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Predicting network abnormal events and behavior can enhance security situation awareness and the ability to infer attack intentions. Most of the existing abnormal event prediction methods usually rely on the temporal relationship features between events and the spatial relationship features between hosts. However, the existing spatio-temporal anoma...
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... the curvature κ(x) everywhere in the curvature space satisfies a uniform distribution, then the curvature space (M, g) is a constant curvature space. According to the positive and negative values of space curvature, it can be divided into Euclidean space with curvature κ = 0, hyperbolic space with curvature κ < 0, and spherical space with curvature κ > 0. An overview of the various curvature spatial properties is shown in Table 3. difference of curvature í µí¼ (í µí±¥) everywhere in the space, the curvature space can be divided into constant curvature space and mixed-curvature space. ...Context 2
... the curvature í µí¼ (í µí±¥) everywhere in the curvature space satisfies a uniform distribution, then the curvature space (ℳ, í µí±) is a constant curvature space. According to the positive and negative values of space curvature, it can be divided into Euclidean space with curvature í µí¼ = 0, hyperbolic space with curvature í µí¼ < 0, and spherical space with curvature í µí¼ > 0. An overview of the various curvature spatial properties is shown in Table 3. ...Context 3
... the curvature í µí¼ (í µí±¥) everywhere in the curvature space satisfies a uniform distribution, then the curvature space (ℳ, í µí±) is a constant curvature space. According to the positive and negative values of space curvature, it can be divided into Euclidean space with curvature í µí¼ = 0, hyperbolic space with curvature í µí¼ < 0, and spherical space with curvature í µí¼ > 0. An overview of the various curvature spatial properties is shown in Table 3. ...Context 4
... the curvature í µí¼ (í µí±¥) everywhere in the curvature space satisfies a uniform distribution, then the curvature space (ℳ, í µí±) is a constant curvature space. According to the positive and negative values of space curvature, it can be divided into Euclidean space with curvature í µí¼ = 0, hyperbolic space with curvature í µí¼ < 0, and spherical space with curvature í µí¼ > 0. An overview of the various curvature spatial properties is shown in Table 3. ...Context 5
... the curvature í µí¼ (í µí±¥) everywhere in the curvature space satisfies a uniform distribution, then the curvature space (ℳ, í µí±) is a constant curvature space. According to the positive and negative values of space curvature, it can be divided into Euclidean space with curvature í µí¼ = 0, hyperbolic space with curvature í µí¼ < 0, and spherical space with curvature í µí¼ > 0. An overview of the various curvature spatial properties is shown in Table 3. ...Context 6
... the curvature í µí¼ (í µí±¥) everywhere in the curvature space satisfies a uniform distribution, then the curvature space (ℳ, í µí±) is a constant curvature space. According to the positive and negative values of space curvature, it can be divided into Euclidean space with curvature í µí¼ = 0, hyperbolic space with curvature í µí¼ < 0, and spherical space with curvature í µí¼ > 0. An overview of the various curvature spatial properties is shown in Table 3. ...Context 7
... the curvature í µí¼ (í µí±¥) everywhere in the curvature space satisfies a uniform distribution, then the curvature space (ℳ, í µí±) is a constant curvature space. According to the positive and negative values of space curvature, it can be divided into Euclidean space with curvature í µí¼ = 0, hyperbolic space with curvature í µí¼ < 0, and spherical space with curvature í µí¼ > 0. An overview of the various curvature spatial properties is shown in Table 3. ...Context 8
... the curvature í µí¼ (í µí±¥) everywhere in the curvature space satisfies a uniform distribution, then the curvature space (ℳ, í µí±) is a constant curvature space. According to the positive and negative values of space curvature, it can be divided into Euclidean space with curvature í µí¼ = 0, hyperbolic space with curvature í µí¼ < 0, and spherical space with curvature í µí¼ > 0. An overview of the various curvature spatial properties is shown in Table 3. ...Context 9
... the curvature í µí¼ (í µí±¥) everywhere in the curvature space satisfies a uniform distribution, then the curvature space (ℳ, í µí±) is a constant curvature space. According to the positive and negative values of space curvature, it can be divided into Euclidean space with curvature í µí¼ = 0, hyperbolic space with curvature í µí¼ < 0, and spherical space with curvature í µí¼ > 0. An overview of the various curvature spatial properties is shown in Table 3. ...Context 10
... this paper, we use the graph engine to mine the relationship between data. In the mixed-curvature space, as shown in Table 3, the local correlation events in the generated graph are mostly tree structures, which are suitable for learning and representation in hyperbolic spaces; the global correlation events in the generated graphs are mostly ring structures, which are ideal for spherical space for learning representation; other associated events with low dimensions are ideal for learning representation using For the convenience of plot representation, we set local_bound_size = 2 in the plot generation example. The size of bound_size determines the order in which the graph is generated and the relationship strength between the current node and the neighbor nodes. ...Context 11
... this paper, we use the graph engine to mine the relationship between data. In the mixed-curvature space, as shown in Table 3, the local correlation events in the generated graph are mostly tree structures, which are suitable for learning and representation in hyperbolic spaces; the global correlation events in the generated graphs are mostly ring structures, which are ideal for spherical space for learning representation; other associated events with low dimensions are ideal for learning representation using Euclidean space. The mixed-curvature space is constructed by the Cartesian product of multiple Riemannian spaces and combined with GNN to obtain the output representation of the mixed-curvature space [11,16]. ...Context 12
... with different curvatures are suitable for representing various types of data. Specifically, refer to the last column of Table 3. ...