Consider monitoring by a high-dimensional data stream, for instance 100-1000 sensors that regularly measure the condition of a large system. The aim is to detect changes to the mean or covariance matrix of this data stream as quickly as possible, while controlling the number of false alarms. Here, we give special attention to the realistic case where only a few of the componenets change; the change is sparse.
Our strategy for sequentially detecting such changes is based on projecting the incoming data onto a few of the principal axes of the pre-change data. But which principal axes are the most sensitive to changes of different type and sparsity? Based on the Hellinger distance, we show that it depends on the pre-change covariance matrix and which changes are of interest, but that the least varying axes in general are more sensitive. In two-dimensional data, this is explained theoretically, while simulations provide insight into higher dimensions. The proposed monitoring procedure automatically selects the most informative principal axes given a covariance matrix and relevant change scenarios, and we show that it is highly efficient in detecting such changes.