The Fidelity of Local Ordinal Encoding

A key question in neuroscience is how to encode sensory stimuli such as images and sounds. Motivated by studies of response properties of neurons in the early cortical areas, we propose an encoding scheme that dispenses with absolute measures of signal intensity or contrast and uses, instead, only local ordinal measures. In this scheme, the structure of a signal is represented by a set of equalities and inequalities across adjacent regions. In this paper, we focus on characterizing the fidelity of this representation strategy. We develop a regularization approach for image reconstruction from ordinal measures and thereby demonstrate that the ordinal representation scheme can faithfully encode signal structure. We also present a neurally plausible implementation of this computation that uses only local update rules. The results highlight the robustness and generalization ability of local ordinal encodings for the task of pattern classification.