Manifold Learning and Deep Clustering with Local Dictionaries

We introduce a novel clustering algorithm for data sampled from a union of nonlinear manifolds. Our algorithm extends a popular manifold clustering framework, which first computes a sparse similarity graph over the input data and then uses spectral methods to find clusters in this graph. While previous manifold learning algorithms directly compute similarity scores between pairs of data points, our algorithm first augments the data set with a small handful of representative atoms and then computes similarity scores between data points and atoms. To measure similarity, we express each data point as sparse convex combination of nearby atoms. To learn the atoms, we employ algorithm unrolling, an increasingly popular technique for structured deep learning. Ultimately, this departure from established manifold learning techniques leads to improvements in clustering accuracy and scalability.