We consider the problem of computing dense correspondences between non-rigid shapes with potentially significant partiality. Existing formulations tackle this problem through heavy manifold optimization in the spectral domain, given hand-crafted shape descriptors. In this paper, we propose the first learning method aimed directly at partial non-rigid shape correspondence. Our approach uses the functional map framework and learns descriptors directly from the data, thus both improving robustness and accuracy in challenging cases. Furthermore, unlike existing techniques, our method is also applicable for partial-to-partial non-rigid matching, in which the overlapping of the region on both shapes is unknown a priori. We demonstrate that the resulting method is data efficient, and achieves state of the art results on several benchmark datasets. Our code and data will be released after publication.