Fast Spectral Clustering algorithm based on wavelet basis decomposition

Spectral clustering is a widely used unsupervised clustering algorithm that performs very well in many cases. However, for complex scenes and high-resolution images, the application is limited due to the high computational complexity. In this paper, we propose an efficient spectral clustering algorithm based on wavelet basis decomposition. According to the hierarchical structure of wavelet decomposition, the algorithm reduces the dimension of the eigendecomposition of the graph Laplacian by wavelet basis matrix, the low-frequency eigenvectors of the whole graph Laplacian are solved hierarchically from wavelet subspaces with different levels. Its computational complexity is $O(n) + O(m3/2)$ , where $n$ and m. are the number of pixels and selected wavelet coefficients in an image, respectively. To verify the effectiveness and performance of the proposed algorithm, a series of experiments were done on both the Weizmann and BSDS500 segmentation datasets and find that our method, which in practice provides on average about 5 × speed-up to the eigendecomposition computation required for the Laplacian matrix with comparable segmentation accuracy.