Recent research on pattern discovery has progressed from mining frequent patterns and sequences to mining structured patterns, such as trees and graphs. Graphs as general data structure can model complex relations among data with wide applications in web exploration and social networks. However, the process of mining large graph patterns is a challenge due to the existence of large number of subgraphs. In this paper, we aim to mine only frequent complete graph patterns. A graph g in a database is complete if every pair of distinct vertices is connected by a unique edge. Grid Complete Graph (GCG) is a mining algorithm developed to explore interesting pruning techniques to extract maximal complete graphs from large spatial dataset existing in Sloan Digital Sky Survey (SDSS) data. Using a divide and conquer strategy, GCG shows high efficiency especially in the presence of large number of patterns. In this paper, we describe GCG that can mine not only simple co-location spatial patterns but also complex ones. To the best of our knowledge, this is the first algorithm used to exploit the extraction of maximal complete graphs in the process of mining complex co-location patterns in large spatial dataset.
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.