Sparse subspace clustering for evolving data streams

The data streams arising in many applications can be modeled as a union of low-dimensional subspaces known as multi-subspace data streams (MSDSs). Clustering MSDSs according to their underlying low-dimensional subspaces is a challenging problem which has not been resolved satisfactorily by existing data stream clustering (DSC) algorithms. In this paper, we propose a sparse-based DSC algorithm, which we refer to as dynamic sparse subspace clustering (D-SSC). This algorithm recovers the low-dimensional subspaces (structures) of high-dimensional data streams and finds an explicit assignment of points to subspaces in an online manner. Moreover, as an online algorithm, D-SSC is able to cope with the time-varying structure of MSDSs. The effectiveness of D-SSC is evaluated using numerical experiments.