A Normalized Spectral Peak Cross-Correlation Metric for Similarity Determination in Clustering-Based Received Signal Strength Fingerprinting Systems

Abstract

Accurate similarity determination is essential for clustering-based received signal strength (RSS) fingerprinting systems. Existing metrics often struggle to consistently capture structural similarities across databases of varying sizes and dimensions. This paper introduces a normalized spectral peak cross-correlation (NSPCC) similarity measure, which transforms fingerprint vectors into the frequency domain via the Discrete Fourier Transform and computes normalized cross-correlation to capture relative RSS patterns rather than absolute magnitude differences. The NSPCC similarity measure is evaluated on four publicly accessible RSS-based fingerprint databases, ranging from 49 to 1000 vectors and dimensions 3 to 11. Its performance is compared against Euclidean distance, context similarity coefficient (CSC), standard deviation score (SD-score), and similarity measure based on the distance of subspaces (SMDS) metrics using k-medoids clustering. Based on standard metric axioms, NSPCC is not a strict metric. It satisfies non-negativity and symmetry but does not satisfy the reverse identity condition or the triangle inequality. It is therefore classified as a non-metric similarity measure. Despite this, results show that the NSPCC similarity measure generally achieves higher Silhouette scores and lower Davies-Bouldin indices across most database sizes, indicating better cluster separation and compactness, although CSC or SMDS match or outperform NSPCC on certain datasets. The SMDS measure performs well only for very small databases before degrading; Euclidean distance shows significant performance loss as database size increases, and CSC produces inconsistent results. Regarding computational complexity, spectral representations can be precomputed offline, after which pairwise similarity calculations require minimal additional computation, making the overall cost moderate for real-time use. The findings demonstrate that the NSPCC similarity measure provides a reliable, scalable, and practical similarity determination for RSS-based fingerprinting systems, offering a balanced alternative between clustering accuracy and computational feasibility for real-world deployments.