  We consider the sequential change-point detection problem of detecting
changes that are characterized by a subspace structure. Such changes are
frequent in high-dimensional streaming data altering the form of the
corresponding covariance matrix. In this work we present a Subspace-CUSUM
procedure and demonstrate its first-order asymptotic optimality properties for
the case where the subspace structure is unknown and needs to be simultaneously
estimated. To achieve this goal we develop a suitable analytical methodology
that includes a proper parameter optimization for the proposed detection
scheme. Numerical simulations corroborate our theoretical findings.
