Ricerc@Sapienza

L1-Principal Component Analysis (L1-PCA) is a powerful computational tool to identify relevant components in data affected by noise, outliers, partial disruption and so on. Relevant efforts have been made to adapt its powerful summarization capacity to time variant data, e.g. in tracking the evolution of L1-PCA components. Here, we analyze a layered version of L1-PCA, to which we refer to as Deep L1-PCA. Deep L1-PCA is obtained by recursive application of two stages: estimation of L1-PCA basis and extraction of the first rank projector.

We consider the problem of detecting a change in an arbitrary vector process by examining the evolution of calculated data subspaces. In our developments, both the data subspaces and the change identification criterion are novel and founded in the theory of L1-norm principal-component analysis (PCA). The outcome is highly accurate, rapid detection of change in streaming data that vastly outperforms conventional eigenvector subspace methods (L2-norm PCA).