New Geometrical Similarity-based Clustering Algorithm for GIS Vector Data

Abstract Geographic Information System(GIS) are usually classified into raster, vector, and raster -vector systems. The research deals with proposing new graph mining algorithm called GIS-GMA. The algorithm is used for clustering the vector features of GIS. The vector data are usually stored in data files called shape files. These files contains the (point, lines, polygons,...,etc). The extracted data is then stored in a dataset to be processed by the proposed algorithm to discover the full and partial similarities among map objects to assist the clustering and analysis of map data. It deals with clustering the polylines and polygonal data. The research results lead to build GIS prototype with spatial data mining facilities to cluster GIS vector data and giving fine clustering results,it is implemented using MicroSoft VS-2005 and ESRI ArcObjects

Geometric Approximations and their Application to Motion Planning

Geometric approximation methods are a preferred solution to handle complexities (such as a large volume or complex features such as concavities) in geometric objects or environments containing them. Complexities often pose a computational bottleneck for applications such as motion planning. Exact resolution of these complexities might introduce other complexities such as unmanageable number of components. Hence, approximation methods provide a way to handle these complexities in a manageable state by trading off some accuracy. In this dissertation, two novel geometric approximation methods are studied: aggregation hierarchy and shape primitive skeleton. The aggregation hierarchy is a hierarchical clustering of polygonal or polyhedral objects. The shape primitive skeleton provides an approximation of bounded space as a skeleton of shape primitives. These methods are further applied to improve the performance of motion planning applications. We evaluate the methods in environments with 2D and 3D objects. The aggregation hierarchy groups nearby objects into individual objects. The hierarchy is created by varying the distance threshold that determines which objects are nearby. This creates levels of detail of the environment. The hierarchy of the obstacle space is then used to create a decom-position of the complementary space (i.e, free space) into a set of sampling regions to improve the efficiency and accuracy of the sampling operation of the sampling based motion planners. Our results show that the method can improve the efficiency (10 − 70% of planning time) of sampling based motion planning algorithms. The shape primitive skeleton inscribes a set of shape primitives (e.g., sphere, boxes) inside a bounded space such that they represent the skeleton or the connectivity of the space. We apply the shape primitive skeletons of the free space and obstacle space in motion planning problems to improve the collision detection operation. Our results also show the use of shape primitive skeleton in both spaces improves the performance of collision detectors (by 20 − 70% of collision detection time) used in motion planning algorithms. In summary, this dissertation evaluates how geometric approximation methods can be applied to improve the performance of motion planning methods, especially, sampling based motion planning method

Redistricting Using Constrained Polygonal Clustering

Redistricting is the process of dividing a geographic area consisting of spatial units—often represented as spatial polygons—into smaller districts that satisfy some properties. It can therefore be formulated as a set partitioning problem where the objective is to cluster the set of spatial polygons into groups such that a value function is maximized [1]. Widely used algorithms developed for point-based data sets are not readily applicable because polygons introduce the concepts of spatial contiguity and other topological properties that cannot be captured by representing polygons as points. Furthermore, when clustering polygons, constraints such as spatial contiguity and unit distributedness should be strategically addressed. Toward this, we have developed the Constrained Polygonal Spatial Clustering (CPSC) algorithm based on the A* search algorithm that integrates cluster-level and instance-level constraints as heuristic functions. Using these heuristics, CPSC identifies the initial seeds, determines the best cluster to grow, and selects the best polygon to be added to the best cluster. We have devised two extensions of CPSC—CPSC* and CPSC*-PS—for problems where constraints can be soft or relaxed. Finally, we compare our algorithm with graph partitioning, simulated annealing, and genetic algorithm-based approaches in two applications—congressional redistricting and school districting

Redistricting Using Constrained Polygonal Clustering

Abstract—Redistricting is the process of dividing a geographic area consisting of spatial units—often represented as spatial polygons—into smaller districts that satisfy some properties. It can therefore be formulated as a set partitioning problem where the objective is to cluster the set of spatial polygons into groups such that a value function is maximized [1]. Widely used algorithms developed for point-based data sets are not readily applicable because polygons introduce the concepts of spatial contiguity and other topological properties that cannot be captured by representing polygons as points. Furthermore, when clustering polygons, constraints such as spatial contiguity and unit distributedness should be strategically addressed. Toward this, we have developed the Constrained Polygonal Spatial Clustering (CPSC) algorithm based on the A search algorithm that integrates cluster-level and instance-level constraints as heuristic functions. Using these heuristics, CPSC identifies the initial seeds, determines the best cluster to grow, and selects the best polygon to be added to the best cluster. We have devised two extensions of CPSC—CPSC * and CPSC*-PS—fo