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?

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#### Best Answer

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.

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