This is probably the most common application of PCA. If your learning algorithm is too slow because the input dimension is too high, then using PCA to speed it up can be a reasonable choice. A more common way of speeding up a machine learning algorithm is by using Principal Component Analysis (PCA).
One of the things learned was that you can speed up the fitting of a machine learning algorithm by changing the optimization algorithm. My last tutorial went over Logistic Regression using Python.
