where the latter equality holds if is a vector space. In general, the dimension of is infinite. This gives rise to the the celebrated 'Kernel trick' in machine learning , where data is embedded in to a high-dimensional space to allow for linear separation. In the context of molecular simulations, the kernel can be interpreted as a way of comparing high-dimensional collective variables simultaneously, side-stepping the need to engineer the collective variables. Below we detail the kernel used in the molecular applications we studied.