What is the difference between spatial interpolation and trend surface analysis?
For example, I read a scientific study that applied a neural network to estimate a surface solely based on the x and y coordinates, claiming that they do spatial inteprolation. However, to my understanding this is trend surface analysis, because Tobler's law is not considered.
Am I right?! Is the difference between these two that spatial interpolation takes neighboring observations into account?
Both methods aim at building a continuous surface based on a set of points. The main difference is that spatial interpolation relies on some weighted average of the points located in a neighborhood (it is thus "local"), while trend surface analysis uses all the points that are available (it is thus "global").
Neural networks are based on some weighted average, so it could be used for interpolation. In your case, without details about the paper, I guess that the NN has adjusted a single function based on a global set of points. It then applies this function based on the xy coordinates. This is a "global" approach, I would say that you are right even if the "surface" is not the more commonly used "least square adjusted polynomial".
