Memristive switching, a nonlinear current-voltage (I-V) characteristic has seen a tremendous surge in interest, as an approach to achieve implementation of synaptic functions. Here, the memristive switching behavior of self-assembled NiO nanocrystals is investigated via scanning probe microscopy, based on first-order reversal curve current-voltage spectroscopy. Synaptic switching is clearly observed as a direct consequence of filament growth (i.e., gradually increased conductance) in the nanocrystals. A spatial dependency of the conduction in the nanocrystals suggests that there is a localization of the switching filament. The current understanding of this localization ignores features related to local lateral variation current which can generate an excessive local heat and temperature such as electrical dissipation. The observation of low electrical dissipation at the edge of the nanocrystals points out that less energy is wasted as heat such that the bias applied can be utilized more efficiently to assist the nucleation of the filament and thus reduces the power consumption. Electrical power dissipation is also found to scale with the nanocrystal height and has spatial dependence within the nanocrystals. The combination of synaptic switching and high density of the nanocrystals demonstrate feasibility to exploit them to create a basic architecture for neuromorphic memory devices.