Sparse coding, manifold learning, and slow feature analysis are typically thought of as three distinct forms of unsupervised learning. Here we describe a new signal representation framework called the sparse manifold transform that combines key ideas from all three of these approaches. Natural signals frequently contain sparse features subject to low dimensional transformations. By learning the topological relationship among sparse features (as shown above), one can model both the sparse features and their transformations simultaneously.  Representing the geometric structure among the features in this way allows one to build hierarchical representations that are potentially useful in many applications. Please keep an eye out for a forthcoming blog post that discusses these concepts in more detail. Follow us on twitter to find out when that becomes available, and until then feel free to check out the paper on arXiv.