A distance-based spectral clustering approach with L0 Gradient Minimization

Abstract

Spectral clustering has recently achieved a plenty of successful applications in the fields of image processing and object pattern recognition. However, it is a frequent challenging problem that many spectral clustering algorithms suffer from the sensitivity in the selection of the parameters for their Gaussian kernel functions and K-means partitioning processes. To alleviate this situation, we first construct a distance matrix and project the data points into the eigen-space spanned by the selected eigenvectors, then we apply the proposed partitioning algorithm inspired by the continuity of data distribution. In order to partition the data points projected on the eigenvectors, we formulate a cost function with quadratic data-fidelity and L0 gradient constraint, and the optimal solution can be obtained with the use of alternating direction method of multipliers (ADMM). The proposed approach has been tested for the image segmentation problems. The experiments on the benchmark image datasets showed that the proposal was able to achieve efficient and effective results with the help of the superpixels.