Mining Spatial Trends by a Colony of Cooperative Ant Agents Ashkan Zarnani † Masoud Rahgozar † Abstract Large amounts of spatially referenced data has been aggregated in various application domains such as geographic information systems (GIS), environmental studies, banking and retailing, which motivates the highly demanding field of spatial data mining. So far many optimization problems have been better solved inspired by the foraging behavior of ant colonies. In this paper we propose a novel algorithm for the discovery of spatial trends as one of the most valuable and comprehensive patterns potentially found in a spatial database. Our algorithm applies the emergent intelligent behavior of ant colonies to handle the huge search space encountered in the discovery of this knowledge. We apply an effective greedy heuristic combined with the trail intensity being laid by ants using a spatial path. The experimental results on a real banking spatial database show that our method has higher efficiency in performance of the discovery process and in the quality of trend patterns discovered compared to other existing approaches using non-intelligent heuristics. 1 Introduction Many organizations have collected large amounts of spatially referenced data in various application areas such as geographic information systems (GIS), banking and retailing. These are valuable mines of knowledge vital for strategic decision making and motivate the highly demanding field of spatial data mining i.e., discovery of interesting, implicit knowledge from large amounts of spatial data [11]. So far many data mining tasks have been investigated to be applied on spatial databases. In [11] spatial association rules are defined and an algorithm is proposed to efficiently exploit the concept hierarchy of spatial predicates for better performance. In [8] and [10] algorithms are designed for the classification of spatial data. Shekhar et al. further improved spatial classification in [12] and also introduced algorithms to mine co-location patterns [9]. Spatial trends are one of the most valuable and comprehensive patterns potentially found in a spatial database. In spatial trend analysis, patterns of change of some non-spatial attributes in the neighborhood of an object are explored [6] e.g. moving towards north-east from the city center the average income of the population increases (confidence 82%). Ester et al. studied this task proposing a general clustering algorithm and its application in trend detection [7] and further improved it in [6] exploiting the database primitives for spatial data mining introduced in [8]. Having constructed the neighborhood graph the algorithm proposed gets a specified start object o from the user. Then it has to examine every possible path in the graph beginning from o. For each path it performs a regression analysis on non- spatial values of the path vertices and their distance from o. But the search space soon becomes tremendously huge by increasing the size of neighborhood graph and makes it impossible to do a full search. In order to prune the search space it assumes that a desired trend will never have its regression confidence below a user given threshold. As we incrementally construct a possible path, we would have to resign from further extending it when the regression confidence of the current path becomes bellow the threshold. But this assumption is a restricting one, as it may mislead us by forcing a trend to stop from growth that would get much higher confidence if not blocked. Many solutions for NP-Complete search and optimization problems have been developed based on the cooperative foraging behavior of ant colonies [2]. However less attention has been given to apply this powerful inspiration from nature in the tasks of spatial data mining. In this research we introduce a new spatial trend detection algorithm that uses the phenomenon of stigmergy i.e. indirect communication of simple agents by means of their surrounding environment, observed in real ant colonies [1]. It also combines this behavior with a new guiding heuristic that is shown to be effective. We succeeded to handle the non-polynomial growth of the search space, and at the same time retain the discovery power of the algorithm, by letting each ant agent to cooperatively exploit the colonies valuable experience. Also in contrast with the algorithm proposed in [6] our algorithm is not dependent on the user. It doesn’t get a specified start object from the user nor needs it to input a pruning threshold. This brings ease of use and wider applicability to our method as its efficiency and performance is independent from the user. We have conducted some experiments on a real banking spatial database to compare the proposed method with the algorithm proposed in [6] which is being widely accepted and used. The results show that the proposed algorithm has higher efficiency in performance of the discovery process and in the quality of trend patterns discovered. 2 Spatial Trend Detection Some spatial relations (called neighborhood relations) like direction, metric and topological relations between the objects are formally defined to be used in spatial data mining [8]. Based on these relations the notions of neighborhood graph and neighborhood path are defined as follows: †Database Research Group, Electrical and Computer Engineering Department, University of Tehran