Memory efficient low-rank non-linear subspace tracking

The task of low-rank subspace tracking is of paramount importance for feature extraction over streaming data. Considering the broad range of applications in which the data fail to adhere to a linear model, the present work proposes a nonlinear subspace tracking algorithm. The proposed algorithm can effectively learn and track an evolving non-linear subspace in an online fashion. The notion of non-linearity is accommodated via exploitation of kernel-induced mappings, whose computational as well as memory requirements, if untreated, will impose scalability issues in large datasets. This issue is addressed by imposing a predefined affordable budget on the number of data vectors to be stored, preventing computational and memory growth of the algorithm, while enabling the tracking of possibly evolving subspaces. Numerical tests corroborate the effectiveness of the proposed algorithm on synthetic as well as real datasets.