Distributed data cleansing via a low-rank decomposition

Data acquired across sensors may contain irrelevant components such as interference and noise. A distributed framework is put forth that enables sensors to extract the `clean´ portion of a data sequence and isolate the corrupted data. Different from outliers, the corrupted data may affect an arbitrary in size portion of the data sequence. The clean informative data usually consist of low-dimensional components giving rise to a low-rank data covariance matrix, while the presence of irrelevant data increases the rank. This property leads to a novel constrained minimization formulation that combines low-rank matrix decomposition and data selection. A separable formulation is further derived which is tackled via coordinate descent techniques and the alternating direction method of multipliers. Numerical tests demonstrate the potential of the novel distributed scheme.