Testing PCA

$\frac{0\mathrm{.}0}{1\mathrm{.}0}$ point $($graded$)$

Use project$\_$onto$\_$PC to compute a $18-$dimensional PCA representation of the MNIST training and test

datasets, as illustrated in main. py $.$

Retrain your softmax regression model $($using the original labels$)$ on the MNIST training dataset and report its

error on the test data, this time using these $18-$dimensional PCA$-$representations rather than the raw pixel

values.

If your PCA implementation is correct, the model should perform nearly as well when only given $18$ numbers

encoding each image as compared to the $784$ in the original data $($error on the test set using PCA features

should be around $0\mathrm{.}15).$ This is because PCA ensures these $18$ feature values capture the maximal amount of

variation from the original $784-$dimensional data.

Error rate for $18-$dimensional PCA features $=$