Tuning properties of noisy cells with application to orientation selectivity in rat visual cortex

Common measures for the tuning of cells that are used in the neuroscience literature break down even in the case of moderately noisy neurons. For this reason, a considerable proportion of recorded neuronal data remains unconsidered. One reason for the unreliability of tuning measures is that least-squares fitting of a function for the tuning curve is likely to give too much influence to outliers. We present an algorithm using a rank-weighted norm to construct a tuning curve which weighs outlying data less strongly. As a model function for the tuning curve, we take a trigonometric polynomial, whose coefficients can be determined using a linear approximation. This approach avoids the occurrence of multiple local minima in the optimization process. A test criterion is given to answer the question whether a trigonometric polynomial of lower degree can account for the data. Throughout, we apply our findings to our own experimental data recorded from a population of neurons from area 17 of the rat.