This paper introduces a framework to predict multi-dimensional haptic attribute values that humans use to recognize the material by using the physical tactile signals (acceleration) generated when a textured surface is stroked. To this end, two spaces are established: a haptic attribute space and a physical signal space. A five-dimensional haptic attribute space is established through human adjective rating experiments with the 25 real texture samples. The physical space is constructed using tool-based interaction data from the same 25 samples. A mapping is modeled between the aforementioned spaces using a newly designed CNN-LSTM deep learning network. Finally, a prediction algorithm is implemented that takes acceleration data and returns coordinates in the haptic attribute space. A quantitative evaluation was conducted to inspect the reliability of the algorithm on unseen textures, showing that the model outperformed other similar models.