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Publication 15-CNA-007
Nicolas García Trillos Dejan Slepčev Abstract: This paper establishes the consistency of spectral
approaches to data clustering. We consider clustering of point clouds
obtained as samples of a ground-truth measure.
A graph representing the point cloud is obtained by assigning weights to
edges based on the distance between the points they connect.
We investigate the spectral convergence of both unnormalized and
normalized graph Laplacians towards the appropriate operators in the
continuum domain. We obtain sharp conditions on how the connectivity
radius can be scaled with respect to the number of sample points for the
spectral convergence to hold. We also show that the discrete clusters
obtained via spectral clustering converge towards a continuum partition
of the ground truth measure. Such continuum partition minimizes a
functional describing the continuum analogue of the graph-based spectral
partitioning. Our approach, based on variational convergence, is
general and flexible.Get the paper in its entirety as 15-CNA-007.pdf |