Vector ℓ0 latent-space principal component analysis

Principal component analysis (PCA) is a widely used signal processing technique. Instead of performing PCA in the data space, we consider the problem of sparse PCA in a potentially higher dimensional latent space. To do so, we zero-out groups of variables using vector `0 regularization. The estimation is based on the maximization of the penalized log-likelihood, for which we develop an efficient coupled expectation-maximization (EM) minorization-maximization (MM) algorithm. For the special case when the latentand observation space are identical, our method corresponds to an existing vector `0 PCA method, which we verify using simulations. The proposed method can also be utilized for penalized linear regression and we use simulations to demonstrate superior estimation performance. As an example of a practical application, we use our method to localize cortical activity from magnetoencephalography (MEG) data.