keyword

local scaling

Local scaling is a technique used in graph-based machine learning and spectral clustering to compute pairwise similarity by adapting the scale parameter to the local neighborhood density around each data point. Rather than applying a single uniform bandwidth across the entire dataset, local scaling assigns a point-specific scale value to every observation, typically determined by the distance to its kth nearest neighbor. The affinity between two points is then evaluated using the combination of their individual local scales in the kernel function, allowing the model to naturally adjust to regions with varying point densities. This adaptive formulation enables clustering algorithms to effectively separate multi-scale structures, clusters with irregular geometries, and data containing non-uniform background noise without requiring manual tuning of a global bandwidth parameter.

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