Before revision:  However, these projection methods come at the cost of approximation errors in both top singular values and vectors . Furthermore, in order to bound the approximation error, an over-sampled projection is required, often much larger in dimension than the desired rank. This latter consideration can still be memory intensive when the data dimension is large or extraneous when the desired rank approximation is close to the full rank.
After revision:  However, these projection methods come at the cost of approximation errors in the singular vectors and values are high when the aforementioned assumption does not hold. Furthermore from a practical perspective, oversampling can still be memory intensive when the data dimension is large or extraneous when the desired rank approximation is close to the full rank.