Covariance tracking from sketches of rapid data streams

Estimating and tracking the covariance matrix of high-dimensional data streams with low complexities in acquisition, storage and computation are of great interest in modern data-intensive applications. This paper develops an online covariance estimation and tracking algorithm for a recently developed covariance sketching framework that requires a single sketch per sample [1], by leveraging the low-rank structure of the covariance matrix. In particular, we devise a discounting mechanism in the aggregation procedure to enable faster tracking when the covariance structure changes over time. The performance of the proposed algorithm is validated through numerical examples.