answer for both questions:

  

 

4. Handwritten Digit Recognition. The goal is to recognize the digit in each image of the dataset given in "Digits Training" which contains some digits from the US Postal Service Zip Code. We are going to decompose the big task of separating ten digits into smaller tasks of separating two of the digits (binary classification). Use two digits: the final number in your UD ID and conveniently choose any other number to replicate the results from the slides chapter "The Learning Problem" (take into account the features that you are going to use for classification to choose the second number). (a) Extract 2 features from the images: average intensity and symmetry. Using this two features, implement the Perceptron Learning Algo- rithm. Use an error metric for binary classification. To compute Eout, use the testing set given to you in "DigitsTesting". Show only 200 iterations. (b) Repeat item (a), for the pocket algorithm. Show the same plots that are in Slide 32 and 33 of the chapter "The Learning Problem", that is, compare errors (Ein, Eout) and classification boundaries of the simple perceptron and the pocket algorithms. 4 images are expected. (c) Extract one more feature from the images that could help to improve your previous results. Describe how you compute this feature and why is it representative of your data?. (d) Repeat items (a) and (b), using the three features (average intensity, symmetry and the one that you choose in (c)). Hint: The classifica- tion boundary would be a plane given a 3D feature space. Dataset description: The first column in Digits Training and Digits Test- ing corresponds to the digit number, following columns correspond to 256 pixels of the 16 x 16 pixel image of the digit. Thus, we have 7291 inputs in Digits Training and 2007 inputs in Digits Testing. From these datasets, work only with those inputs that correspond to the digits you chose. Re- member, one of the digits corresponds to the final number in your UD ID.