kNN regressor is based on learning by comparing the given test instances with the training set \cite{cover1968estimation}. Let $T=\{(x_1,y_1)$, $(x_2,y_2)$, $\cdots$,$(x_N,y_N)\}$ be the training set with distance metrics $d$, where $x_i=(x_{i1},x_{i2},\cdots, x_{im})$ is the $i$th instance denoted by $m$ attributes with its label $y_i$, and $N$ is the number of instances. When given a test instance $x$, it needs to compute the distance $d_{i}$ between $x$ and each instance $x_i$ in $T$, and sorts the distance $d_{i}$ by its value.
If $d_{i}$ ranks in the $i$th place, then the distance $d_{i}$ corresponding instance is called the $i$th nearest neighbor $NN_i(x)$, and its label is noted as $y_i(x)$. Finally the prediction label $\widehat{y}$
If $d_{i}$ ranks in the $i$th place, then the distance $d_{i}$ corresponding instance is called the $i$th nearest neighbor $NN_i(x)$, and its label is noted as $y_i(x)$. Finally the prediction label $\widehat{y}$