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Implement the support vector machine classifier

Derive from the raw pixel data a feature that quantifies "how much ink" a digit costs. Report the average and standard deviation of this feature within each class. If you look at these statistics, can you see which pairs of classes can be distinguished well, and which pairs will be hard to distinguish using this feature? Hint: Use the R function "tapply" to compute the mean and standard deviation per digit. If your feature is called "ink", then "tapply(ink,mnist.dat[,1],mean)" will compute the mean value of ink for each digit.

Using only the ink feature, fit a multinomial logit model and evaluate, by looking at the confusion matrix, how well this model can distinguish between the different classes. Since in this part of the assignment we only consider very simple models, you may use the complete data set both for training and evaluation. For example, how well can the model distinguish between the digits "1" and "8"? And how well between "3" and "8"? Use the R function "scale" to scale your feature before you apply "multinom" to fit the multinomial logit model.

In addition to "ink", come up with one other feature, and explain why you think it might discriminate well between the digits. Your report should contain an unambiguous description of how the feature is derived from the raw data. Perform the same analysis for this new feature as you did for the ink feature.

You may reduce the level of detail to, for example, a 14x14 pixel image (the function "down_sample_image" from the "OpenImageR" package may come in very handy here). In that case you will have only 196 features instead of 784.
If you choose to do so, indicate this clearly in the report.