Abstract: This paper presents a novel use of spectral clustering algorithms to support cases where the entries in the affinity matrix are costly to compute. The method is incremental – the spectral clustering algorithm is applied to the affinity matrix after each row/column is added – which makes it possible to inspect the clusters as new data points are added. The method is well suited to the problem of appearance-based, on-line topological mapping for mobile robots. In this problem domain, we show that we can reduce environment-dependent parameters of the clustering algorithm to just a single, intuitive parameter. Experimental results in large outdoor and indoor environments show that we can close loops correctly by computing only a fraction of the entries in the affinity matrix. The accompanying video clip shows how an example map is produced by the algorithm.