Suppose we have a very simple online k-means where each new data-point is assigned to its nearest center (the mean is updated incrementally). Each center (cluster) is labelled with the most common label of data-points assigned to that cluster. In this special configuration: is it possible to compute a sort of "posterior probability"? I.e., can the posterior probability of a class label $y$ given a data-point $x$ ($P(y|x)$) just be $1/\text{distance}(x, m_y)$, where $m_y$ is a center labelled with $y$ which is nearest to $x$?
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