A well-known data set is the MNIST handwritten digit database, containing many thousands of digitalized numbers (from 0 to 9 ), each described by a \(28 \times 28\) matrix of gray scales. A similar but much smaller data set is described in [63]. Here, each handwritten digit is summarized by a \(8 \times 8\) matrix with integer entries from 0 (white) to 15 (black). Figure 7.14 shows the first 50 digitized images. The data set can be accessed with Python using the sklearn package as follows.

(a) Divide the data into a \(75 \%\) training set and \(25 \%\) test set.

(b) Compare the effectiveness of the \(K\)-nearest neighbors and naïve Bayes method to classify the data.

(c) Assess which \(K\) to use in the \(K\)-nearest neighbors classification.

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from sklearn import datasets. digits datasets. load_digits () x digits digits.data explanatory variables y digits = digits.target #responses