st.statistics - What is the probabilistic counterpart of weighted K-Means

pKNN+AL (Jain and Kapoor, 2009) is a probabilistic modification of the KNN classifier. Given a set of points ${x_1, ldots, x_n}$ from $mathbb{R}^d$, labels ${y_1, ldots, y_n}$ from $[1,C]$, and a Mercer kernel $K$, the probability of $x$ belonging to class $c$ is

$$frac{frac{1}{n_c} sum_{{i : y_i = c}} K(x, x_i)}{sum_{t=1}^C frac{1}{n_t} sum_{{i : y_i = c}} K(x, x_i)}$$

where $n_c$ is the number of $x_i$ that belong to class $c$. It is also an active learning algorithm and comes with a MATLAB implementation.