区域数据表现为两种尺度的空间特性:反映全局特征的空间依赖性和反映局域特征的空间波动性.空间波动性表现为空间数据在局部地区的聚集或高低交错现象.在研究区域数据时空预测性建模时,从降低数据的空间波动和不平稳性对模型预测能力的影响角度出发,提出了一种基于分区的局域神经网络时空非线性建模的思路.分区过程由基于空间邻接关系的K-means聚类算法完成.不同的分区方案通过相关性、波动性、紧凑性等指标进行评价和优选.在确定最优分区方案的基础上,对各子区分别采用两层前馈网络进行建模,模型的输入不仅要考虑本区内单元的作用,而且要考虑相邻子区的边界效应.各神经网络模型的时空预测能力通过平均相均差和动态相似率等指标进行衡量.最后,通过对法国94个县每周流感报告病例的时空建模分析表明,与全局神经网络模型相比,基于分区的局域神经网络模型具有更好的预测能力.

This paper focuses on space-tmi e nonlinear intelligent modeling for lattice data. Lattice data refers to attributes attached to fixed, regular or irregular, polygonal regions such as districts or census zones in two-dmi ensional space.Lattice data space-tmi e analysis is ami ing at detecting, modeling and predicting space-tmi e patterns or trends of lattice attributes changed with tmi e while spatial topological structures are smi ultaneously kept invariable. From the perspective of space, lattice objects have two different scale spatial properties influencing lattice data modeling: global dependence and local fluctuation. Global spatial dependence or autocorrelation quantifies the correlation of the same attribute at different spatial locations, and local spatial fluctuation or rough,coexisted with global dependence, is represented in the form of local spatial clustering ofsmi ilarvalues or local spatialoutliers. To consider smi ultaneously the effects of two properties above, local neural networks (NN) model is studied for space-tmi e nonlinear autoregressive modeling. Themain research contents include: (1) To reduce influence of spatial fluctuation on prediction accuracy of NN, all regions are partitioned into several subareas by an mi proved k-means algorithm. (2) Differentpartition schemes are evaluated and compared according to three essential criteria including dependence, continuity,fluctuation.Dependencemeans that an optmi al partition must guarantee that there is real and significant spatial dependence among regions in a subarea because the results ofoutput layernodes in aNNmodel depending on the interactions of input layer nodes through hidden layers nodes. Spatial autocorrelation of a subarea can be measured by globalMoran’s I and its significance test can be done based on z-score ofMoran’s I. Continuity means that only neighboring regions can be grouped into a subarea, and this criterion is fused into themodified k-means algorithm. When the algorithm judges one regionwhich subarea itbelongs to, not only should the distance be considered to the centroid of a subarea but also the common bordersbetween this region and the regions in a subarea. As to fluctuation, although it is mi possible tomake each subarea have complete spatial stability through partitioning, the less fluctuationmeans the better predicting results ofNN\nmode.l For a subarea, standard deviation between localMoran’s I of all regions in the subarea and globalMoran’s I of the subarea is regarded as an evaluation index to the fluctuation ofthe subarea. (3) Eachmulti-layerperceptrons (MLPs)network is used respectively inmodeling and predicting for each subarea. The output nodes are the predicting values at tmi etof an attribute for all regions in a subarea. The inputnodes are observations before tmi etof the same attribute of both regions in the subarea and regions neighboring to the subarea and the latter is called boundary effect. Finally, as a case study,all localmodels of all the subareas are trained,tested and compared with a single global MLPs network by modeling one-step-ahead prediction of an epidemic datasetwhich records weekly influenza cases of 94 departments in France from the firstweek of1990 to the 53th of1992. Two performancemeasures, including average relative variance(ARV)and dynamic smi ilarity rate (DSR), indicate that localNN model based on partitioning has better predicting capability than globalNNmode.l Several issues are stillworth further study: (1) The initial subareas ofpartitioning are selected randomly in our research. In the further study,a reasonable approach should combine selection with spatial patterns, for instance considering the center of local cluster.(2)Partition criteria should be another issue and different types of spatial and space-tmi e processes,such as rainfal,l price waves, public data,etc,may have different objective criteria for choosing an optmi alpartition.(3) Itmay bemore mi perative to study feasiblemeasures forquantifying global and local space-tmi e dependence of lattice data and testing significance of this dependence.