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Using a tactile array sensor to recognize an object often requires multiple touches at different positions. This process is prone to move or rotate the object, which inevitably increases difficulty in object recognition. To cope with the unknown object movement, this paper proposes a new tactile-SIFT descriptor to extract features in view of gradients in the tactile image to represent objects, to allow the features being invariant to object translation and rotation. The tactile-SIFT segments a tactile image into overlapping subpatches, each of which is represented using a dn-dimensional gradient vector, similar to the classic SIFT descriptor. Tactile-SIFT descriptors obtained from multiple touches form a dictionary of k words, and the bag-of-words method is then used to identify objects. The proposed method has been validated by classifying 18 real objects with data from an off-the-shelf tactile sensor. The parameters of the tactile-SIFT descriptor, including the dimension size dn and the number of subpatches sp, are studied. It is found that the optimal performance is obtained using an 8-D descriptor with three subpatches, taking both the classification accuracy and time efficiency into consideration. By employing tactile-SIFT, a recognition rate of 91.33% has been achieved with a dictionary size of 50 clusters using only 15 touches.