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Linearly nonseparability and class imbalance of very high resolution (VHR) imagery make feature selection for object-oriented classification quite challenging, while such characteristics, especially class imbalance, have usually been ignored in open literature. To cope with the challenges, this paper proposes a new graph-based feature selection method named locally weighted discriminating projection (LWDP). First, the popular graph-based criteria of feature selection are reformulated to present linear or nonlinear mapping in feature space. Second, weight matrices of graphs characterize dissimilarity rather than similarity between pairwise neighbors, to well-preserved local structure when the difference of distance between a sample and its neighbors is large. Finally, LWDP provides a new perspective to alleviate class imbalance at both global and local levels, by restricting the pairwise relationships in the weight matrices. Specifically, neighborhood unions are introduced to employ the local class distribution and class size to constrain pairwise relationships in the weight matrices when classifying unbalanced sample sets. To evaluate the performances of LWDP in low dimensions, a holistic scoring scheme is proposed to stress the performances under low dimensions. In addition, overall accuracy curves and Kappa Index of Agreement (KIA) curves, which exhibit KIA in dimensions, are also used. The experimental results show that LWDP and its kernel extension outperform the other classic or latest methods in processing unbalanced sample set of VHR airborne imagery.