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For an object classification system, the most critical obstacles toward real-world applications are often caused by large intra-class variability, arising from different lightings, occlusion, and corruption, in limited sample sets. Most methods in the literature would fail when the training samples are heavily occluded, corrupted or have significant illumination or viewpoint variations. Besides, most of the existing methods and especially deep learning-based methods, need large training sets to achieve a satisfactory recognition performance. Although using the pre-trained network on a generic large-scale data set and fine-tune it to the small-sized target data set is a widely used technique, this would not help when the content of base and target data sets are very different. To address these issues simultaneously, we propose a joint projection and low-rank dictionary learning method using dual graph constraints. Specifically, a structured class-specific dictionary is learned in the low-dimensional space, and the discrimination is further improved by imposing a graph constraint on the coding coefficients, that maximizes the intra-class compactness and inter-class separability. We enforce structural incoherence and low-rank constraints on sub-dictionaries to reduce the redundancy among them, and also make them robust to variations and outliers. To preserve the intrinsic structure of data, we introduce a supervised neighborhood graph into the framework to make the proposed method robust to small-sized and high-dimensional data sets. Experimental results on several benchmark data sets verify the superior performance of our method for object classification of small-sized data sets, which include a considerable amount of different kinds of variation, and may have high-dimensional feature vectors.