Spike-triggered covariance
Encyclopedia
Spike-triggered covariance (STC) analysis is a tool for characterizing a neuron's response properties using the covariance of stimuli that elicit spikes from a neuron. STC is related to the spike-triggered average (STA), and provides a complementary tool for estimating linear filters in a linear-nonlinear-Poisson (LNP)
cascade model. Unlike STA, the STC can be used to identify a multi-dimensional feature space in which a neuron computes its response.
STC analysis identifies the stimulus features affecting a neuron's response via an eigenvector decomposition of the spike-triggered covariance matrix
. Eigenvectors with eigenvalues significantly larger or smaller than the eigenvalues of the raw stimulus covariance correspond to stimulus axes along which the neural response is enhanced or suppressed.
STC analysis is similar to principal components analysis
(PCA), although it differs in that the eigenvectors corresponding to largest and smallest eigenvalues are used for identifying the feature space. The STC matrix is also known as the 2nd-order Volterra
or Wiener kernel.
Linear-nonlinear-Poisson cascade model
The linear-nonlinear-Poisson cascade model is a simplified functional model of neural spike responses. It has been successfully used to describe the response characteristics of neurons in early sensory pathways, especially the visual system...
cascade model. Unlike STA, the STC can be used to identify a multi-dimensional feature space in which a neuron computes its response.
STC analysis identifies the stimulus features affecting a neuron's response via an eigenvector decomposition of the spike-triggered covariance matrix
Covariance matrix
In probability theory and statistics, a covariance matrix is a matrix whose element in the i, j position is the covariance between the i th and j th elements of a random vector...
. Eigenvectors with eigenvalues significantly larger or smaller than the eigenvalues of the raw stimulus covariance correspond to stimulus axes along which the neural response is enhanced or suppressed.
STC analysis is similar to principal components analysis
Principal components analysis
Principal component analysis is a mathematical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of uncorrelated variables called principal components. The number of principal components is less than or equal to...
(PCA), although it differs in that the eigenvectors corresponding to largest and smallest eigenvalues are used for identifying the feature space. The STC matrix is also known as the 2nd-order Volterra
Volterra Series
The Volterra series is a model for non-linear behavior similar to the Taylor series. It differs from the Taylor series in its ability to capture 'memory' effects. The Taylor series can be used to approximate the response of a nonlinear system to a given input if the output of this system depends...
or Wiener kernel.