# A Network Traffic Prediction Method for AIOps Based on TDA and Attention GRU
## 5 Experimental Results and Analysis
### Topology Data Analysis  
This experiment used topological data to analyze and mine hidden topological features in point cloud data. Through a continuous homology process, homologous topological structures were obtained at different scales. Figure 5 shows the homology group states four times during the continuous homology process. In Figure 5, points with different colors represent different homology groups, and each subgraph is controlled by different super parameters. Among the four super parameters, n_cubes is the resolution, representing the number of hypercubes in each dimension. The n_cubes in chronological order is respectively 30, 15, 10, and 5. n_nodes is the number of nodes, representing the number of topology. The n_nodes in chronological order is respectively 600, 250, 125, and 25. In this experiment, the Euclidean distance was used as the measure of distance, and other super parameters include eps = 0.1, which represents the maximum distance that one of the two samples was considered to be near the other, and min_samples = 15, indicating the number of samples in the neighborhood where a point is regarded as a core point. The upper-left figure shows the initial state for the first time. The distribution of homology groups is relatively discrete, and there is a spiral topology in the center, indicating that there is some periodicity in the original time series data. There are also many outliers around, which indicates that there is a large fluctuation in the original time-series data. The upper-right figure shows the state at the second time, and the central spiral structure still exists, indicating that the cycle is relatively significant. With the development of homology, an increasing number of old homology groups have died, and new homology groups have emerged. In the bottom-left figure, the homology group gradually converges to the three-layer structure, corresponding to the evenly distributed three-layer topology in the bottom-right figure, representing the simple, efficient, and easy-to-use topological features extracted from the original data. In addition, the process fully demonstrates the smoothing and noise reduction functions of the TDA. The node distributions corresponding to each state in Figure 5 are shown in Figure 6.  
In Figure 6, columns with different colors represent different node types, and the color corresponds to Figure 5. As shown in Figure 6, the change in node type is divided into two stages. In the first stage, with the continuous increase in resolution, the node types increase, and the observed topology becomes increasingly diversified and deeper. For example, at the resolution of 30, a clear spiral structure is observed. In the second stage, with a continuous increase in resolution, the node type decreased, and the dimension of the data decreased. Outliers and noise were gradually fused in the second stage to weaken or even eliminate their influence on the feature representation. For example, when the resolution was 10, the outliers in the lower left corner of Figure 5 were eliminated when the resolution was reduced to five. This also explains the powerful capability of TDA in the field of noise reduction. Figure 5: Continuous homology process, the time sequence is: top left (1), top right (2), bottom left (3), bottom right (4). The result of continuous homology is the birth-death point pair of a series of topological features, and its visual display is shown in Figure 7.  
In Figure 7, the blue dot represents the birth and death of the 0 th order homologous group, and the persistence of the blue dot represents the dispersion of the points in the point cloud. The larger the number of blue dots are near the diagonal, the more dispersed the point cloud. The red dots indicate birth and death in the first-order homologous group. The red dot is far from the diagonal, and the topological property is more significant in the characterization data.