Solved – the time complexity of spectral clustering and why is it so

What is the time complexity of spectral clustering and why (mathematically speaking) is it so?

What are possible existing alternatives to speed up the computations required by the algorithm?

Spectral Clustering is a clustering method that uses the spectrum (eigenvalues) of the similarity matrix of the data to perform dimensionality reduction before clustering the data in fewer dimensions.

It is a flexible class of clustering algorithms that can produce high-quality clusterings on small data sets, but which has limited applicability to largescale problems due to its computational complexity of O(n^3).

You can check the link below where a general framework for fast approximate spectral clustering is described.

Fast Approximate Spectral Clustering

Also at the second link below, a kernel based approach is decribed.

Fast kernel spectral clustering

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