| Spectral clustering method is an important direction of clustering and achieved many valuable applications ranging from computer science,biology to social sciences.The traditional spectral clustering methods use data pair-wise distance or the similarity to construct the distance or affinity matrix and then cluster in eigen-vectors decomposed from distance or affinity matrix.The traditional spectral clustering methods often suffer sensitive parameters problem,such as choosing parameters of distance metric and parameters in clustering method in eigen-space,leading to performance reduction and negative effect.Based on this problem,we propose a new spectral clustering framework with sparsity constraint to cluster in eigenvectors.Our cost function includes two parts: the data fidelity of eigenvector with L2 norm constraint and sparsity of gradient of eigenvectors with L0 norm constraint.Thus,the only sparsity parameter in our method reflect degree of sparsity constraint,which has a clear interpretation.Finally the cost function can be converted to three sub-problem with alternating direction method of multiplier(ADMM)and get the closed-form solution.We apply our improved spectral clustering method to large size image segmentation and test in synthetic data sets and standard data set.In order to handle the high complexity eigen-decomposition problem,we propose superpixels method as the image reduction method.The experiment result shows that our method is better than Normalized cutting(N-cut)as a classic traditional spectral clustering method. |
