期刊论文

An anisotropic IDW interpolation method with multiple parameters cooperative optimization

Wu, Bo(wavelet778@sohu.com)

中文

测绘学报

1001-1595

2021

50

5

675-684

10.11947/j.AGCS.2021.20200148

Abstract:Theinversedistanceweighting(IDW)isoneofwidelyacceptedmethodsemployedfor predictinganunknownspatialvalueusingknownvaluesobservedatasetofsamplelocations．Many factorsincludingspatialproximity,samplesizeanddistancedecayafecttheestimationofthe method simultaneously．However,mostofIDWＧbasedmethodsdonotconsidertheefectofspatialanisotropy．In addition,mostofthesemethodscannotpredictaccurateinterpolatingvaluesbecausetheyonlyinvolvea solefactorforoptimization．ToobtainaccuratemisingvaluesandhighＧresolutionspatialsurfacemodel, thepaperproposesanovelmultipleparameterssynchronizationoptimizationIDWalgorithmwhichinvolves anisotropy．Theproposedmethodsimultaneouslyoptimizestheparametersofanisotropy,neighborsizeand distancedecaytoimprovetheaccuracyofIDWinterpolationbyparticleswarmoptimization(PSO)． Moreover,scalinganddirectionfactorareintroducedtocapturethevaryingofdistanceindiferent direction,andanewfitnesfunctionisschemedviacrosvalidationtechnique．Two diferentresolution datumareselectedtovalidatetheefectivenesofproposed method,andtheexperimentalresults demonstratethatourmethodsignificantlyoutperformthetypicalIDW method．Comparisonswiththerecently developedIDWＧbasedmethod,i．e．CIDW(clasicalIDW),FIDW(fourquadrantIDW),AIDW(adaptiveＧIDW) andKAIDW(KＧnearestneighboradaptiveIDW),OK(ordinaryKriging),aswelasAnisOK(anisotropic OrdinaryKriging)arealsoimplemented,andtheexperimentsshowthatouralgorithmcanachievethebest interpolationresultsintermsofreliableandaccuracy． Key words:inverse distance weighting(IDW);spatial proximity;anisotropy;multiple parameters optimization;ParticleSwarmoptimization Foundationsupport:The National Natural Science Foundation of China (Nos．４１９６１０５;４１７１５０; ４１８３０１０８);TheOutstandingYouthProjectofEducationDepartmentofHunanProvince(Nos．１９B０７８; １９C０２７２);TheNationalKeyResearchandDevelopmentProgramofChina(No．２０１８YFE０２０７８０);The SocialSciencePlanningProjectofHunanProvince(No．１７ZDB０５１)

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反距离加权插值（inverse distance weighting, IDW）的精度受到空间邻近度、距离衰减系数及最邻近点数等多个参数共同的影响。然而,目前的IDW插值算法大多仅考虑单参数的调优,或对各参数独立调优,难以实现插值模型的整体优化。此外,传统的IDW插值算法没有顾及各向异性对空间邻近度的影响。本文提出一种顾及空间各向异性的多参数协同优化IDW插值算法（PIDW）。首先,引入距离调节参数以及方向参数,将经典各向同性的欧氏空间距离扩展为各向异性的"椭圆"距离;然后,引入粒子群优化算法对最邻近点数、距离衰减系数、距离调节及各向异性方向的多参数进行协同优化,获得插值精度的偏差与方差在全局意义下...

The inverse distance weighting (IDW) is one of widely accepted methods employed for predicting an unknown spatial value using known values observed at a set of sample locations. Many factors including spatial proximity, sample size and distance decay affect the estimation of the method simultaneously. However, most of IDW-based methods do not consider the effect of spatial anisotropy. In addition, most of these methods cannot predict accurate interpolating values because they only involve a sole factor for optimization. To obtain accurate missi...