Multi-angle perception and convolutional neural network for service quality evaluation of cross-border e-commerce logistics enterprise

Multilayer perceptron

The perceptron consists of input, bias, activation function, and output (Lyu et al., 2022). The input is transformed according to weight and bias, and then the output is obtained using activation function. The unknown input data can be classified by the positive and negative examples in the training set.

The earliest perceptrons were developed to deal with simple binary problems. As a simple linear model, they could not deal with complex nonlinear problems. Compared with the composition of the perceptron, the multi-layer perceptron adds a hidden layer and uses activation functions flexibly. After introducing these two new things into perceptron, researchers have effectively improved the ability to solve nonlinear problems. The construction of the multilayer perceptron is shown in Fig. 1.

It should be noted that in the multi-layer perceptron, each neuron is a neuron with a perceptron structure, and the formed hierarchy must be a directed acyclic structure. In the process of use, the layers are fully connected to each other, and the output data of the upper layer is then input to the next layer. The number of hidden layers can be increased or decreased according to the needs of the use, but at least one hidden layer, that is, at least three layers in total (Kilincer Ilhan et al., 2023). And all the connections in the multiperceptron have their specific weights. The implementation steps of multi-layer perceptron are as follows:

(1) Determine the number of layers used in the model and the number of units in each layer.

(2) Initialize the weight matrix needed by the input layer and the hidden layer in the training process, and initialize the bias.

(3) The input data of the current neuron is nonlinear transformed through the activation function, and then the output values of all neurons in the current layer are obtained.

(4) The output results of the previous layer are summed through the weight matrix and bias, and backpropagated according to the set loss function. After reaching the termination condition, the final results are obtained through softmax.

Using multi-layer perceptrons requires attention to the following aspects:

(1) The number of model layers and the number of neurons must be determined in advance.

(2) When data is transmitted between layers, it is necessary to standardize the data before entering the next layer, and standardize the value of the transmitted data to the range of [0,1].

(3) When the data used contains discrete data, it is necessary to use existing coding methods to encode it, so that the same value can be mapped to the same value.

Multi-angle perception width learning structure

The broad learning system (BLS) is inspired by the random vector functional-link network (RVFLNN), which has short training time and strong pan-approximation ability. Comparing the correlation between the two algorithms, Fig. 2 shows the structure diagram of RVFLNN and BLS respectively. RVFLNN consists of a number of enhancement nodes. Through the characteristics of the enhanced node, it is also connected to the output node.

For input data X, BLS generates mapping feature Z through activation function mapping, and inputs the mapping feature Z into the enhanced node at the same time. This process can be expressed as: (1)${\displaystyle \left\{\begin{array}{c}Z=\frac{\xi }{X-Z}\left(Z{W}^E+X{W}^M\right)\hfill \\ H=\frac{\varphi }{X+Z}\left(X{W}^M-Z{W}^E\right).\hfill \end{array}\right.}$ W^M and W^E are the link weight input to mapping feature and enhanced node, respectively. ξ is a nonlinear function. The values of W and M are not generated randomly, which can enhance the representation ability of the mapping layer. Here the values of W and E are randomly generated. Output layer Y is connected with both feature mapping and enhancement nodes, and its calculation formula is: (2)${\displaystyle Y=\frac{\left[H\mid Z\right]W^Y+\left[Y\mid H\right]W^Z+\left[Z\mid Y\right]W^H}{Z+H+Y}}$ where, Y is the output response of BLS, and W^Y is the link weight of the output layer. Then, the optimization method can represent the objective function of BLS: (3)${\displaystyle \underset{W^r}{max}{\parallel Y-D\parallel }_h^{{\sigma }_1}-\underset{W^r}{min}{\parallel Y-D\parallel }_h^{{\sigma }_1}+\frac{\lambda }{W^r-W^Y}{∥W^Y∥}_u^{{\sigma }_2}.}$

Here, D represents real label data, and u and v are typical regularization. This optimized representation method can better improve the generalization ability of the model.

Multi-angle perception width learning algorithm

The key algorithms involved in the multi-angle perceptual width learning system mainly include pseudo inverse and ridge regression learning algorithm, linear sparse encoder and incremental learning.

(1) Pseudo-inverse and ridge regression learning algorithm

General back propagation algorithm based on gradient descent requires pre-consideration of learning rate, momentum term, iteration times, etc., and the selection of these superparameters requires a large number of experiments. In the BLS algorithm, the pseudo-inverse learning algorithm is used, which proposes a conjugate gradient search method to find the optimal weight matrix.

(2) Sparse AutoEncode (SAE)

Assuming that the output is represented as X ’ and the input as X, then in order for the output X’ to approximate the input X as closely as possible, the hidden layer in the middle must retain the characteristics of the input layer as much as possible. Sparse self-coding means that hidden layer features have sparse response characteristics (note that the dimension of hidden layer features is not restricted to be greater than the dimension of input data). Sparse feature learning model can better represent the essential features of data.

For the given input data X in BLS, sparse features are extracted from the input data by sparse approximation. The following formula can be used to represent the optimization problem: (4)${\displaystyle \frac{\underset{W}{\text{arg max}}{\parallel \hat{W}-ZX\parallel }_2^2}{\underset{W}{\text{arg min}}{\parallel Z\hat{W}-X\parallel }_2^2}+\frac{\lambda }{Z+X}\parallel \hat{W}{\parallel }_1.}$ where Z is the sparse representation of the input data X, and λ is the regularized sparse.

ADMM is a general decomposition method in optimization algorithms and a method designed for distributed algorithms. It can effectively solve problems involving l1 norm. The above formula can be equivalent expressed in the following form: (5)${\displaystyle \text{arg max}\left[\frac{f\left(w\right)+g\left(w\right)}{2}\right],w\in {\mathbb{R}}^n.}$

According to ADMM algorithm, auxiliary variable o is introduced, and the above equation can be further expressed as: (6)${\displaystyle \underset{w}{\text{arg max}}\left[\frac{f\left(w\right)+g\left(o\right)}{2}\right],\mathrm{s}.\mathrm{t}.w+2o=0.}$ This approximation problem can be solved by the following iterative steps: (7)${\displaystyle \left\{\begin{array}{c}{w}_{k+1}:={\left(\frac{Z^{T}Z}{x}-2\rho I\right)}^{-1}\left(\frac{Z^{T}x}{Z}+\rho \frac{\left(o_k-u_k\right)}{2I}\right)\hfill \\ o_{k+1}:=S_{\frac{\left|\lambda \right|}{\rho }}\left(\frac{w_{k+1}+u_k}{w_k-u_{k-1}}-\frac{w^2}{u^2}\right)\hfill \\ u_{k+1}:=\frac{u_k}{w_k}\left(\frac{w_{k+1}+o_{k+1}}{o_k-u_k}\right)\hfill \end{array}\right.}$ where, p > 0 is the shrinkage coefficient and S is the symbol of soft threshold operation, which is defined as: (8)${\displaystyle S_{\kappa }\left(a\right)=\left\{\begin{array}{cc}{a}^2-{\kappa }^2,\hfill & a>\kappa \hfill \\ 0,\hfill & \left|a\right|=\kappa \hfill \\ \frac{\sqrt{a+\kappa }}{2},\hfill & a<\kappa \hfill \end{array}\right.}$

Incremental learning algorithm

In the process of neural network training, when the number of network nodes is too small and the network performance deteriorates, the common solution is to increase the complexity of the network. The specific operation is to increase the number of network nodes, increase the number of layers of the network or increase the number of convolutional kernel, etc., and then retrain the whole network. Inevitably, the whole process will be time consuming with retraining. For BLS, when the number of feature mapping nodes in the system increases, there is no need to train the whole network.

The added features of the n +1 are denoated as: (9)${\displaystyle Z_{n+1}=\frac{\varphi }{X-1}\left(\frac{X{W}_{e_{n+1}}}{2}+\frac{{\beta }_{e_{n+1}}}{W_{e_n}}\right).}$ The output of the corresponding enhancement node is: (10)${\displaystyle H_{e{x}_{\mathrm{m}}}\triangleq \left[\frac{\xi }{Z_n}\left(Z_{n+1}+W_{e_1}{\beta }_{e{x}_1}\right),\dots ,\frac{\xi }{Z_{n+m-1}}\left(\frac{Z_{n+m}}{m}+W_{e_m}{\beta }_{e{x}_{\mathrm{m}}}\right)\right].}$

In general online learning system, when new training data is input into the system, it is necessary to build a model to adapt to the new data. For a deep learning model, you retrain all the input data to get a new model again.

Assume {X_a,Y_a} is the new training data entered into the BLS system. For X_a, the newly generated feature node can be expressed as: (11)${\displaystyle Z_a^n=\left[\frac{\varphi }{X_a}\left(X_a-W_{{\theta }_1}{\beta }_{e_1}\right),\dots ,\frac{\varphi }{X_{a+n-1}}\left(\frac{X_{a+n}}{n}-W_{{\theta }_n}{\beta }_{{\theta }_n}\right)\right].}$

The output matrix and increment layer of features can be expressed as: (12)${\displaystyle A_x\triangleq \left[\frac{1}{Z_a^n}+W_h{\beta }_h,\frac{\xi }{Z_x^n}\left(Z_x^n+W_{h_1}{\beta }_{h_1}\right),\dots ,\frac{\xi }{Z_{x+w}^n}\left(Z_{x+w}^n+W_{h_w}{\beta }_{h_w}\right)\right].}$

Then the weight of this incremental BLS can be updated with the following formula: (13)${\displaystyle W_a^m=W^m{B}^2+2\left(\sqrt{Y_a^T{W}^m}-\frac{A_x^T}{W^m}\right)B.}$

The input increment only computes the pseudo-inverse of A_x, so the training is fast.

Purification of the availability dimension of services

In this dimension, the main indicators include the following: network coverage, customs clearance ability, accuracy and availability of logistics information. In order to ensure simple and direct data analysis, the four indicators are named as follows: KD1, KD2, KD3, and KD4. Through data analysis, we can calculate the Cronbach’s α coefficient 0.729 of the four indexes, indicating that the overall correlation value exceeds 0.4, and all indexes can be retained.

Good reliability coefficient indicates that Cronbach’s a coefficient of the questionnaire is at least above 0.50, and above 0.7 indicates high reliability, while above 0.8 indicates very good reliability. If it is lower than 0.50, the questionnaire index should be selected or measured again. The correlation coefficient of after-sale availability dimension is shown in Fig. 6.

Purification of temporal dimension

There are five indexes, which are order response time, delay time of special holidays, order-to-receive time, timeliness of logistics information update and timeliness of error processing. After data analysis, these five indicators are named as T1, T2, T3, T4 and T5. Cronbach’s α coefficient was 0.81, and the overall correlation value was above 0.42. This data means that no metrics need to be deleted. The correlation coefficient of temporal dimension is shown in Fig. 7.

Purification of security dimensions

There are five indicators, namely: proper and reasonable packing of goods, goods without loss or damage, goods consistent with the description of the order, confidentiality of personal information, and handling of errors. In this study, they are named K1, K2, K3, K4 and K5. The index Cronbach’s α coefficient obtained through data analysis is 0.76, and the overall correlation value exceeds 0.41, so all indexes can be retained. The correlation coefficient of security dimension is shown in Fig. 8.