I have a matrix $\mathbf{X}$ and I use the eigenvectors of the symmetric matrix $\mathbf{X}^{\top}\mathbf{X}$ for further analysis. But the $\mathbf{X}$ is always growing, as new data points are added to it. I do not want to calculate the eigenvectors each time new rows are added to $\mathbf{X}$. One fairly good assumption regarding the new rows are: in most cases the newly added rows are linear combinations of the existing rows. But in rare cases, it can be independent also.
Is there any quantification of the changes in the eigenvectors of $\mathbf{X^\top X}$ as new rows are added to $\mathbf{X}$ ?. Any one can point me to me related papers ?