Characterizing the sparseness of neural codes

It is often suggested that efficient neural codes for natural visual information should be 'sparse'. However, the term 'sparse' has been used in two different ways-firstly to describe codes in which few neurons are active at any time ('population sparseness'), and secondly to describe codes in which each neuron's lifetime response distribution has high kurtosis ('lifetime sparseness'). Although these ideas are related, they are not identical, and the most common measure of lifetime sparseness-the kurtosis of the lifetime response distributions of the neurons-provides no information about population sparseness. We have measured the population sparseness and lifetime kurtosis of several biologically inspired coding schemes. We used three measures of population sparseness (population kurtosis, Treves-Rolls sparseness and 'activity sparseness'), and found them to be in close agreement with one another. However, we also measured the lifetime kurtosis of the cells in each code. We found that lifetime kurtosis is uncorrelated with population sparseness for the codes we used. Lifetime kurtosis is not. therefore, a useful measure of the population sparseness of a code. Moreover, the Gabor-like codes, which are often assumed to have high population sparseness (since they have high lifetime kurtosis), actually turned out to have rather low population sparseness. Surprisingly, principal components filters produced the codes with the highest population sparseness.