Nonlinear demixed component analysis for neural population data as a low-rank kernel regression problem

Many studies of neural activity in behaving animals aim to discover interpretable low-dimensional structure in largescale 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.