Complex spatial relationships

We describe the need for mining complex relationships in spatial data. Complex relationships are defined as those involving two or more of: multifeature colocation, self-colocation, one-to-many relationships, self-exclusion and multifeature exclusion. We demonstrate that even in the mining of simple relationships, knowledge of complex relationships is necessary to accurately calculate the significance of results. We implement a representation of spatial data such that it contains known 'weak-monotonic' properties, which are exploited for the efficient mining of complex relationships, and discuss the strengths and limitations of this representation.