Learning Doubly Stochastic Affinity Matrix via Davis-Kahan Theorem

Building an ideal graph which reveals the exact intrinsic structure of the data is critical in graph-based clustering. There have been a lot of efforts to construct an affinity matrix satisfying such a need in terms of a similarity measure. A recent approach attracting attention is on using doubly stochastic normalization of the affinity matrix to improve the clustering performance. In this paper, we propose a novel method to build a high-quality affinity matrix via incorporating Davis-Kahan theorem of matrix perturbation theory in the doubly stochastic normalization problem. We interpret the goal of the doubly stochastic normalization problem as minimizing the relative distance between the eigenspaces of the corresponding matrices. Also, for the doubly stochastic normalization problem we include an additional constraint that each eigenvalue be on the unit interval to fully conform to the spectral graph theory. Experiments on our framework present superior performance over various datasets.