Abstract 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 any 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.
In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.  Despite many empirical successes of spectral clustering methods— algorithms that cluster points using eigenvectors of matrices derived from the data—there are several unresolved issues. First. there are a wide variety of algorithms that use the eigenvectors in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze the algorithm, and give conditions under which it can be expected to do well. We also show surprisingly good experimental results on a number of challenging clustering problems.