A topological approach to spectral clustering
Antonio Rieser · Foundations of Data Science · 2021
We propose two related unsupervised clustering algorithms which, for input, take data assumed to be sampled from a uniform distribution supported on a metric space \begin{document}$ X $\end{document} , and output a clustering of the data based on the selection of a topological model for the connected components of \begin{document}$ X $\end{document} . Both algorithms work by selecting a graph on the samples from a natural one-parameter family of graphs, using a geometric criterion in the first case and an information theoretic criterion in the second. The estimated connected components of \begin{document}$ X $\end{document} are identified with the kernel of the associated graph Laplacian, which allows the algorithm to work without requiring the number of expected clusters or other auxiliary data as input.