Wed, 20 Aug 2008 22:16:40 BST CiteULike: bigbossman spatial http://www.citeulike.org/user/bigbossman/tag/spatial CiteULike.org en-gb Copyright © 2004-2008 citeulike.org http://www.citeulike.org/user/bigbossman/article/1444016 <i>(6 Jul 2007)</i><br /><br />This paper introduces a model that identifies spatial relationships for a structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer and a contextual layer. The identified spatial relationships are represented as a simplical complex, in which simplices and vertices respectively represent two layers of objects. The model relies on the simplical complex for structural representation and analysis. To quantify structural properties of individual primary objects (or equivalently simplices), and the simplicial complex as a whole, we define a set of centrality measures by considering multidimensional chains of connectivity, i.e. the number of contextual objects shared by a pair of primary objects. With the model, the interaction and relationships with a geographic system are modeled from both local and global perspectives. The structural properties and modeling capabilities are illustrated with a simple example and a case study applied to the structural analysis of an urban system. Spatial Topology and its Structural Analysis based on the Concept of Simplicial Complex Bin Jiang Itzhak Omer (6 Jul 2007) 2007-07-09T12:00:29-00:00 2007 simplicial spatial topology http://www.citeulike.org/user/bigbossman/article/973764 <i>Biometrika, Vol. 81, No. 3. (1 September 1994), pp. 425-455.</i><br /><br />With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline, or variable bandwidth kernel, to the unknown function. Estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels; however, it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone. We describe a new principle for spatially-adaptive estimation: selective wavelet reconstruction. We show that variable-knot spline fits and piecewise-polynomial fits, when equipped with an oracle to select the knots, are not dramatically more powerful than selective wavelet reconstruction with an oracle. We develop a practical spatially adaptive method, Risk Shrink, which works by shrinkage of empirical wavelet coefficients. RiskShrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so. A new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n, where n is the sample size. Moreover no estimator can give a better guarantee than this. Within the class of spatially adaptive procedures, RiskShrink is essentially optimal. Relying only on the data, it comes within a factor log2n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle. In contrast, it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone. 10.1093/biomet/81.3.425 Ideal spatial adaptation by wavelet shrinkage David Donoho Jain Johnstone doi:10.1093/biomet/81.3.425 Biometrika, Vol. 81, No. 3. (1 September 1994), pp. 425-455. 2006-12-04T18:51:08-00:00 1994 Biometrika 81 3 425 455 shrinkage spatial wavelet http://www.citeulike.org/user/bigbossman/article/607415 <i>(2005), pp. 218-227.</i> Detection of emerging space-time clusters Daniel Neill Andrew Moore Maheshkumar Sabhnani Kenny Daniel doi:10.1145/1081870.1081897 (2005), pp. 218-227. 2006-04-30T08:44:45-00:00 2005 218 227 ACM Press clusters spatial temporal http://www.citeulike.org/user/bigbossman/article/600787 <i>(2001), pp. 83-90.</i> A Hypergraph Based Clustering Algorithm for Spatial Data Sets Jong-Sheng Cherng Mei-Jung Lo (2001), pp. 83-90. 2006-04-26T00:06:27-00:00 2001 83 90 IEEE Computer Society clustering data hypergraph spatial http://www.citeulike.org/user/bigbossman/article/600777 <i>SIGMOD Rec., Vol. 33, No. 2. (June 2004), pp. 126-131.</i> Spatial, temporal and spatio-temporal databases - hot issues and directions for phd research John Roddick Erik Hoel Max Egenhofer Dimitris Papadias Betty Salzberg doi:10.1145/1024694.1024724 SIGMOD Rec., Vol. 33, No. 2. (June 2004), pp. 126-131. 2006-04-25T23:33:25-00:00 2004 SIGMOD Rec. 0163-5808 33 2 126 131 ACM Press databases spatial temporal