A more common way of speeding up a machine learning algorithm is by using Principal Component Analysis (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. This is probably the most common application of PCA. Another common application of PCA is for data visualization.
To understand the value of using PCA for data visualization, this tutorial post goes over a basic visualization of the IRIS dataset after applying PCA.