  Spectral clustering algorithms typically require a priori selection of input
parameters such as the number of clusters, a scaling parameter for the affinity
measure, or ranges of these values for parameter tuning. Despite efforts for
automating the process of spectral clustering, the task of grouping data in
multi-scale and higher dimensional spaces is yet to be explored. This study
presents a spectral clustering heuristic algorithm that obviates the need for
an input by estimating the parameters from the data itself. Specifically, it
introduces the heuristic of iterative eigengap search with (1) global scaling
and (2) local scaling. These approaches estimate the scaling parameter and
implement iterative eigengap quantification along a search tree to reveal
dissimilarities at different scales of a feature space and identify clusters.
The performance of these approaches has been tested on various real-world
datasets of power variation with multi-scale nature and gene expression. Our
findings show that iterative eigengap search with a PCA-based global scaling
scheme can discover different patterns with an accuracy of higher than 90% in
most cases without asking for a priori input information.
