Abstract

We introduce a novel framework, called sparse embedding (SE), for simultaneous dimensionality reduction and dictionary learn- ing. We formulate an optimization problem for learning a transformation from the original signal domain to a lower-dimensional one in a way that preserves the sparse structure of data. We propose an efficient optimiza- tion algorithm and present its non-linear extension based on the kernel methods. One of the key features of our method is that it is computa- tionally efficient as the learning is done in the lower-dimensional space and it discards the irrelevant part of the signal that derails the dictionary learning process. Various experiments show that our method is able to capture the meaningful structure of data and can perform significantly better than many competitive algorithms on signal recovery and ob ject classification tasks.