One of the problems with k$-$nearest neighbor learning is selecting a value for k$.$ For this exercise, you will empirically determine a reasonable value for $k,$ given a specific training set. Say you are given the data set shown below. This is a binary classification task in which the instances are described by two real$-$valued attributes.

a$)$ Find a value of k $($using $*.....,$ Matlab, o$.)$ that minimizes leave$-$one$-$out crossvalidation error. What we'll be doing here is using our training set to help us select a good value for k $.$ We take our training instances and divide them into two groups, so that some are used for training and others serve as validation $($i$.$e$.,$ "test"$)$ examples. Specifically, for the given training set of $14$ examples, we divide it into a set of $13$ for training and a set of $1$ for testing. There are obviously $14$ ways to choose $13($i$.$e$.,$ "leave one out"$),$ and we will consider all $14.$

For each training$-$validation split of the data $($remember that there are $14$ of these$),$ we run the k $-$nearest neighbor algorithm for all possible values of to $13).$ We then compute how well we did at classifying the validation instances for each value of k $.$ The k that performs best is selected as the value to use for future $($unseen$)$ test instances. the K number should be odd