more or less abrupt, with smoother transitions for increasing numbers of nearest neighbors. Whereas volume conduction results in smoother (or smeared) surface potential topographies, stretching any local minimum or maximum to neighboring scalp locations (cf. isopotential lines in Fig. 6A), the topographic pattern is markedly sharper for local Hjorth estimates, particularly for those based on fewer nearest neighbors, yielding a more focal left-lateralized N1 and a more constrained mid-parietal P3. Less accurate surface Laplacian estimates are obtained for locations around the edge of the EEG montage, where fewer neighbors are available, thereby preventing a symmetric sampling of the field around each site. However, these adverse effects are notably mitigated when including additional (up to all 66) nearest neighbors, which is equivalent to the smoothing effect in the one-dimensional case by widening the differentiation span. While employing many ‘nearest’ neighbors may be counterintuitive, seemingly upending the purpose of a local Hjorth, the impact or weight for signal differentiation will nevertheless be greater for the immediate neighbors compared to those at more distant locations (i.e., any subtracted potential is scaled by the inverse of its distance).
