  A problem of classification of local field potentials (LFPs), recorded from
the prefrontal cortex of a macaque monkey, is considered. An adult macaque
monkey is trained to perform a memory-based saccade. The objective is to decode
the eye movement goals from the LFP collected during a memory period. The LFP
classification problem is modeled as that of classification of smooth functions
embedded in Gaussian noise. It is then argued that using minimax function
estimators as features would lead to consistent LFP classifiers. The theory of
Gaussian sequence models allows us to represent minimax estimators as finite
dimensional objects. The LFP classifier resulting from this mathematical
endeavor is a spectrum based technique, where Fourier series coefficients of
the LFP data, followed by appropriate shrinkage and thresholding, are used as
features in a linear discriminant classifier. The classifier is then applied to
the LFP data to achieve high decoding accuracy. The function classification
approach taken in the paper also provides a systematic justification for using
Fourier series, with shrinkage and thresholding, as features for the problem,
as opposed to using the power spectrum. It also suggests that phase information
is crucial to the decision making.
