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Suppose we have matrix $A$ of size $N_t \times N_m$, containing $N_m$ measurements corrupted by some (e.g. Gaussian) noise. An SVD of this data $A = U_AS_A{V_A}^T$ can reveal the singular vectors $U_A$ that span a low dimensional basis for these measurements (which may itself be inaccurate due to noise).

Say we consider now only a subset of those measurements $B$ of size $N_t \times N_n$, with $N_n < N_m$ (e.g. only the first $N_n$ columns of $A$). The corresponding SVD $B = U_BS_B{V_B}^T$ will define its' corresponding low rank subspace $U_B$.

Is there a way to "average" the estimates of $U_A$ and $U_B$ into a single subspace?

Thanks in advance :)

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