基于多重分形的城市地价场构建方法研究

研究目的：基于常规插值方法不可避免造成对数据的平滑,未能客观反映局部地价奇异信息的现状，探索运用多重分形模型构建城市地价标量场，为研究地价空间分布规律提供新的方法借鉴。研究方法：多重分形插值模型。研究结果：（1）城市地价数据主体部分服从近似对数正态分布，两端数据显著偏离对数正态分布，这是有效应用多重分形方法构建城市地价场的前提；（2）插值结果不仅有效地表达了研究区住宅地价空间分布，而且能够很好地度量地价的奇异性分布特征。研究结论：多重分形插值模型弥补了滑动平均方法构建城市地价场的不足，能有效突出地价局部奇异信息，可为社会经济领域类似数据空间场构建提供参考。

Developing Urban Land Price Field Using Multi-fractal Method

The purpose of this paper was to explore a multi-fractal method to characterize urban land price field for its spatial distribution in the context of that the conventional interpolation method inevitably smoothed the data set and concealed the realities of local anomaly information. Multi-fractal interpolation model was employed in the paper. The results indicated that 1） the main parts of urban land price data were approximately lognormal distribution. Both ends of the data significantly deviated from the lognormal distribution, which was the precondition for applying the multi-fractal method to characterize urban land price distribution; 2） the interpolation result not only effectively characterized the spatial distribution of urban residential land price, but also actively measured the singularity of the land price distribution. It was concluded that multi-fractal interpolation method could make up for the disadvantage of average smoothing method, which could highlight the local singularity information of land price distribution. This method could be used as references for characterizing the spatial distribution of similar socio-economic data.