Learning Data Representations with Sparse Coding Neural Gas

We consider the problem of learning an unknown (overcomplete) basis from an unknown sparse linear combination. Introducing the “sparse coding neural gas” algorithm, we show how to employ a combination of the original neural gas algorithm and Oja’s rule in order to learn a simple sparse code that represents each training sample by a multiple of one basis vector. We generalise this algorithm using orthogonal matching pursuit in order to learn a sparse code where each training sample is represented by a linear combination of k basis elements. We show that this method can be used to learn artificial sparse overcomplete codes.