Adaptive affinity matrix for unsupervised metric learning

Spectral clustering is one of the most popular clustering approaches with the capability to handle some challenging clustering problems. Only a little work of spectral clustering focuses on the explicit linear map which can be viewed as the distance metric learning. In practice, the selection of the affinity matrix exhibits a tremendous impact on the unsupervised learning. In this paper, we propose a novel method, dubbed Adaptive Affinity Matrix (AdaAM), to learn an adaptive affinity matrix and derive a distance metric. We assume the affinity matrix to be positive semidefinite with ability to quantify the pairwise dissimilarity. Our method is based on posing the optimization of objective function as a spectral decomposition problem. The provided matrix can be regarded as the optimal representation of pairwise relationship on the manifold. Extensive experiments on a number of image data sets show the effectiveness and efficiency of AdaAM.