A fast leading eigenvector approximation for segmentation and grouping

We present a fast non-iterative method for approximating the leading eigenvector so as to render graph-spectral based grouping algorithms more efficient. The approximation is based on a linear perturbation analysis and applies to matrices that are non-sparse, non-negative and symmetric. For an N×N matrix, the approximation can be implemented with complexity as low as O(4N²). We provide a performance analysis and demonstrate the usefulness of our method on image segmentation problems.