Modeling of Spatio-Temporal Co-occurrence Patterns: An Approach to Knowledge Discovery from Spatio-Temporal Databases A. TECHNICAL RELEVANCE A.1. Problem: Traditional data mining methods (e.g. association rules, classifications and clustering) often assume that data observations have the same properties regardless of their spatial location. This violates Tobler’s First Law of Geography: everything is related to everything else, but nearby objects in space are more related than distant objects [2,3]. The same principle also applies to objects near or far in time from one another (as shown in time series modeling). As a result, the values of attributes of neighboring spatio-temporal (ST) data objects tend to affect each other. Traditional knowledge discovery techniques (which assume that data objects are independent and identically distributed with regard to space and time) perform poorly on ST data. New models, objective functions, and patterns more suited for ST databases and their unique properties are needed for knowledge discovery from these databases. The focus of this proposal is to create and explore new models of ST co-occurrence patterns. Formally, given a collection of Boolean (binary) ST features and their instances, these new models will identify the subsets of features frequently located together in space and time. These models will form a new ST dataset analysis framework to discover and identify interesting, useful, non-trivial patterns, and to facilitate their uses in descriptive as well as predictive tasks. As an example, one can examine ST co-occurrence patterns in the context of Improvised Explosive Devices (IEDs) in Iraq. The proficiency of IED attacks in Iraq has increased in parallel with the frequency of attacks directed toward interdicting convoys. Most Iraqi highways are paved roads with 4 to 8 lanes. They have many bridges and overpasses as well as frequent traffic circles, all of which are potential convoy chokepoints. Built-up or vegetated medians divide most roadways, and many IEDs have been placed in these medians. Soda cans, manholes, tunnels burrowed under roads, cement-encased bomb projectiles, and even dead animal carcasses have been used to conceal IEDs. Some of the IEDs have been remotely detonated using garage door openers, car alarms, key fobs, door bells, toy car remotes, twoway radios, cellular telephones and pagers. This implies that target area observation requires line-of-sight attacker observation points, but the adaptation of radios and cell phones has given the attackers a greater ability to watch convoys from a distance and not be compromised. Some Boolean ST features related to IEDs include: time of IED emplacement, time of day of detonation, day of week of detonation, day of month of detonation, explosion location, distance to nearest highway, closest highway type, distance to nearest bridge, distance to nearest traffic circle, distance to nearest buildings, building types of nearest buildings, vegetation and vegetation height of surrounding area, soil type and slope of surrounding area, and demographics of surrounding area. Other ST features specifically tied to moving objects include military vehicles and types, convoy size, and whether a civilian vehicle is following or leading a military vehicle. A simple ST co-occurrence pattern, for example, would be {IED, road, time_of_day,civilian_vehicle_front} if frequency is the interest measure, a certain road had a high incidence of IED attacks, and the attacks were most likely at a certain time of day or when a civilian vehicle led the convoy. One may also categorize ST co-occurrence patterns by frequency of occurrence. For example, emerging co-occurrence patterns may be categorized by a significant increase in frequency, and vanishing patterns may be categorized by a significant decrease in frequency. This example will be referenced in section C.2.4. A.2. Technical Barriers: Adapting classical data mining methods to mine ST patterns is far from trivial. For example, co-occurrence patterns often look similar to association patterns [1], which identify subsets of item-types that co-occur frequently in a given collection of transactions, each specifying a subset of item-types. However, instances of ST features are embedded in continuous space and time, and share a variety of ST relationships. Conceptual modeling of these patterns is challenging due to the absence of pre-defined transactions in many datasets and the unique interest measures. Using association rule mining for ST data requires a transaction database which is not natural [2,4], because the transaction boundaries may split co-occurrence pattern instances across distinct transactions, for example, those defined by cells of a rectangular grid. No standard taxonomy for ST co-occurrence patterns exists in the current literature. The challenge in creating this taxonomy is to find categories of interesting and nontrivial patterns. The proposed research will explore and define new ST co-occurrence patterns using concepts such as periodicity, moving objects, emergence and disappearance, time merging, and time fragmenting. Another problem and challenge is the incorporation of temporal data. Current cooccurrence patterns have been defined for spatial data features, but not for ST data types. Also, these defined spatial data feature patterns assume stationarity in space and not for nonstationary features such as are frequently found in ST data. The most challenging technical barrier is to create and formalize new interest measures to mine interesting and non-trivial ST co-occurrence patterns. Current scalar interest measures are not sufficient to mine interesting and non-trivial ST co-occurrence patterns. To the best of our knowledge, there are no such composite interest measures to handle these kinds of patterns. These and other new methods will be created and explored to achieve this goal. There are also no existing methods to mine ST co-occurrence patterns out of massive ST datasets in a computationally efficient manner. In terms of data size, ST datasets will be larger than the classical datasets because of addition of the time dimension. To handle these massive datasets the challenge will be to explore efficient and scalable methods. A.3. Innovation: This project will create new models for ST datasets with a new taxonomy of ST co-occurrence patterns and interest measures. In contrast to current scalar interest measures, new composite interest measures will be designed to characterize interesting and useful ST co-occurrence patterns. These new interest measures such as temporal, spatial and spatio-temporal probabilities of co-occurrence patterns will be used to characterize where and when a co-occurrence is prevalent and will be compared with traditional ST statistical measures (such as the K function) [20] to assess the quality of the patterns. Also, while current interest measures are scalars, there is a need for new, non-scalar types of patterns and composite interest measures that are functions of time, location, or other parameters. Figure 1(a) shows how interest measures change for emerging and varnishing ST co-occurrence patterns. The xaxis shows time and y-axis shows the interest measure. Further, scalar interest measure for a given feature subset may be periodic or have a trend (e.g. increase or decrease over time) defining periodic, emerging and vanishing co-occurrence patterns. Composite interest measures, e.g. spatial map of locations of co-occurrence instances, may show complete spatial randomness [6], hot-spots or regularity. In addition, the hot-spots may be merging (or fragmenting) over time. These give rise to merging or fragmenting co-occurrence patterns. Feature sets may include static or moving objects leading to additional classes. In recent years, many studies have focused on finding spatial co-location [4] patterns, which are subsets of features whose instances are frequently located together in geographic space. However, traditional co-location patterns are based purely on geographic proximity and do not account for temporal relationships. For example, they cannot differentiate between emerging ST co-occurrence patterns and vanishing ones. They also cannot identify ST cooccurrence of moving objects, such as a civilian vehicle traveling in front of an Army vehicle to block traffic and stall the Army vehicle near an IED (Figure 1(b)). (a) Composite interest measure (b) Example of ST co-occurrence patterns of moving objects Figure 1: Composite interest measures and ST co-occurrence patterns Computationally, novel ST co-occurrence pattern mining methods will be developed to reduce computational cost. We plan to identify the performance bottleneck tasks and explore new methods to control their computational cost. B. CONNECTIONS TO THE BROADER RESEARCH COMMUNITY B.1. Significance/Potential Impact: The Army generates, accesses, and manages huge amounts of ST data in a variety of databases. This data is stored in attributes, values and tables, with important relationships and information obscured by great masses of irrelevant information. This information is vital to increasing knowledge and understanding of terrain effects on modern tactical warfare and strategic battlefield planning. The current state of data mining makes little use of spatial information in the mining process, does not integrate spatial and temporal information, and as a result is limited in the patterns, models and metrics which are currently available to discover new knowledge. Scientific examination of further use of spatial information, ST correlation, patterns and relationships mined by new ST data mining techniques can greatly increase the discovery of this new knowledge. For example, tools for summarizing the ST patterns of enemy troop movement can be invaluable for military commanders. Also, ST techniques such as co-occurrence models can be used to predict near-future locations of enemy units given current location based on a sensor network, battlefields terrain, and historic war tactics. This research will explore novel ST co-occurrence approaches to handle ST datasets. This work will also help improve capabilities of information processing in many domains, including Earth Science, environmental management, government services, and transportation. B.2. Related Work: Most studies on spatial co-location mining have focused on discovering co-location patterns at a particular time and ignored the temporal aspects of the spatial colocation patterns. These studies can be collected in two groups: spatial statistics and data mining [4]. Spatial statistics-based approaches use measures of spatial correlation to characterize the relationship between different types of spatial features [5,6]. Data mining approaches are based on spatial proximity of the spatial features and can be classified as clustering-based map overlay approaches [15] and association rule-based approaches. A clustering-based map overlay approach treats every spatial attribute as a map layer and considers spatial clusters (regions) of point-data in each layer as candidates for mining associations. Association rule-based approaches include transaction-based approaches and distance-based approaches. Transaction based approaches [1,7] focus on defining transactions over space so that an Apriori-like approach can be used. Zhang et al [10] proposed a referencefeature centric model by using multi-way spatial join methods to mine spatial co-locations. The association rules are derived using the Apriori approach. A distance-based approach was proposed concurrently by Morimoto [8] and Shekhar and Huang [9, 4]. Morimoto defined distance-based patterns called k-neighboring class sets. In his work, the number of instances for each pattern is used as the interest measure, which does not possess an anti-monotone property by nature. Anti-monotonic interest measures [1] can help reduce the computational cost and search space. However, Morimoto used a non-overlapping-instance constraint to get the anti-monotone property for this measure. In contrast, Shekhar and Huang developed an event centric model, which does away with the nonoverlapping- instance constraint, as well as a new interest measure called the participation index (which possesses the desirable antimonotone property). Existing literature focuses on finding the spatial co-location patterns and cannot model ST co-occurrence patterns, such as periodic co-occurrence patterns, co-occurrence patterns of the moving objects, emerging or vanishing co-occurrence patterns and co-occurrence patterns merging and fragmenting with time. In contrast, this proposal will identify these unique ST cooccurrence patterns. B.3. Leveraging Other’s Work: This proposal is unique and is not leveraging efforts funded elsewhere. B.4. Collaborative Activities: The PIs (James Rogers and Dr. James Shine) at TEC are collaborating with the Spatial Databases Research Group at The University of Minnesota. C. RESEARCH METHODOLOGY C.1. Strategy / Rationale: The strategy of this research can be depicted as shown in Figure 2, with the boxes showing the process phases, the arrows representing flow direction, and the loop outlining the iterative part of the ST co-occurrence pattern mining process. The phases are described as follows: Create and Define ST Pattern Taxonomy Create and Define Models of ST Co-occurrence Patterns Create and Define Composite Interest Measures Create and Design Computationally Efficient Methods Mine Patterns Validate Patterns Figure 2: Phases of the ST co-occurrence pattern mining The phases of the ST co-occurrence pattern mining process: 1) Create and Define ST Pattern Taxonomy Based on Army Objectives: We will create and define a taxonomy using Army objectives, requirements, assumptions and constraints as listed in D.3. From this knowledge, we will outline data mining problems, collect initial ST data, examine characteristics of this data, verify data quality, and explore initial hypotheses. 2) Create and Define Conceptual Model of ST Co-occurrence Patterns: We will create and define a conceptual model of ST co-occurrence patterns and prepare initial ST raw data as an input for the mining method. The model helps define concepts and expand the taxonomy for ST co-occurrence patterns. 3) Create and Define Composite Interest Measures: These measures will quantify new composite definitions such as temporal, spatial and ST probabilities of ST data. These measures shall capture the characteristics of ST datasets. 4) Create and Design Computationally Efficient Methods: Existing data mining methods will be examined and new computationally efficient methods for mining ST cooccurrence patterns will be created and tested. 5) Mine Patterns: Run the new methods to mine the ST co-occurrence patterns, defined by ST taxonomy, from the ST datasets. 6) Validate Patterns: We will check accuracy and completeness of the newly discovered ST co-occurrence patterns, via user evaluation. C.2. Methods / Techniques: The goal of a conceptual model of ST co-occurrence patterns is to provide a framework to identify interesting and non-trivial ST co-occurrence patterns and to facilitate their uses in descriptive as well as predictive tasks. Key challenges in exploring a conceptual model of ST co-occurrence patterns include taxonomy, requirements and interest measures. In that context research tasks can be listed as: 1. To create/define taxonomy for ST co-occurrence patterns and their use-cases, 2. To create/define new composite interest / confidence measures, 3. To use new composite interest measures to get better computational efficiency, 4. To mine interesting and non-trivial ST co-occurrence patterns, 5. Validation and experimentation for patterns and composite interest measures. C.2.1 Create/define taxonomy for ST co-occurrence patterns and their use-cases. Current taxonomy of spatial data deals with the patterns/objects, which are fixed at a time. These patterns/objects are associated with geometry and position in space. OGIS [21] defines a taxonomy for spatial data and provides a framework for exchanging spatial data. In contrast to this, there is no accepted framework for taxonomy of ST data, which deals with the patterns in space and time and captures relationship between a pattern and space-time such as periodic co-occurrence patterns, patterns moving, emerging, merging, vanishing and fragmenting over time. A taxonomy of ST co-occurrence patterns provides a classification of the patterns listed in section C.2.4. It is natural to ask if there are other interesting and useful classes of ST cooccurrence patterns. One approach to address this issue is to examine current application domains and application domain scientists and create a consensus classification scheme. Another approach is to use taxonomies for ST data types and their relationships, and study their implications for classes of ST data [11]; taxonomies of spatial data types may even be extended for this purpose. Object and field are two common models of spatial data [12]. An object model is ideal for representing discrete identifiable entities such as lakes, road networks, and cities. This model may be generalized to ST datasets by categorizing objects into stationary and mobile objects [11] as well as subclasses such as rigid and deforming. A field model is defined by a spatial framework (SF) and a set of field functions mapping the SF to attribute value domains. This model may be generalized to ST datasets by defining a ST framework (STF) and field mapping the STF to attribute domains. STF fields may be categorized as largely static (e.g., elevation) or dynamic (e.g., temperature) for a given time scale [11]. We plan to use a combination of these approaches by leveraging the work of application domain scientists in military terrain, ecology, climatology, and Earth science to create a new taxonomy for ST data [11, 13]. It is also important to create a taxonomy of the common usages of ST patterns by domain scientists. Common activities include evaluation, explanation, and prediction, where scientists observe where and when the co-occurrence patterns are valid. As part of this research we would explore use-cases of how ST co-occurrence patterns will be used by the Army. C.2.2 Create/define new composite interest / confidence measures Interest measures are designed to characterize interesting and useful ST co-occurrence patterns. Interest measures may be used to specify a subset of patterns in a post-processing phase to evaluate, interpret, and use these patterns. Alternatively, they may be used to reduce computational costs for ST data mining methods. One key challenge in the design of interest measures for ST co-occurrence patterns arises from “where and when” questions posed by the domain scientist. For example, Earth scientists may be more interested in a co-occurrence pattern if it occurs in geographic areas of homogeneous forest types, such as shrubland or grassland, since it may allow an explanation of the co-occurrence rule. Similarly, scientists may wish to identify co-occurrence rules whose temporal occurrence correlates with a special time series, for example El Niño index time series, to understand the impact of climate disturbance events. To support a where and when analysis, we propose to use composite interest measures which are functions of time, location, or other parameters (e.g., time-lags or distance). A basic set of disjoint events for defining temporal probability is a collection of time instances. Temporal probability of a Boolean ST event represents the time dependency of the probability of the event happening across time. In other words it defines probability or probability density of a ST event at a given time. For example, the temporal probability (interest measure) at a location, e.g., Alexandria, VA, in Figure 3(b) is computed from local data about co-occurrence events in Alexandria for different months over a 17-year series. Similarly, a basic set of disjoint events for defining spatial probability is a collection of spatial instances. Spatial probability of a Boolean ST event represents the spatial dependency of the probability of the event happening in space. It defines probability or probability density of a ST event at a given location. Figure 3(a) shows an interest measure, which is a function of space and is defined by aggregating over all locations for each time snapshot. A basic set of disjoint events for defining ST probability is a collection of ST instances. The ST probability of a Boolean ST event represents the temporal and spatial dependency of the probability of the event happening across time and in space. It defines probability or probability density of a ST event at a given time and location. (a) Spatial variation (gray scale=% of months supporting the co-occurrence pattern at a location) (b) Temporal variance Figure 3: Visualization of where and when co-occurrence pattern occurred Composite interest measures provide useful information to domain scientists for evaluating and explaining ST co-occurrence patterns. However, there is a risk of information over-loading, particularly when the mining algorithm produces a large number of co-occurrence patterns. One way to address this problem is to define ST Boolean constraints on the composite interest measures, which may be used by either a post-processing method or the a cooccurrence method to eliminate many uninteresting patterns. Examples of Boolean constraints on time series interest measures include many well-known tests for periodicity [14], stationary as well as binary tests for correlation [6, 17] with a given time series (such as the El Niño index time series). Many binary time series similarity measures have been identified [16]. Boolean constraints on spatial maps include well-known unary tests for clusteredness [6]. Binary map similarity measures are sparse in current literature, and we will explore new and more detailed use of such measures. The use of composite interest measures raises the issue of whether the ST Boolean constraints on the composite interest measure are anti-monotonic. We will explore common ST Boolean constraints on composite interest measures for the anti-monotone property. C.2.3 Use new composite interest measures to get better computational efficiency Due to the increasing volume of data and ST co-occurrence patterns, computational costs are likely to be very high. We will create new algorithms to reduce this computational cost. In current data mining algorithms, most time is consumed during the preprocessing and generation of candidate sets. We also plan to explore new methods for generation of cooccurrence rules using composite interest measures. The idea behind preprocessing is to partition ST dataset for generating neighborhood transactions. In literature, there are many partition based preprocessing methods, such as, maximal cliques [18] and max-clique[19]. We will explore these pre-processing methods to determine the most appropriate one for ST datasets and different ST co-occurrence patterns. Apriori-based approaches may be used to generate candidate co-occurrences because of the anti-monotone property of participation index. Size k co-occurrences may be used to generate size k+1 co-occurrences. Pruning may be done if produced co-occurrences do not satisfy appropriate interest measures such as the participation index. For large and dense datasets, and long-length frequent itemsets, the computation cost of this step may be very high. To overcome this problem we will explore new solutions such as top-down approaches [1]. A top-down approach starts with the maximum possible itemsets and checks subsets to find frequent ones. The top-down approach is based on two lemmas: “all subsets of a frequent itemset are also frequent” and “all supersets of an infrequent itemset are also infrequent” [1]. Whenever such an approach finds frequent subsets, it does not check subsets of them because of anti-monotonic property. For this work a new composite interest measure, with an antimonotone property will be created and developed for pruning. To generate co-occurrence rules conditional probability of co-occurrence rule c1 c2 is used and can be defined as fraction of events where c1 occurs that (c1 c2 ) also occurs ( | C1 (table _ ins tan ce(c1 c 2 ) | / | table _ ins tan ce(c1 ) | ). To make efficient computing bitmap or other data structures will be used. C.2.4 Mine interesting and non-trivial ST co-occurrence patterns We will mine interesting and non-trivial ST co-occurrence patterns by creating new methods. New types of ST co-occurrence patterns can be listed in four major categories: 1.Periodic co-occurrence patterns: If a new feature or a new instance of existing features is introduced to the space or extracted from the space, new co-occurrence patterns can appear or existing ones may disappear, or a new co-occurrence pattern may reflect periodicity. Assume that an “insurgent neighborhood” feature is added to the space in the IED example discussed in Section A.1. The features, {insurgent_neighborhood} and {IED, road, time_of_day}, could form a new ST co-occurrence pattern, {IED, road, time_of_day, near_insurgent_neighborhood}. In contrast, extraction of an instance, such as {time_of_day}, may break the {IED, road, time_of_day, near_insurgent_neighborhood} pattern. Another example can be ST cooccurrence patterns that occur on Fridays but not on other weekdays. 2.Co-occurrence patterns of moving objects: In this kind of ST co-occurrence pattern, at least one of the co-occurring objects can be a moving object (i.e., IED attacks moving from one road or area to another). On the other hand, all co-located objects can be moving objects (i.e., IED attacks, location of suspected insurgents). An example for this pattern can be seen in Figure 1(b). The x-axis gives the time information and the y-axis gives the location information (highway mile point). In the figure the tracks represent the movement of the military and civilian vehicles in space. The civilian vehicle leads the Army vehicle until they reach a specific location and then stalls the Army vehicle at this location when an IED is detonated. After a certain time an attack event also occurs on the Army vehicle. 3.Emerging or vanishing co-occurrence patterns: Users may want to know which cooccurrence patterns have interest measures getting stronger or weaker with time (i.e., road locations or municipal areas where the incidence of IED attacks increase or decrease over a period of time). 4.Co-occurrence patterns merging or fragmenting with the time: Baath neighborhoods, Shiite neighborhoods, and neighborhoods harboring non-Iraqi insurgents may merge into neighborhoods likely to be the source of an IED attack. As the political process evolves, the Shiite neighborhoods may no longer be sources of these attacks. C.2.5. Validation and experimentation for patterns and composite interest measures. To evaluate the performances of different preprocessing methods and candidate cooccurrence generation algorithms, new composite interest measures will be defined. We will conduct numerous experiments by controlling different combinations of parameters. We will answer questions such as the followings: What are the dominance zones (the parameter values for which a specific algorithm is fastest) among the different preprocessing methods for large ST datasets? Which method, bottom-up or top-down, is suitable for ST datasets in what conditions? Top-down approaches may be the most suitable when datasets are dense or length of co-occurrence pattern is long. What is the effect of the number of co-occurrences patterns and/or co-occurrence pattern lengths on the computational cost of different approaches? How do the composite interest measures affect the solution set or performance of the algorithms? To evaluate the algorithms, synthetic and real-world datasets (i.e. IED datasets) will be used. Synthetic datasets can be used to test algorithms from various aspects by controlling dataset generation parameters. The experimental setup can be seen in Figure 4. Generation Parameters Neighborhood Parameters Generate Dataset Generate Neighborhoods Real-world data Preprocessing Methods Co-occurrence Interest Methods Measures Synthetic Data Preprocessing ST Co-occurrence Methods Analysis Figure 4: Experimental setup and design C.3. Anticipated Results: This research will help define a taxonomy for interesting and nontrivial ST co-occurrence patterns and will give a conceptual framework for these patterns. In contrast to the limitations of current data mining methods, we expect to create and explore new methods and composite interest measures overcoming these limitations for different ST cooccurrence pattern mining problems. The performances of these new methods will be compared and dominance zones of each of them will be determined. An Iraqi IED dataset will be used for discovery, test and evaluation. In the first year we expect to create and define an ST pattern taxonomy, to collect and test initial data and hypotheses, and to create and define new interest measures for ST cooccurrence patterns. In the second year we will explore computationally efficient ST cooccurrence pattern mining methods. In the third year validation and experimentation for patterns and new interest measures will be done. D. OPERATIONAL RELEVANCE AND TECHNOLOGY TRANSITION D.1. Opportunities for Transition: This proposed research for modeling ST co-occurrence patterns will support the Geospatial Information Integration and Generation Tools (GIIGT) and Distributed Geospatial Intelligence work packages. D.2. Productions of the Research: Papers will be published in conferences and journals such as the Army Science Conference (ASC), the Association for Computing Machinery Symposium on Advances in Geographic Information Systems (ACMGIS), the Conference on Geographic Information Science (GIScience), the Symposium on Spatial and Temporal Databases (SSTD), and the IEEE Transactions on Knowledge and Data Engineering (TKDE). D.3. ERDC and Army Relevance Impacts on the Army and Relevance to the Future Force: The knowledge and models provided from this research will support geospatial intelligence tasks for Future Combat System (FCS) as specified in the Situational Awareness section of the FCS Mission Needs Statement (MNS). The results of this research could be effectively utilized in urban and non-urban environments. The results will also address Force Operating Capabilities (FOC) described in TRADOC Pamphlet 525-66. For FOC-01-04, an automated running estimate of the situation incorporating predictive analysis, the results of this research will provide a capability for more rapid decision action cycles with much less effort required to understand what is happening; improved situational understanding; improved information superiority; and timely, relevant and predictive intelligence. For FOC-02-01, Sensor Fusion, this research will utilize data from multiple sensors and products of the research will provide streaming ST data correlated and mined to create information and knowledge. The results will draw relationships, provide meaning to the information, convert information into actionable information, sense the environment quickly, and provide automated pattern analysis. For FOC-02-02, Situational Understanding, the research products will support the goal of understand first, identify a pattern or critical elements, and develop adaptive reasoning tools that provide knowledge discovery. For FOC-02-04, Understand the Battlespace Environment, the research will directly support the goal of understanding of the environment including terrain, weather, infrastructure, hazards, populations, and their interaction thru the ability to both predict and understand, in real time, the impact of the environment. ERDC Relevance: The results of this research will identify important relationships that are critical for understanding ST data and identifying useful, nontrivial patterns in the ST data from existing databases or from a network of sensors and probes for use in descriptive and predictive tasks. The results could also be used to predict missing values in ST datasets, and identify potential errors in ST datasets. REFERENCES [1] J. Han and M. Kamber, Data Mining: Concepts and Techniques, Morgan Kaufmann, ISBN:1558604898, 2000. [2] S. Shekhar, P. Zhang, Y. Huang, and R. R. Vatsavai, Spatial Data Mining, Book Chapter in Data Mining: Next Generation Challenges and Future Directions (Ed. H. Kargupta et al), MIT Press, ISBN:0262612038, 2004. [3] S. Shekhar,S. Chawla, Spatial Databases:A Tour, Prentice Hall, ISBN:0130174807, 2003. [4] Y. Huang, S. Shekhar, and H. Xiong, Discovering Co-location Patterns from Spatial Datasets: A General Approach, IEEE Trans. on Knowledge and Data Eng., 16(12), pp.1472-1485, Dec. 2004. [5] Y. Chou. Exploring Spatial Analysis in Geographic Information System, Onward Press, ISBN:1566901197, 1997. [6] N.A.C. Cressie, Statistics for Spatial Data, Wiley and Sons, ISBN:0471843369, 1991. [7] K. Koperski and J. Han, Discovery of Spatial Association Rules in Geographic Information Database, in Proc. of the 4th Int’l Symp. on Spatial Databases, pp. 47-66, 1995. [8] Y. Morimoto, Mining Frequent Neighboring Class Sets in Spatial Databases. in Proc. ACM SIGKDD Int’l Conf. on Knowledge Discovery and Data Mining, pp. 353-358, 2001. [9] S. Shekhar and Y. Huang, Co-location Rules Mining: A Summary of Results, In Proc. 7th Int’l. Symp. on Spatio-temporal Databases, 2001. [10] X. Zhang, N. Mamoulis, D. W. Cheung, & Y. Shou, Fast Mining of Spatial Collocations, in Proc. ACM SIGKDD Int’l Conf. on Knowledge Discovery and Data Mining, pp.384-93,2004. [11] A. Frank, Ontology for Spatio-temporal Databases, In Spatio-Temporal Databases: The Chorochronos Approach, (Ed. M. Koubarakis, T. Sellis et al), Springer, 2003 [12] M.F. Worboys, GIS:A Computing Perspective, Taylor and Francis, ISBN:0748400648, 1995. [13] M.F. Mokbel, W.G. Aref, S.E. Hambrusch, and S. Prabhakar, Towards scalable locationaware services: requirements and research issues, ACMGIS, pp. 110-117, 2003 [14] G. Box, G. Jenkins, and G. Reinsel, Time Series Analysis: Forecasting and Control, Prentice Hall, ISBN:0130607746 1994. [15] P. Rigaux, M.O. Scholl, and A. Voisard, Spatial Databases: With Application to GIS, Morgan Kaufmann, ISBN:1558605886, 2001. [16] D. Gunopulos and G. Das. Time Series Similarity Measures and Time Series Indexing. SIGMOD Records, 30(2), 2001. [17] P.Zhang, Y. Huang, S. Shekhar, and V. Kumar, Exploiting Spatial Autocorrelation to Efficiently Process Correlation-Based Similarity Queries, In the Proc. Of the 8th Int’l Symp. On Spatial and Temporal Databases, pp. 179-198, 2003. [18] C. Berge, Graphs and Hypergraphs. American Elsevier, 1976. [19] Y.Zhao and G. Karypis, Evaluation of Hierarchical Clustering Algorithms for Document Datasets, In Proc. Of ACM Conference on Information and Knowledge Management (CIKM), pp. 515-524, 2002. [20] S. Hwang, Temporal Extensions of K Function, UCGIS Assembly (conjunction with GIScience 2004), 2004. [21] OGIS. Open GIS consortium: Open GIS Simple Features Specification for SQL (Revision 1.1) in URL http://www.opengis.org/techno/specs.htm.