When first studying Mining Spatial Associations. Spatial association or spatial frequent patterns share some commonalities as a general association and frequent patterns. For example, the association rules are also in the form of A in plus B, with certain support and a confidence. In this context, A and B could be sets of spatial or non--spatial predicates. The spatial predicates may indicate topological relations or spatial orientations or distance information like close to, within certain distance. And it measures support and confidence are very similar to the general ones. The rules with him find it could be like if x is a large town then x intersect with the highway, then x is likely to be adjacent to water. Like lakes and the rivers and ocean so that with certain support and a confidence. In spatial rail mining, quite often we would like to explore spatial autocorrelation. That means spatial data tends to be highly self-correlated, nearby things are more related than the remote things. For example when we study neighborhood, study temperature, likely would pay more attention to find interesting relationship in the nearby objects. In spatial association mining, there's a interesting heuristic called progressive refinement. The general philosophy of this for a spatial relationship, there are some rough ones like close to which is generalization of some more refined one like nearby, touch, intersect, contain, they are somewhat or close to. Just give you an example. Like here, if we can see, near a highway intersection, you may be able to find shopping centers and gas stations. But how close to, whether they are very nearby or they are almost touch the highway intersection. So in that sense, those are detail refine relationships. However, if we first find those close to there frequent together, okay. Then we, if we want to find the more refine, how close to are they really to the intersection. So we can say if the close to is a frequent pattern, then we are going to study the more refined watch. To that extent, this is the philosophy of progressive refinement. That means, we first search for rough relationships, and then refine for, to study more refined relationships. The general philosophy is, if the rough relationship is not frequent. So there's no need to study the very final because they are not frequent as well. So to that extent, we can do two step mining of spatial association. The first step, as we use and we shape or low cost algorithm. Like minimum bounding rectangle or R-trees for some rough pattern mining. That means we first compute the rough spatial frequent patterns. Then we know if the rough one is frequent, then we are going to get into refinement process. That means we may study a more detailed algorithm using more refined data structure. So this principle can save a lot of mining cost. Because we first using rough lines, we get a big filter. A lot of unnecessary pairs because they are not frequent already. We don't have to refine it. We don't have to use a refine measure to study more refined patterns. Close to, you can find