Multi-Scalar Spectral Clustering: A New Approach to Capture Scale-Dependent Persistent Clusterings

Clustering is an unsupervised learning technique that is used to group a given set of data, typically requiring careful parameter tuning to achieve meaningful results. Spectral clustering, based on pairwise similarities between data points, can be sensitive to scale when similarity is defined by distance between points. This paper introduces a new multiscale spectral clustering algorithm that identifies persistent, scale-dependent clustering structures by applying the eigengap heuristic across a continuous range of scale values. The method is validated using synthetic and real-world datasets. In addition, cluster quality is assessed using both external and internal performance metrics. The proposed algorithm detects robust clusterings at multiple scales, capturing global patterns and locally homogeneous groupings. This approach reveals significant structures that may be missed by single-scale methods.