Using a regularizer borrowed from k-sparse autoencoders, this is interesting:
Improving approximate RPCA with a k-sparsity prior by Maximilian Karl, Christian Osendorfer
A process centric view of robust PCA (RPCA) allows its fast approximate implementation based on a special form o a deep neural network with weights shared across all layers. However, empirically this fast approximation to RPCA fails to find representations that are parsemonious. We resolve these bad local minima by relaxing the elementwise L1 and L2 priors and instead utilize a structure inducing k-sparsity prior. In a discriminative classification task the newly learned representations outperform these from the original approximate RPCA formulation significantly.
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