Hebbian-based mean shift for learning the diverse shapes of V1 simple cell receptive fields

The L0-norm constraint in sparse coding has the advantage of producing the same diversity of receptive field shapes as physiology data, but is difficult for analysis. It remains a challenging issue to understand how the diverse shapes of V1 simple cell receptive fields emerge in visual cortex. This paper presents a biologically plausible learning algorithm, named Hebbian-based mean shift, for this problem. The L0-norm constraint optimizes the number of basis functions rather than their coefficients. We report that the optimization procedure is essentially a 0–1 programming of the selection of basis functions. By assuming that the basis functions are independently selected from a basis set, we find the spatial distribution of input samples containing a special basis function has a star shape and peaks at this basis function. Thus, learning the basis functions for sparse coding with the L0-norm can be interpreted as mode detection where the basis functions are the modes of the kernel density estimate. We employ mean shift to detect modes and prove that the updating rule for the mean shift is Hebbian. The simulation results demonstrate the robustness of the proposed algorithm in producing both Gabor-like and blob-like basis functions.