Application of nonlinear clustering optimization algorithm in web data mining of cloud computing

3.1 Similarity clustering

Generally, the similarity of the data category is judged according to the distance between the center point and other points. Compare the distance between the two points with the preset threshold, in order to determine whether the point belongs to the same category as the center point. In the actual operation process, the distance between the two points is not directly calculated, instead, a Gaussian function is introduced to assist in calculating the similarity. In this way, according to the Gaussian distribution function graph, it is more intuitive to judge the degree of aggregation of categories and the distribution of data points of the same category [17]. Assuming a center point, x i , the calculation method of the similarity relationship between other points and the center point is given as follows:

In the clustering process, in order to effectively classify all points in the dataset, and to minimize the distance between all data points after classification and the center points of various types, the following optimization function is established:

where x j ∈ N ˆ ( x i ) indicates that x j is all nodes except x i in the N sample points, and there are

where x k represents the kth node. To simplify Eq. (4), let

Substitute Eq. (5) in Eq. (4) to get Eq. (6).

Therefore, the mathematical description of clustering optimization is the solution.

After solving S i j , the similarity matrix can be obtained to determine whether x i and x j belong to the same class.

3.2 Combination of similarity clustering and wolf pack algorithm

In the process of similar clustering, the optimal solution of formula (2) is mainly solved. Considering the large amount of data and high dimension of the cloud computing platform, in the process of solving the distance between all sample points and the center point, Eq. (2) needs to be re-executed after each center point update, at this time, under the condition of the preset number of iterations, it is not easy to obtain the global optimal solution, therefore, in the clustering process, an efficient algorithm needs to be introduced to quickly obtain the global optimal solution [18]. The steps of combining similarity clustering and wolf pack algorithm are as follows:

1. After initializing K center points, establish a clustering model;

2. According to formulas (1) and (2), the optimization function of K center points is obtained;

3. In formula (2), the optimization is carried out according to the wolf pack algorithm, and the position of the head wolf is the center point of the cluster when the algorithm iteration stops, so that the positions of the K center points can be determined;

4. Solve the optimal S i j of formula (7) according to K center points;

5. After substituting S i j in Eq. (2), continue to use the wolf pack algorithm to update the position of the center point;

6. Repeatedly update the position of the center point until the clustering requirements are met.

3.3 Evaluation of clustering results

The choice of the evaluation index of the clustering results will affect the applicability of the clustering algorithm. Under the cloud computing platform, the data have large differences and high dimensions, which makes data mining more difficult, the evaluation of clustering results will directly affect the effect of data mining, under different application requirements, the focus of evaluation of clustering results is also different. At present, the commonly used clustering evaluation methods mainly include PBM-index and DB-index, and the authors mainly use these two evaluation methods [19].

The mathematical description of the PBM-index evaluation method is as follows. Suppose the samples are divided into K categories, with a total of K center points, the k-th center point is c k , μ k j , which means the correlation factor is between k and j, and the mathematical expression is [ μ k j ] K × n . Then, there are

where E K represents the distance of all nodes x j from the k-th center point, and D K is the distance between two center points with the largest distance from each other among all the K center points [20]. According to formulas (8) and (9), the clustering evaluation method can be obtained as follows:

where E 1 represents the distance of all nodes x j from the first center point; σ represents the evaluation factor, and the value range is σ ≥ 1 .

The mathematical description of the DB-index evaluation method is as follows. Suppose the samples are divided into K categories, with a total of K center points, the center point of the k-th class is c k , and the center point of the k ′ class is c k ′ , then the evaluation formula is as follows:

4.1 PBM and DB evaluation of clustering performance

The simulation data object is the Iris dataset in UCI. N = 500 samples are selected for simulation, and the initial value K of similar clustering is set to 3, the initial value of the wolf pack algorithm is λ = 0.5 , T num = 100 . Similar clustering of wolves was performed in the experiment, and the visualization result of the clustering is shown in Figure 2.

Figure 2

Clustering visualization of data samples when K = 3.

As can be seen from Figure 2, the 500 samples are well divided into 3 categories. Although the center points of the 2 categories are relatively close, it does not affect the 500 sample points all belong to some category, and there is no isolated sample point.

4.2 Operation time of different clustering algorithms

It can be obtained from Section 4.1 that when the number of attributes of the training samples is P = 10, for the UCI dataset used by the authors, the four clustering algorithms showed good clustering performance. The author simulated the operation time of four different clustering algorithms under the condition of P = 10, PBM >0.2, and DB <0.5. The statistical results are listed in Table 5 and Figure 3.

Figure 3

The computation time of each clustering algorithm with different sample sizes.

It can be seen from Table 5 and Figure 3 that in terms of clustering operation time, the K-means algorithm has obvious advantages, the DBSCAN algorithm is the most time-consuming, and the operation time of wolf pack clustering and Mean-shift is in the middle. In the actual application process, the number of samples for each training can be dynamically adjusted according to actual needs, so as to improve the applicability of the wolf pack clustering algorithm in specific application scenarios.