The potential of large tactile arrays to improve robot perception for safe operation in human-dominated environments and of high-resolution tactile arrays to enable human-level dexterous manipulation is well accepted. However, the increase in the number of tactile sensing elements introduces challenges including wiring complexity, power consumption, and data processing. To help address these challenges, we previously developed a tactile sensing technique based compressed sensing that reduces hardware complexity and data transmission, while allowing accurate reconstruction of the full-resolution signal. In this paper, we apply tactile compressed sensing to the problem of object classification. Specifically, we perform object classification on the compressed tactile data. We evaluate our method using BubbleTouch, our tactile array simulator. Our results show our approach achieves high classification accuracy, even with compression factors up to 64.