We present a novel approach for haptic material classification based on an adaptation of human haptic exploratory procedures executed by a robot arm with an optical force sensor. A multi-channel neural architecture informed by findings from human haptic perception performs a spectral analysis on vibration and texture data gathered during material exploration and integrates this analysis with information gathered on material compliance. Experimental results show a high classification accuracy on a test set of 32 common household materials. Furthermore, we show that haptic material properties, relevant for robot grasping, can be classified with a simple haptic exploration while actual material classification requires more complex exploration and computation.