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self-tuning spectral clustering

Self-tuning spectral clustering is an unsupervised machine learning algorithm that groups data points using the spectrum of a similarity graph while automatically determining critical hyperparameters. Unlike traditional spectral clustering, which typically requires manual selection of a global scaling parameter to measure pairwise affinities and a predefined number of clusters, this approach calculates local scale parameters based on the neighborhood density around each point. This adaptive scaling allows the method to separate clusters characterized by varying densities, multiple spatial scales, and background clutter. Furthermore, the algorithm estimates the number of groups directly from the structure of the graph Laplacian eigenvectors, enabling direct cluster assignment while eliminating the need for a separate, randomly initialized k-means step.

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Self-Tuning Spectral Clustering

Self-Tuning Spectral Clustering

Lihi Zelnik-Manor, P. Perona

OrganizationsCalifornia Institute of Technology

Why you should read this

Introduces a self-tuning spectral clustering method that computes local scaling for each data point and infers the number of groups directly from eigenvector structure, effectively clustering multi-scale, cluttered datasets without manual parameter selection or randomized k-means initialization.

We study a number of open issues in spectral clustering: (i) Selecting the appropriate scale of analysis, (ii) Handling multi-scale data, (iii) Clustering with irregular background clutter, and, (iv) Finding automatically the number of groups. We first propose that a ‘local’ scale should be used to compute the affinity between each pair of points. This local scaling leads to better clustering especially when the data includes multiple scales and when the clusters are placed within a cluttered background. We further suggest exploiting the structure of the eigenvectors to infer automatically the number of groups. This leads to a new algorithm in which the final randomly initialized k-means stage is eliminated.

Added

2026-09-14