Choosing a good k
It is important to pick a proper value of hyperparameter k, since it can improve a model's performance as well as degrade it when chosen incorrectly. One popular rule of thumb is to take a square root of the number of training samples. Many popular software packages use this heuristic as a default k value. Unfortunately, this doesn't always work well, because of the differences in the data and distance metrics.
There is no mathematically-grounded way to come up with the optimal number of neighbors from the very beginning. The only option is to scan through a range of ks, and choose the best one according to some performance metric. You can use any performance metric that we've already described in the previous chapter: accuracy, ...
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