Projection error measure

Let $v_{ij}$ be the $j^{th}$ eigenvector of the $i^{th}$ frame. The noise subspace is given by the span of the noise eigenvectors, $v_{\mathcal{N}k}$:

$$\mathcal{S_N}=span\{v_{\mathcal{N}k}\vert k=1,\ldots,D\}$$

The projection error measure for the $i^{th}$ frame is given by

$$\begin{array}{lll} & & \frac{1}{D} \sum_{j=1}^{D} \Vert v_... ...l{N}}V_{\mathcal{N}}')V_{i} \Vert _{columns} \\ \end{array}$$