Classifying handwritten digits: Using the MNIST dataset, we will build a simple threshold$-$based classifier that classifies $0$ digits from non$-0$s$.$

Create a new training, validation, and test set as you did in problem $1,$ but this time includes only the $0$ and $1$ digits. Hint: From the test set, select only $0$s and $1$s$.$ Repeat this for the training set. Then, create a validation set as done in the previous assignment.

Convert each image to one attribute by calculating the average of all the pixel values in the center $3$x$3$ grid of the image.

Randomly select $500$ of the images from the training data. Plot the attribute values that you calculated in part $($b$).$ Use different colors and shapes for $0$s and $1$s$.$ The x$-$axis in your figure is the image number $(1$ to $500),$ and the y$-$axis is the calculated attribute. Label the axes and add legends appropriately. Note that these $500$ images are your validation set.

Based on your observation from the plot $($i$.$e$.,$ validation set$),$ guess a threshold on the attribute that you think would differentiate the two classes with the highest accuracy.

Calculate the training, validation, and testing accuracies based on the selected threshold on the corresponding sets and print them.