Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 218 / 3 / e / i / Solution

The one-nearest-neighbour classification boundary consists of the portions of the Voronoi diagram separating cells whose observed labels differ. For these nine grid points it forms diagonal and vertical or horizontal perpendicular-bisector segments around the three triangular observations. Every training point is its own nearest neighbour, so, absent a distance tie convention that excludes the query itself, its training error is zero.