The correct answer is A.
The elbow method is a graphical method for selecting the number of principal components to retain. It works by plotting the cumulative variance explained by each principal component, and then looking for a “elbow” in the curve. The number of principal components corresponding to the elbow is then chosen as the number of components to retain.
However, the elbow method is not always reliable. It can be difficult to identify the elbow in the curve, and the choice of the number of components can be sensitive to the choice of the scaling of the data.
A more robust approach is to choose the number of principal components so that at least a certain amount of the variance is retained. In this case, we are interested in retaining at least 99% of the variance. This can be done by calculating the cumulative variance explained by each principal component, and then choosing the number of components corresponding to the point where 99% of the variance is explained.
This approach is more robust than the elbow method because it is not sensitive to the choice of the scaling of the data. It is also more likely to select the correct number of components, even if the data is not well-represented by a small number of principal components.
Options B and C are not reasonable ways to select the number of principal components. Option B would select a very small number of principal components, which would not capture much of the variance in the data. Option C would select a very large number of principal components, which would be unnecessary and could lead to overfitting.