Algorithm 1 Incremental PCA with mean update

1:Compute the mean vectors ${\overline{I}}_B=\frac{1}{m}{\sum }_{i=n+1}^{n+m}{I}_i$, and ${\overline{I}}_C=\frac{n}{n+m}{\overline{I}}_A+\frac{m}{n+m}{\overline{I}}_B$. 2:Form the matrix $\widehat{B}=\left[(I_{n+1}-I_B)...(I_{n+m}-I_B)\sqrt{\frac{nm}{n+m}}(I_B-I_A)\right]$. 3:Compute $\tilde{B}=\mathrm{orth}(\widehat{B}-U{U}^T\widehat{B})$ and $R=\left[\begin{array}{cc}f\mathsf{\Sigma }& U^T\widehat{B}\\ 0& \tilde{B}(\widehat{B}-U{U}^T\widehat{B})\end{array}\right]$. 4:Compute the SVD of R: $R=\tilde{U}\tilde{\mathsf{\Sigma }}{\tilde{V}}^T$. 5:Finally, $U^{\prime }=\left[U\tilde{B}\right]\tilde{U}$ and ${\mathsf{\Sigma }}^{\prime }=\tilde{\mathsf{\Sigma }}$. 6:Repeat for each new block of frames. Now with $A=U^{\prime }$.