In this problem you will classify digits from small handwritten images. 1. (5 marks) Use principle components analysis to produce a 5 dimensional feature vector for each 64 dimensional digit image. 2. (5 mark) Split your low dimensional data into training and test sets. 3. (10 marks) Fit a logistic regression classifier to the training set and estimate the the predictive power of the model using the test set. Plot a bar chart showing the prediction accuracy for each digit. 4. (10 mark) Open ended question: Using any method you wish, build a digit classifier with the best possible predictive power. Credit will be given for for clear coding and comments, creative and rigourous use of methods, and quality of predictions on the test data.