Figure 1.

Data reduction scheme. (a) Running spectral clustering is impractical on data that contains thousands of points. (b) Faithful sampling picks up a reasonable subset of points such that running spectral clustering is possible on them. However, all information about the local density is lost by considering only these sample points. (c) We assign weights to the edges of the graph; the edges between the nodes in denser regions are weighted considerably higher. The information about the local density is retrieved in this way.