Image retrieval with relevant feedback on large and high-dimensional image databases is a challenging task. In this paper, we propose an image retrieval method, called BCFIR (Binary Codes for Fast Image Retrieval). BCFIR utilizes sparse discriminant analysis to select the most important original feature set, and solve the small class problem in the relevance feedback. Besides, to increase the retrieval performance on large-scale image databases, in addition to BCFIR mapping real-valued features to short binary codes, it also applies a bagging learning strategy to improve the ability general capabilities of autoencoders. In addition, our proposed method also takes advantage of both labeled and unlabeled samples to improve the retrieval precision. The experimental results on three databases demonstrate that the proposed method obtains competitive precision compared with other state-of-the-art image retrieval methods