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.
Most of the previous research and to the best of our knowledge, previous work has used Apriori type algorithms for mining interesting co-location patterns. However, we embedded GLIMIT @cite_14 as the underlying pattern mining algorithm as already discussed in . To the best of our knowledge, no previous work has used the concept of .
@cite_14
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In our geometric view, an itemset is a vector (itemvector) in the space of transactions. Linear and potentially non-linear transformations can be applied to the itemvectors before mining patterns. Aggregation functions and interestingness measures can be applied to the transformed vectors and pushed inside the mining process. We show that interesting itemset mining can be carried out by instantiating four abstract functions: a transformation (g), an algebraic aggregation operator (o) and measures (f and F). For frequent itemset mining (FIM), g and F are identity transformations, o is intersection and f is the cardinality. Based on this geometric view we present a novel algorithm that uses space linear in the number of 1-itemsets to mine all interesting itemsets in a single pass over the data, with no candidate generation. It scales (roughly) linearly in running time with the number of interesting item- sets. FIM experiments show that it outperforms FP-growth on realistic datasets above a small support threshold (0.29 and 1.2 in our experiments).