Title: Nonlinear demixed component analysis for neural population data as a low-rank kernel regression problem,
Abstract: Here I introduce an extension to demixed principal component analysis (dPCA),
a linear dimensionality reduction technique for analyzing the activity of
neural populations, to the case of nonlinear dimensions. This is accomplished
using kernel methods, resulting in kernel demixed principal component analysis
(kdPCA). This extension resembles kernel-based extensions to standard principal
component analysis and canonical correlation analysis. kdPCA includes dPCA as a
special case when the kernel is linear. I present examples of simulated neural
activity that follows different low dimensional configurations and compare the
results of kdPCA to dPCA. These simulations demonstrate that nonlinear
interactions can impede the ability of dPCA to demix neural activity
corresponding to experimental parameters, but kdPCA can still recover
interpretable components. Additionally, I compare kdPCA and dPCA to a neural
population from rat orbitofrontal cortex during an odor classification task in
recovering decision-related activity.