Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to the best of our knowledge, all existing theoretical guarantees for it assume that the data and the corrupting noise are mutually independent, or at least uncorrelated. This is valid in practice often, but not always. In this paper, we study the PCA problem in the setting where the data and noise can be correlated. Such noise is often also referred to as ``data-dependent noise. We obtain a correctness result for the standard eigenvalue decomposition (EVD) based solution to PCA under simple assumptions on the data-noise correlation. We also develop and analyze a generalization of EVD, cluster-EVD, that improves upon EVD in certain regimes.

Principal components analysis~(PCA) is the optimal linear encoder of data. Sparse linear encoders (e.g., sparse PCA) produce more interpretable features that can promote better generalization.

Since its inception in 1982, Oja's algorithm has become an established method for streaming principle component analysis (PCA).

In CEED, we assume that waveforms are already extracted from an extracellular recording. Each waveform is then passed through our stochastic view generation module, where different views are obtained by applying transformations.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Instead,compositional datamust be first transformed before analysis.