# SSKM_DP: Differential Privacy Data Publishing Method via SFLA-Kohonen Network
## 4 The Proposed Data Publishing Method
### SFLA-Kohonen Data Clustering Algorithm  
The general data publishing method based on differential privacy protection is to add noise to each record of the data to meet the differential privacy protection and publish universal data where data users can perform any query operation. However, this method introduces a large amount of noise, which greatly reduces the availability of published data. By reducing the sensitivity of differential privacy and allocating the privacy budget reasonably, the amount of noise added to satisfy differential privacy can be effectively reduced, and the availability of published data can be improved. The literature [31] points out that the method of clustering or grouping is used to process the original data, and then noise is added to each cluster after conversion, which can greatly reduce the amount of noise added to satisfy the differential privacy. Based on this, the idea of clustering was introduced in this paper to divide data attributes into clusters, reduce the sensitivity of differential privacy, and reduce the required intake noise. The traditional and classical clustering methods include k-means [32] and the DBSCAN [33] algorithm, but both of them and their improved methods have some problems. k-means is very sensitive to the selection of the initial point, and the number of clustering \(k\) is artificially selected according to experience. This setting method is extremely unreasonable, resulting in different clustering results, which are bound to result in insufficient or excessive privacy protection ability and reduce the availability of released data. Although DBSCAN does not need to set the number of clusters and has high robustness, it is unable to obtain better clustering results from data on many dimensions. Aiming at the limitations of the above methods, a clustering method based on the Kohonen neural network was introduced in this paper, and the neural network model was combined with differential privacy to improve the privacy protection ability of sensitive data and the utility of published data. However, in the training process of the Kohonen network, the initial connection weight must be specified in advance, which depends on the setting of experience, and the accuracy of clustering results depends very much on the selection of the initial connection weight. Aiming at the shortcomings in the clustering method based on the Kohonen network, the single population frog leaping algorithm (SFLA) was used to optimize the initial connection weight of the Kohonen network, and a clustering method based on the SFLA-Kohonen network was proposed to improve the fitting accuracy of connection weight to training data and the accuracy of clustering results. Algorithm 2 of the initial optimization process of Kohonen networks using SFLA is as follows:Input: data \(U=\{x_{1},x_{2},\ldots,x_{n}\}\); the number of neurons in the input layer of the Kohonen network; the number of frogs. Output: The optimal initial weight of the SOM network. Step 1.The initial population is generated composed of \(N\) frog \(R=\{X_{1},X_{2},\ldots,X_{N}\}\), and the generation method follows the Gaussian distribution formula, as shown in (8):  
\[X(s)=\frac{1}{\sqrt{2\pi\sigma}}\exp(-\frac{(s-u)^{2}}{2\sigma^{2}}) \tag{8}\]  
where \(\mu=0,\sigma=1\). Step 2. After the frog population \(R\) is generated, all frogs are substituted for the Kohonen network model. The input vectors are randomly selected to calculate the fitness value of all frogs in \(R\), \(fit(X_{i})\). The fitness calculation method used in this paper is shown in (9):  
\[fit(X_{i})=\frac{1}{1+E[\sum\limits_{a_{1},a_{2}}N_{x}(b_{1}-a_{1},b_{2}-a_{2}) \|x_{i}-W(a_{1},a_{2})\|]} \tag{9}\]  
where \(E\) is the mathematical expectation, \(N_{x}(\) ) is the domain function, \(W(a_{1},a_{2})\) is the weight of the neuron \((a_{1},a_{2})\), and \((b_{1},b_{2})\) represents the coordinate of the winning neuron in \(U\). Step 3.