Flexible Component Analysis for Sparse, Smooth, Nonnegative Coding or Representation

In the paper, we present a new approach to multi-way Blind Source Separation (BSS) and corresponding 3D tensor factorization that has many potential applications in neuroscience and multi-sensory or multidimensional data analysis, and neural sparse coding. We propose to use a set of local cost functions with flexible penalty and regularization terms whose simultaneous or sequential (one by one) minimization via a projected gradient technique leads to simple Hebbian-like local algorithms that work well not only for an over-determined case but also (under some weak conditions) for an under-determined case (i.e., a system which has less sensors than sources). The experimental results confirm the validity and high performance of the developed algorithms, especially with usage of the multi-layer hierarchical approach.