Unsupervised Transformation Learning via Convex Relaxations
Our goal is to extract meaningful transformations from raw images, such as varying the thickness of lines in handwriting or the lighting in a portrait. We propose an unsupervised approach to learn such transformations by attempting to reconstruct an image from a linear combination of transformations of its nearest neighbors. On handwritten digits and celebrity portraits, we show that even with linear transformations, our method generates visually high-quality modified images. Moreover, since our method is semiparametric and does not model the data distribution, the learned transformations extrapolate off the training data and can be applied to new types of images.
The paper proposes an algorithm for unsupervised learning of transformations based on modeling nearest neighbor pairs as linear combination of transforms. The technique only models the transformations, and not the full data distribution and so can (in principle) be applied to other data sets (for eg, learning from MNIST, but applying to characters from other languages). While this problem/objective function is non-convex, they provide a convex relation by approximating the true transformation matrix as a linear combination of rank-1 matrices derived from sampling the data (and they show that this is a good approximation to the true transform matrix).  They show that the technique recovers known transforms such as stroke thickness/rotation in addition to new transforms (blur, loop size). 
Overall, I found the ideas in the paper interesting, and the paper well written.