Identification of neural feature space from spike triggered covariance expressed as a function of PRC
© Ota et al; licensee BioMed Central Ltd. 2010
Published: 20 July 2010
For the purpose of elucidating the neural coding process based on the neural excitability mechanism, some researchers have investigated the relationship between the neural dynamics and the spike triggered stimulus ensemble (STE), which indicates what stimuli are more likely or less likely to induce neural spikes. Ermentrout et al. have analytically derived the relational equation between the phase response curve (PRC) and the spike triggered average (STA), which is the average of the STE, when regular spikes with a period are disturbed by sufficiently small white noise, as (1). Here, is the time relative to a spike, is the noise intensity, and is PRC . Furthermore, they showed that Eq. (1) holds true for real neurons. Their study has made meaningful progress in relating the neural dynamics to the neural coding for real neurons. However, the STA is the first cumulant of the STE. In order to approximately identify the distribution of STE as a Gaussian, we should determine its second cumulant, called spike triggered covariance (STC).
where represents the Heaviside function which takes 1/2 at . Moreover, we analyze the eigenfunctions of in order to extract the neural feature space, which is a low dimensional subspace of the full stimulus space characterizing the stimulus encoded by neurons. The eigenfunctions associated with the positive and negative eigenvalues of are called the excitatory and suppressive eigenfunction, respectively. In this case, the stimuli in the subspace spanned by excitatory eigenfunctions cause shorter interspike intervals (ISIs) than , while the stimuli in the subspace spanned by suppressive eigenfunctions cause longer ISIs.
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