Object Clustering via Link Counts and Triangular Inequality

The patent segments the clustering process into two distinct approaches: a first clustering process that compares all objects for high accuracy, and a second clustering process that uses circular structures for faster computation. The system selectively applies the appropriate segmentation based on the triangular inequality condition, thereby resolving the contradiction between accuracy and computational efficiency.

The patent implements a dynamic clustering system that adapts its approach based on the triangular inequality condition. When the condition is satisfied, the system dynamically switches to the more efficient second clustering process; when not satisfied, it uses the comprehensive first clustering process. This dynamic adaptation resolves the contradiction by adjusting the method based on data characteristics.

The triangular inequality condition acts as an intermediary that mediates between the two clustering processes. It determines when the simplified second clustering process (using circular structures) is sufficient for maintaining accuracy while improving speed, and when the comprehensive first clustering process is necessary. This intermediary resolves the contradiction by providing a decision criterion for selecting the appropriate method.

The patent changes the parameter of comparison completeness based on the triangular inequality condition. When the condition is satisfied, it reduces the comparison parameter from all object pairs to only those within circular structures, thereby improving speed while maintaining sufficient accuracy. This parameter change resolves the contradiction between speed and accuracy.

The patent segments the computational approach based on dataset characteristics by evaluating the triangular inequality condition. For large datasets where the condition is satisfied, it uses the segmented second clustering process with circular structures, reducing computational complexity while maintaining coverage of all objects. This segmentation resolves the contradiction between data coverage and computational complexity.

The second clustering process performs partial comparisons (only within circular structures) rather than exhaustive comparisons of all object pairs. This partial action is sufficient when the triangular inequality condition is satisfied, thereby reducing computational complexity while still achieving comprehensive clustering coverage for large datasets.