Metric Nearness Made Practical

Given a square matrix with noisy dissimilarity measures between pairs of data samples, the metric nearness model computes best approximation from set valid distance metrics. Despite its wide applications in machine learning and processing tasks, faces non-trivial computational requirements seeking solution due to large number constraints associated feasible region. Our work designed practical approach two stages tackle challenge improve model's scalability applicability. The first stage fast yet high-quality approximate isometrically embeddable metrics, further improved by an effective heuristic. second refines Halpern-Lions-Wittmann-Bauschke projection algorithm, which converges quickly optimal solution. In empirical evaluations, proposed runs at least order magnitude faster than state-of-the-art solutions, significantly scalability, complete conformity constraints, less memory consumption, other desirable features real applications.