Sharing and cooperation in geo-information technology

Aziz, T. Lukman

Bibliographic data

Monograph

Persistent identifier:: 856479470

Author:: Aziz, T. Lukman

Title:: Sharing and cooperation in geo-information technology

Sub title:: ISPRS Commission VI Symposium, April 15 - 17, 1999, Bandung, Indonesia

Scope:: 1 Online-Ressource (130 Seiten)

Year of publication:: 1999

Place of publication:: London

Publisher of the original:: RICS Books

Identifier (digital):: 856479470

Illustration:: Illustrationen, Diagramme

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Monograph

Collection:: Earth sciences

Chapter

Title:: WG VI/3: INTERNATIONAL COOPERATION AND TECHNOLOGY TRANSFER

Write comment:: Der Aufsatz "Promotion Of The General Understanding And Improvement Of Public Relations, [...] ist im Original nicht enthalten.

Document type:: Monograph

Structure type:: Chapter

Chapter

Title:: DISCRETE MATHEMATIC FOR SPATIAL DATA CLASSIFICATION AND UNDERSTANDING. Luigi Mussio, Rossella Nocera, Daniela poli

Document type:: Monograph

Structure type:: Chapter

75 2. CLUSTER ANALYSIS (CRIPPA, MUSSIO, 1995) Cluster analysis collects different statistical procedures and algorithms, able to classify data, to gather them in sets and to give a preliminary explanation about their behavior. The aim of cluster analysis is to minimize the internal dispersion of a group of data (cluster), respect their center (cluster point), and to maximize, at the same time, the distance among the above defined clusters. The procedures of cluster analysis could be subdivided, taking into account the starting point, the collection strategy and the end point respectively in: • agglomerative or divisive techniques • hierarchical or not- techniques • clustering of clumping Qualitative and quantitative cluster analysis could be performed different kinds of algorithms; MEDOIDS algorithm is recommendable in the first case, whilst the second task could be achieved by ISODATA algorithm. The main steps of ISODATA algorithm are the following: • selection of preliminary cluster points and thresholds for the iterations • clustering in a cluster the elements neighboring a cluster point. • division of clusters, whose internal dispersion is greater than the chosen threshold • new clustering • fusion of cluster, whose distance is less than the chosen threshold • starting a new iteration from the 2 nd step, or stopping the algorithm if a reproducing point is achieved. The step of clustering could be done in a different way. When the objects are well configured, the Euclidean norm or the Manhattan distance help to cluster the surrounded elements. On the contrary, when the objects are ill configured, these norms show evident difficulties to cluster the elements. Hence specific techniques of parsing, like line following, region growing, to be repeated by means of split and merge iterations, provide the expected results. The parsing is a methodology of Linguistics which has already been applied to artificial intelligence, image processing and robotics. Thus the clustering of ill-configured object could be obtained by using these techniques whose main steps are the following: • • selection in a cluster of the element which is the closest to its cluster point • selection in the same cluster of (if any) elements slightly more distant from the cluster point, thus taking into account possible bifurcations • attribution of the role of cluster point to the just selected elements • reiteration of the 1 st step • reiteration of the 2 nd step • reiteration of the 3 rd , 4 th and 5 th steps as long as selection of elements is possible • selection of a possible not yet selected element as a new cluster point; otherwise stop the algorithm • reiteration, for the new cluster point only, of the 1 st 5 th steps as long as a selection of elements is possible when preliminary cluster points are not available, the algorithm begins flatly at the 7 th step and it proceeds to form isolated clusters. Notice that the construction of cluster the one after the other, instead of all together, is less robust respect to wrong selection of elements. Finally the same strategy, used for the clustering, could be applied for the cluster fusion by means of a cluster of clusters. 3. GRAPH THEORY (BELLONE, ET AL., 1996B) Graph theory permits to study topological relations underlying the geometry of different kinds of objects. A graph is a set of nodes connected by arcs. In a connected graph a path always exists between two nodes; the shortest path is called distance and the largest distance called diameter. Each node of a connected graph is reached by at least one arc; the number of arcs of a node is called degree. A connection matrix could be associated to each graph, being its main diagonal elements coincident with the nodes and its off diagonal elements coincident with the arcs. A corresponding design matrix supplies in form of chart the connections between arcs and nodes. A second and more refined design matrix supplies in forma of chart the independent circuits and constrained polylines among the arcs. Since connection and design matrices are generally very sparse ones, they should be stored avoiding their zero elements. Design matrices tabulated by rows or columns and banded, profile or sparse connection matrices are very suitable way to store them. Connection matrices may have non-zero elements near their main diagonal ones or anyway located. The arrangement of non-zero elements could be improved by changing the order of elements. The arrangement of the elements inside design matrices could be also improved according to the order of the elements achieved for the corresponding connection matrices. The most important algorithms for numeration, ordering and dissection of matrix elements use graph theory. A level structure is a partition of a graph in different levels whose nodes are connected to the ones of the preceding and/or following level only. A level structure whose first level has one node only, said root, is a tree. The number of nodes belonging to a level is called width; the width of a level structure is the maximum of the level width, whilst the number of levels is called depth. The nodes belonging at each last local level are called leaves. The distance of a generic node from the root represents its (local) depth and the distance of same generic node from the leaves represents its (local) height. Relationship among matrices, graphs and level structures show that the bandwidth of connection matrices depends upon the numeration of the nodes of corresponding graphs’, an adequate numeration requires a small width of the level structures and this last property is easily achieved as their depth is large. Furthermore since the minimization of bandwidth and profile could not always be performed at the same time, the preliminary dissection of a graph and the subsequent ordering of its dissected parts supply the expected results. I' 1 algorithm - Search of a diameter of a graph The reiteration of the construction of level structures allows to find the diameter of a graph. An arbitrary starting root initiates the first level structure, whilst the nodes in the last level initiate new level structure, to be substituted to the first one, if their depth is greater. The same procedure has to be repeated until two level structures of equal depths are found.

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