Providing effective support for intelligent vision tasks without image reconstruction can save numerous computational costs in the era of big data. With the help of the Deep Neural Network (DNN), integrating image compression and intelligent vision tasks at a feature representation level becomes a new promising approach. But how to perform non-linear transformation for image compression and extract image patterns for intelligent vision tasks simultaneously within a shared DNN remains an open problem. In this paper, a versatile framework is studied to explore the common feature representations for both image compression and classification. A fully-shared latent representation is extracted in a more compact way to support compression and classification task. The General Feature Extraction and Feature-analytic Classifier are proposed to generate and utilize compact and general shared latent representation. Then the whole framework is joint optimized by considering multiple factors (i.e., rate, quality and accuracy). Extensive experiments are carried out to validate that the proposals can improve the performance of both learning-based image compression and classification.The results show that the proposed method outperforms conventional codecs like BPG and JPEG2000 in compression efficiency, while achieving acceptable accuracy on different datasets without image reconstruction.