Accelerated D2-Clustering Algorithm for Large-Scale Data

The patent segments the large-scale clustering problem into multiple smaller sub-problems by dividing the data set into batches. Each batch is processed independently to compute local centroids, which are then aggregated to form global centroids. This segmentation reduces the polynomial computational complexity of processing the entire data set at once, enabling scalable clustering while maintaining Wasserstein distance-based quality metrics.

The patent performs preliminary actions by pre-computing and storing distance matrices between data points and potential centroids before the main clustering iteration. This pre-computation step caches reusable distance information, avoiding redundant calculations during subsequent clustering iterations and significantly reducing the overall computational burden for large data sets.

The patent performs preliminary computation of distance matrices between all pairs of points in the discrete distributions before solving the linear programming problem. These pre-computed distances are stored and reused during the centroid update iterations, eliminating the need to recompute them repeatedly and significantly reducing the total computational time while preserving accurate Wasserstein distance measurements.

The patent dynamically updates only the necessary portions of distance information during clustering iterations rather than recomputing entire distance matrices. By tracking which distance values need updating based on current centroid positions and data assignments, the method adapts the computational effort to the actual state of the clustering process, reducing redundant calculations.