\) 192 for each GPU.  
Same process happen in the fourth layer with the output of 13 \(\times\) 13 \(\times\) 192.  
In the fifth layer, the input data are two sets of 13 \(\times\) 13 \(\times\) 192 with 128 convolution kernels of size \(3*3*192\). The scale of the pooling operation is \(3*3\), the step size of the operation is 2, and then the output of \(6\times 6\times 256\) is obtained.  
The sixth layer is a fully connected layer with the input of 6 \(\times\) 6 \(\times\) 256. There are a total of 4096 filters with size of \(6*6*256\) that can perform convolution operations. Since the size of convolution kernel is same as the size of input, there is only one value after convolution operation. Therefore, the size of the convolution pixel layer is 4096 \(\times\) 1 \(\times\) 1. Namely, there are 4096 neurons. The 4096 neurons are processed by ReLu function and output 4096 values.  
There are same fully connected, ReLu function and Dropout process in the seventh layer with the 4096 input. Finally, the 4096 data are fully connected to the 1000 neurons in the eighth layer. The probability of the 4096 data moving toward the 1000 categories can be calculated accordingly. The category corresponding to the largest probability value is selected as the category of the initial input image.  
Unlike the SVM method, which has an uncalibrated computation process and scores for all classes that are not easily interpretable, the Softmax classifier allows the user to compute \"probabilities\" for all labels. For example, given an image, the SVM classifier might give scores [12.5, 0.6, \(-\)23.0] for the classes \"cat\", \"dog\", and \"ship\". The Softmax classifier can instead compute the probabilities of the three labels as [0.9, 0.09, 0.01], which allows the confidence in each class to be interpreted