In order to better understand and validate the RPA algorithm, we first conducted some synthetic experiments.
we simulated a highdimensional matrix X ∈ R n×p , with n data samples realizing p "words" and p n, using the following generative model: That is, each p-dimensional data point x i was generated from a hidden lower k-dimensional z i and Figure 2: Hyper-plane learned by PA on XΦ (left pane) compared to hyper-plane and data representations learned by RPA (right pane).