  Many studies of neural activity in behaving animals aim to discover
interpretable low-dimensional structure in large-scale neural population
recordings. One approach to this problem is demixed principal component
analysis (dPCA), a supervised linear dimensionality reduction technique to find
components that depend on particular experimental parameters. Here, I introduce
kernel dPCA (kdPCA) as a nonlinear extension of dPCA by applying kernel
least-squares regression to the demixing problem. I consider simulated examples
of neural populations with low-dimensional activity to compare the components
recovered from dPCA and kdPCA. These simulations demonstrate that neurally
relevant nonlinearities, such as stimulus-dependent gain and rotation,
interfere with linear demixing of neural activity into components that
represent to individual experimental parameters. However, kdPCA can still
recover interpretable components in these examples. Finally, I demonstrate
kdPCA using two examples of neural populations recorded during perceptual
decision-making tasks.
