Clustering Objects Using Circular Structures

The patent segments the clustering process into two distinct approaches: a first clustering process that compares all objects pairwise to achieve high accuracy, and a second clustering process that uses circular structures to reduce comparisons. The system selectively applies the appropriate segmentation based on data characteristics, allowing accuracy to be maintained when needed while reducing complexity when possible.

The patent implements a dynamic selection mechanism that determines which clustering process to use based on the triangular inequality condition. This dynamic approach allows the system to adapt its computational complexity level based on the specific dataset being analyzed, switching between the comprehensive first process and the optimized second process as needed.

The second clustering process implements partial action by not comparing all objects pairwise. Instead, it uses circular structures to perform a subset of necessary comparisons, achieving sufficient clustering results without the exhaustive comparisons of the first process. This partial approach significantly reduces processing time for large datasets while maintaining acceptable clustering quality.

The patent changes the computational parameters of the clustering process by introducing the triangular inequality condition as a filtering criterion. This parameter change allows the system to skip unnecessary comparisons in the second clustering process, reducing processing time while handling large datasets effectively.

The patent introduces the triangular inequality condition as an intermediary criterion that mediates between the two clustering processes. This intermediary allows the system to determine when the second clustering process (with circular structures) is sufficient, and when the more accurate first clustering process should be used, thus balancing efficiency and accuracy through a decision-making intermediary.

The system dynamically adjusts the level of computational optimization based on the data characteristics. When the triangular inequality condition is satisfied, the system uses the more efficient second process; when it is not satisfied, it falls back to the more accurate first process. This dynamic adjustment ensures accuracy is maintained when needed while maximizing efficiency when possible.