Starting from an extended Rayleigh quotient defined on the noncompact Stiefel manifold, in this paper, we present a novel dual purpose subspace flows for subspace tracking. The proposed algorithm can switch from principal subspace to minor subspace tracking with a simple sign change of its stepsize parameter. More interestingly, the proposed dual purpose gradient system behaves the same invariant property as that of the well-known Chen-Amari-Lin system. The stability of the discrete version of the proposed subspace flow is guaranteed by an additional added stabilizing term. No tunable parameter is required for the proposed algorithm as opposed to the modified Oja algorithm. The strengths of the proposed algorithm is demonstrated using a de facto benchmark example.
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