# What is Spectral clustering?

What is spectral clustering? I have little background in statistics. I have tried to search for notes online but they assume quite a lot of knowledge.

Would be good if you are able to find some notes online which teach the basics and the math foundations for spectral clustering

I have found notes like this one which require a lot of background knowledge which are not suitable for me

• Are there specific things that you'd like to understand? What do you need spectral clustering for? Jul 10 '18 at 12:39
• This tutorial on spectral clustering is very good imo arxiv.org/pdf/0711.0189.pdf Dec 6 '18 at 17:46

Spectral clustering is an algorithm for data clustering that uses the spectrum (eigenvalues) of the similarity matrix of the data to perform dimensionality reduction before clustering in fewer dimensions.

The similarity matrix includes the relative similarity of each pair of points in the available dataset.

• Would be good if you are able to find some notes online which teach the basics and the math foundations for spectral clustering I have found notes like this [one][1] which require a lot of background knowledge which are not suitable for me [1]: ranger.uta.edu/~chqding/Spectral/spectralA.pdf Jun 22 '18 at 8:05
• Check this one below, it seems to me simpler than the one you mentioned slideshare.net/hnly228078/spectral-clustering-tutorial Jun 22 '18 at 9:52

Spectral clustering is a family of algorithms for treating larger datasets with complex-network representations. "Large" means "more than a few thousands of nodes but not gigantic". The slides you've linked to say the mathematical theory was developed since the 1970s for undirected graphs. Extensions exist for directed graphs and undirected graphs (see slide 20/20 in the tutorial you've linked to).

For some background, maybe read chapter 11, specifically 11.2 and 11.5 of M.E.J. Newman's Book "Networks". The 11.2 Chapter Title is called "Dividing networks into clusters". Chapter 11.5 is "Spectral [graph] partitioning" - the method from which spectral clustering evolved according to slide 20 in http://ranger.uta.edu/~chqding/Spectral/spectralA.pdf you've linked to.

The thick (800 page) book "Networks" is an interdiciplinary introduction, and it is very verbose, and it starts from basics. However the book discusses many other things besides clustering. It is also not online, maybe get it through inter-library loan.

I also like the introduction of Andrew Ng's et al's 2002 short Paper "On spectral clustering: Analysis and an algorithm" see "https://ai.stanford.edu/~ang/papers/nips01-spectral.pdf

... Despite the empirical successes, different authors still disagree which eigenvectors to use and how to derive clusters from them [...] also, the analysis of these algorithms [...] focus on simplified algorithms that only use one eigenvector at a time"

But this was 2002, a lot might have changed since then.