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We propose a randomized algorithm of spectral clustering and apply it to appearance-based image/video segmentation. Spectral clustering is a kernel-based method of grouping data on separate nonlinear manifolds. However, its high computational expensive restricts the applications. Our algorithm exploits random projection and subsampling techniques for reducing dimensionality and cardinality of data. The computation time can be independent of data dimensionality in appearance-based methods, and is quasilinear with respect to the data cardinality. We demonstrate our spectral clustering algorithm in image and video shot segmentation.