Learning-based image compression was shown to achieve a competitive performance with state-of-the-art transform-based codecs. This motivated the development of new learning-based visual compression standards such as JPEG-AI. Of particular interest to these emerging standards is the development of learning-based image compression systems targeting both humans and machines. This paper is concerned with learning-based compression schemes whose compressed-domain representations can be utilized to perform visual processing and computer vision tasks directly in the compressed domain. In our work, we adopt a learning-based compressed-domain classification framework for performing visual recognition using the compressed-domain latent representation at varying bit-rates. We propose a novel feature adaptation module integrating a lightweight attention model to adaptively emphasize and enhance the key features within the extracted channel-wise information. Also, we design an adaptation training strategy to utilize the pretrained pixel-domain weights. For comparison, in addition to the performance results that are obtained using our proposed latent-based compressed-domain method, we also present performance results using compressed but fully decoded images in the pixel domain as well as original uncompressed images. The obtained performance results show that our proposed compressed-domain classification model can distinctly outperform the existing compressed-domain classification models, and that it can also yield similar accuracy results with a much higher computational efficiency as compared to the pixel-domain models that are trained using fully decoded images.