Projective unsupervised flexible embedding with optimal graph

Graph based dimensionality reduction techniques have been successfully applied to clustering and classification tasks. The fundamental basis of these algorithms is the constructed graph which dominates their performance. Usually, the graph is defined by the input affinity matrix. However, the affinity matrix is sub-optimal for dimension reduction as there is much noise in the data. To address this issue, we propose the projective unsupervised flexible embedding with optimal graph (PUFE-OG) model. We build an optimal graph by adjusting the affinity matrix. To tackle the out-of-sample problem, we employ a linear regression term to learn a projection matrix. The optimal graph and projection matrix are jointly learned by integrating the manifold regularizer and regression residual into a unified model. An efficient algorithm is derived to solve the challenging model. The experimental results on several public benchmark datasets demonstrate that the presented PUFE-OG outperforms other state-of-the-art methods.