Error-Based Metrics for Fingerprint Vector Similarity Assessment in Clustering-Based Fingerprinting Systems

Abstract

In clustering-based fingerprinting systems, theaccuracy of similarity determination between fingerprint vectors directly affects how well the vectors are clustered in the database. The metric used to assess this similarity is known as the similarity metric. Magnitude-aware metrics such as Euclidean and Manhattan distances are the most commonly used. Despite their popularity, magnitude-aware metrics have several limitations, including sensitivity to differences in vector magnitudes, vulnerability to outliers, and constraints imposed by geometric assumptions. As an alternative, this paper investigates two error-based metrics, mean absolute error (MAE) and mean squared error (MSE), for fingerprint vector similarity determination. The MAE-based metric is proportional to Manhattan distance, and the MSE-based metric is proportional to squared Euclidean distance for a fixed vector dimension. However, their interpretation as average prediction errors offers a different perspective that emphasizes robustness and interpretability. The investigation was conducted using k-means and k-medoids clustering algorithms across four publicly available fingerprint databases with varying properties: SEUG_IndoorLoc, MSI_IndoorLoc, JKKNIUIndoorLoc, and PIEP_UM. The magnitude-aware metrics considered for comparison are Euclidean distance, Manhattan, Minkowski L3, Chebyshev, and Canberra distance. Similarity determination performance was evaluated using mean silhouette scores obtained from 50 independent iterations. Results indicate that the MSE-based metric, despite satisfying only three of the four metric axioms, consistently produces clusters with the highest silhouette scores across all databases considered. The MAE-based metric, while satisfying all four metrics, axioms generally underperform compared to the magnitude-aware metrics considered. These findings indicate that the MSE-based metric is a viable alternative for clustering fingerprint vectors with both k-means and k-medoids algorithms.