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A. Carreño, A. Vidal-Ferrándiz, D. Ginestar and G. Verdú

matrix W in equation ( 13 ) is chosen as the previous approximation for the invariant subspace, that is, W = Z ¯ ( k ) $\begin{array}{} \displaystyle W=\bar{Z}^{(k)} \end{array}$ . Using the definition of K ( k ) on ( 10 ), system ( 13 ) is decoupled into the q linear systems ( M − L λ i ( k ) L Z ¯ ( k ) Z ¯ ( k ) † 0 ) ( Δ z ¯ i ( k ) − Δ λ i ( k ) ) = ( M z ¯ i ( k ) − L z ¯ i ( k ) λ i ( k ) 0 ) $$\begin{array}{} \displaystyle \begin{pmatrix} M-L\lambda_i^{(k)} & L\bar{Z}^{(k)}\\ \bar{Z}^{(k)^{\dagger}} &0 \end{pmatrix} \begin{pmatrix}\Delta \bar

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Linli Zhu, Yu Pan and Jiangtao Wang

˜ − D T u ) T ( V ˜ T V ˜ ) † ( V ˜ T y ˜ − D T u ) , ‖ u ‖ ∞ ≤ λ , D T u ∈ span ( V ˜ T ) . $$\begin{array}{c} \min\limits_{u\in\mathbb{R}^{p-1}}\frac{1}{2}(\tilde{{\bf V}}^{T}\tilde{{\bf y}}-{\bf D}^{T}{\bf u})^{T}(\tilde{{\bf V}}^{T}\tilde{{\bf V}})^{\dagger}(\tilde{{\bf V}}^{T}\tilde{{\bf y}}-{\bf D}^{T}{\bf u}),\\ \|u\|_{\infty}\le\lambda,{\bf D}^{T}{\bf u}\in {\rm span}(\tilde{{\bf V}}^{T}). \end{array}$$ The other version of ontology framework can be simply expressed as min w 1 2 | | y − V w | | + λ | | w | | 1 . $$\begin{array}{} \displaystyle {\min