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The recently emerged spectral clustering surpasses conventional clusteringmethods by detecting clusters of any shape without the convexity assumption.Unfortunately, with a computational complexity of $O(n^3)$, it was infeasiblefor multiple real applications, where $n$ could be large. This stimulatesresearchers to propose the approximate spectral clustering (ASC). However, mostof ASC methods assumed that the number of clusters $k$ was known. In practice,manual setting of $k$ could be subjective or time consuming. The proposedalgorithm has two relevance metrics for estimating $k$ in two vital steps ofASC. One for selecting the eigenvectors spanning the embedding space, and theother to discover the number of clusters in that space. The algorithm used agrowing neural gas (GNG) approximation, GNG is superior in preserving inputdata topology. The experimental setup demonstrates the efficiency of theproposed algorithm and its ability to compete with similar methods where $k$was set manually.

Approximate spectral clustering with eigenvector selection and self-tuned $k$