Return the Average Value
One possible solution is to return the average value in the neighborhood, i.e.
$$ \mathbb{M}_{k}(q) = \frac{1}{k} \sum_{i=1}^{k} t_i $$
We can improve this by using weighted \(k-NN\):
$$ \mathbb{M}_{k}(q) = \frac{ \sum_{i=1}^{k} \left( \frac{1}{dist(q, d_i)^2} \cdot t_i \right) }{ \sum_{i=1}^{k} \frac{1}{dist(q, d_i)^2} } $$
Note that we don’t need to worry about \(k\) being odd, because ties don’t matter.
The formula looks new. However, if \(x_1\) is weighted by \(w_1\) and \(x_2\) by \(w_2\), then the weighted average is:
$$ \frac{w_1 x_1 + w_2 x_2 }{w_1 + w_2} $$
Usually, \(\sum w_i = 1\), so the denominator is frequently omitted.