"GOOD" AND "BAD" k-OCCURRENCES

When labels are present, k-occurrences can be distinguished based on whether labels of neighbors match.

• $BN_k(\mathbf x)$: We define the number of "bad" k-occurrences of $\mathbf x, BN_k(\mathbf x)$, as the number of points from data set $D$ for which $\mathbf x$ is among the first k-NNs, and the labels of $\mathbf x$ and the points in question do not match.
• $GN_k(\mathbf x)$: Conversely, $GN_k(\mathbf x)$, the number of "good" k-occurrences of $\mathbf x$, is the number of such points where labels do match.
• Naturally, for every $\mathbf x \in D, N_k(\mathbf x) = BN_k(\mathbf x)+GN_k(\mathbf x)$.