田毅-Spark in GrowingIO

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Fireworks Algorithm for Optimization 烟花算法

Fireworks Algorithm for OptimizationYing Tan and Yuanchun ZhuKey Laboratory of Machine Perception(MOE),Peking UniversityDepartment of Machine Intelligence,School of Electronics Engineering and Computer Science,Peking University,Beijing,100871,China{ytan,ychzhu}@Abstract.Inspired by observingﬁreworks explosion,a novel swarm in-telligence algorithm,called Fireworks Algorithm(F A),is proposed forglobal optimization of complex functions.In the proposed F A,two typesof explosion(search)processes are employed,and the mechanisms forkeeping diversity of sparks are also well designed.In order to demon-strate the validation of the F A,a number of experiments were conductedon nine benchmark test functions to compare the F A with two vari-ants of particle swarm optimization(PSO)algorithms,namely StandardPSO and Clonal PSO.It turns out from the results that the proposed F Aclearly outperforms the two variants of the PSOs in both convergencespeed and global solution accuracy.Keywords:natural computing,swarm intelligence,ﬁreworks algorithm,particle swarm optimization,function optimization.1IntroductionIn recent years,Swarm Intelligence(SI)has become popular among researchers working on optimization problems all over the world[1,2].SI algorithms,e.g.Par-ticle Swarm Optimization(PSO)[3],Ant System[4],Clonal Selection Algorithm [5],and Swarm Robots[6],etc.,have advantages in solving many optimization problems.Among all the SI algorithms,PSO is one of the most popular algorithm for searching optimal locations in a D-dimensional space.In1995,Kennedy and Eberhart proposed PSO as a powerful global optimization algorithm inspired by the behavior of bird blocks[3].Since then,the PSO has attracted the attentions of researchers around the globe,and a number of variants of PSO have been con-tinually proposed[7,8].Like PSO,most of swarm intelligence algorithms are inspired by some intelli-gent colony behaviors in nature.In this paper,inspired by the emergent swarm behavior ofﬁreworks,a novel swarm intelligence algorithm called Fireworks Al-gorithm(FA)is proposed for function optimization.The FA is presented and implemented by simulating the explosion process ofﬁreworks.In the FA,two explosion(search)processes are employed and mechanisms for keeping diversity of sparks are also well designed.To validate the performance of the proposed FA,comparison experiments were conducted on nine benchmark test functions Y.Tan,Y.Shi,and K.C.Tan(Eds.):ICSI2010,Part I,LNCS6145,pp.355–364,2010.c Springer-Verlag Berlin Heidelberg2010356Y.Tan and Y.C.Zhuamong the FA,the Standard PSO(SPSO),and the Clonal PSO(CPSO)[8].It is shown that the FA clearly outperforms the SPSO and the CPSO in bothoptimization accuracy and convergence speed.The remainder of this paper is organized as follows.Section2describes theframework of the FA and introduces two types of search processes and mecha-nisms for keeping diversity.In Section3,experimental results are presented to validate the performance of the FA.Section4concludes the paper.2Fireworks Algorithm2.1F A FrameworkWhen aﬁrework is set oﬀ,a shower of sparks willﬁll the local space around the ﬁrework.In our opinion,the explosion process of aﬁrework can be viewed asa search in the local space around a speciﬁc point where theﬁrework is set oﬀthrough the sparks generated in the explosion.When we are asked toﬁnd a point x j satisfying f(x j)=y,we can continually set oﬀ‘ﬁreworks’in potential space until one‘spark’targets or is fairly near the point x j.Mimicking the process ofsetting oﬀﬁreworks,a rough framework of the FA is depicted in Fig.1.In the FA,for each generation of explosion,weﬁrst select n locations,wherenﬁreworks are set oﬀ.Then after explosion,the locations of sparks are obtained and evaluated.When the optimal location is found,the algorithm stops.Oth-erwise,n other locations are selected from the current sparks andﬁreworks for the next generation of explosion.From Fig.1,it can be seen that the success of the FA lies in a good designof the explosion process and a proper method for selecting locations,which arerespectively elaborated in subsection2.2and subsection2.3.Fig.1.Framework ofﬁreworks algorithmFireworks Algorithm for Optimization357 2.2Design of Fireworks ExplosionThrough observingﬁreworks display,we have found two speciﬁc behavior of ﬁreworks explosion.Whenﬁreworks are well manufactured,numerous sparks are generated,and the sparks centralize the explosion center.In this case,we enjoy the spectacular display of theﬁreworks.However,for a badﬁrework explosion, quite few sparks are generated,and the sparks scatter in the space.The two manners are depicted in Fig.2.From the standpoint of a search algorithm,a goodﬁrework denotes that theﬁrework locates in a promising area which may be close to the optimal location.Thus,it is proper to utilize more sparks to search the local area around theﬁrework.In the contrast,a badﬁrework means the optimal location may be far from where theﬁrework locates.Then, the search radius should be larger.In the FA,more sparks are generated and the explosion amplitude is smaller for a goodﬁrework,compared to a bad one.(a)Good explosion(b)Bad explosionFig.2.Two types ofﬁreworks explosionNumber of Sparks.Suppose the FA is designed for the general optimization problem:Minimize f(x)∈R,x min x x max,(1) where x=x1,x2,...,x d denotes a location in the potential space,f(x)is anobjective function,and x min and x max denote the bounds of the potential space.Then the number of sparks generated by eachﬁrework x i is deﬁned as follows.s i=m·y max−f(x i)+ξni=1(y max−f(x i))+ξ,(2)where m is a parameter controlling the total number of sparks generated by the nﬁreworks,y max=max(f(x i))(i=1,2,...,n)is the maximum(worst) value of the objective function among the nﬁreworks,andξ,which denotes the smallest constant in the computer,is utilized to avoid zero-division-error.To avoid overwhelming eﬀects of splendidﬁreworks,bounds are deﬁned for s i,which is shown in Eq.3.358Y.Tan and Y.C.Zhuˆs i=⎧⎪⎨⎪⎩round(a·m)if s i<amround(b·m)if s i>bmround(s i)otherwise,a<b<1,(3)where a and b are const parameters.Amplitude of Explosion.In contrast to the design of sparks number,the am-plitude of a goodﬁrework explosion is smaller than that of a bad one.Amplitude of explosion for eachﬁrework is deﬁned as follows.A i=ˆA·f(x i)−y min+ξni=1(f(x i)−y min)+ξ,(4)whereˆA denotes the maximum explosion amplitude,and y min=min(f(x i))(i= 1,2,...,n)is the minimum(best)value of the objective function among the n ﬁreworks.Generating Sparks.In explosion,sparks may undergo the eﬀects of explosion from random z directions(dimensions).In the FA,we obtain the number of the aﬀected directions randomly as follows.z=round(d·rand(0,1)),(5) where d is the dimensionality of the location x,and rand(0,1)is an uniform distribution over[0,1].The location of a spark of theﬁrework x i is obtained using Algorithm1. Mimicking the explosion process,a spark’s location˜x j isﬁrst generated.Then if the obtained location is found to fall out of the potential space,it is mapped to the potential space according to the algorithm.Algorithm1.Obtain the location of a sparkInitialize the location of the spark:˜x j=x i;z=round(d·rand(0,1));Randomly select z dimensions of˜x j;Calculate the displacement:h=A i·rand(−1,1);for each dimension˜x j k∈{pre-selected z dimensions of˜x j}do˜x j k=˜x j k+h;if˜x j k<x mink or˜x jk>x maxk thenmap˜x j k to the potential space:˜x j k=x mink+|˜x jk|%(x maxk−x mink);end ifend forTo keep the diversity of sparks,we design another way of generating sparks—Gaussian explosion,which is show in Algorithm2.A function Gaussian(1,1), which denotes a Gaussian distribution with mean1and standard deviation1,is utilized to deﬁne the coeﬃcient of the explosion.In our experiments,ˆm sparks of this type are generated in each explosion generation.Fireworks Algorithm for Optimization359Algorithm2.Obtain the location of a speciﬁc sparkInitialize the location of the spark:ˆx j=x i;z=round(d·rand(0,1));Randomly select z dimensions ofˆx j;Calculate the coeﬃcient of Gaussian explosion:g=Gaussian(1,1);for each dimensionˆx j k∈{pre-selected z dimensions ofˆx j}doˆx j k=ˆx j k·g;ifˆx j k<x mink orˆx jk>x maxk thenmapˆx j k to the potential space:ˆx j k=x mink +|ˆx j k|%(x maxk−x mink);end ifend for2.3Selection of LocationsAt the beginning of each explosion generation,n locations should be selected for theﬁreworks explosion.In the FA,the current best location x∗,upon which the objective function f(x∗)is optimal among current locations,is always kept for the next explosion generation.After that,n−1locations are selected based on their distance to other locations so as to keep diversity of sparks.The general distance between a location x i and other locations is deﬁned as follows.R(x i)=j∈K d(x i,x j)=j∈Kx i−x j ,(6)where K is the set of all current locations of bothﬁreworks and sparks.Then the selection probability of a location x i is deﬁned as follows.p(x i)=R(x i)j∈KR(x j).(7)When calculating the distance,any distance measure can be utilized including Manhattan distance,Euclidean distance,Angle-based distance,and so on[9]. When d(x i,x j)is deﬁned as|f(x i)−f(x j)|,the probability is equivalent to the deﬁnition of the immune density based probability in Ref.[10].2.4SummaryAlgorithm3summarizes the framework of the FA.During each explosion genera-tion,two types of sparks are generated respectively according to Algorithm1and Algorithm2.For theﬁrst type,the number of sparks and explosion amplitude depend on the quality of the correspondingﬁrework(f(x i)).In the contrast,the second type is generated using a Gaussian explosion process,which conducts search in a local Gaussian space around aﬁrework.After obtaining the locations of the two types of sparks,n locations are selected for the next explosion gener-ation.In the FA,approximate n+m+ˆm function evaluations are done in each generation.Suppose the optimum of a function can be found in T generations, then we can deduce that the complexity of the FA is O(T∗(n+m+ˆm)).360Y.Tan and Y.C.ZhuAlgorithm 3.Framework of the FARandomly select n locations for ﬁreworks;while stop criteria=false doSet oﬀn ﬁreworks respectively at the n locations:for each ﬁrework x i doCalculate the number of sparks that the ﬁrework yields:ˆs i ,according to Eq.3;Obtain locations of ˆs i sparks of the ﬁrework x i using Algorithm 1;end for for k=1:ˆm doRandomly select a ﬁrework x j ;Generate a speciﬁc spark for the ﬁrework using Algorithm 2;end forSelect the best location and keep it for next explosion generation;Randomly select n −1locations from the two types of sparks and the current ﬁreworks according to the probability given in Eq.7;end while3Experiments3.1Benchmark FunctionsTo investigate the performance of the proposed FA,we conducted experiments on nine benchmark functions.The feasible bounds for all functions are set as [−100,100]D .The expression of the functions,initialization intervals and di-mensionalities are listed in Table 1.Table 1.Nine benchmark functions utilized in our experiments Function ExpressionInitializationD SphereF 1= D i =1x 2i [30,50]D 30Rosenbrock F 2= D −1i =1(100(x i +1−x 2i )2+(x i −1)2)[30,50]D 30Rastrigrin F 3= D i =1(x 2i −10cos(2πx i )+10)[30,50]D 30Griewank F 4=1+ D i =1x 2i 4000− D i =1cos(x i √i )[30,50]D 30Ellipse F 5= D i =1104i −1D−1x 2i [15,30]D 30Cigar F 6=x 21+ D i =2104x 2i [15,30]D 30Tablet F 7=104x 21+ D i =2x 2i [15,30]D 30Schwefel F 8= Di =1((x 1−x 2i )2+(x i −1)2)[15,30]D 30AckleyF 9=20+e −20exp −0.2 1DD i =1x 2i[15,30]D30−exp 1D D i =1cos(2πx 2i )3.2Comparison Experiments among the F A,the CPSO and the SPSOIn this section,we compare the performance of the FA with the CPSO and the SPSO in terms of both convergence speed and optimization accuracy.Fireworks Algorithm for Optimization361 Table2.Statistical mean and standard deviation of solutions found by the F A,the CPSO and the SPSO on nine benchmark functions over20independent runsFunctionFunction F A’s mean CPSO’s mean SPSO’s mean evluations(StD)(StD)(StD)Sphere5000000.0000000.0000001.909960 (0.000000)(0.000000)(2.594634)Rosenbrock6000009.56949333.403191410.522552 (12.12829)(42.513450)(529.389139)Rastrigrin5000000.0000000.053042167.256119 (0.000000)(0.370687)(42.912873)Griewank2000000.0000000.6324032.177754 (0.000000)(0.327648)(0.294225)Ellipse5000000.0000000.00000053.718807 (0.000000)(0.000000)(68.480173)Cigar6000000.0000000.0000000.002492 (0.000000)(0.000000)(0.005194)Tablet5000000.0000000.0000001.462832 (0.000000)(0.000000)(1.157021)Schwefel6000000.0000000.0950990.335996 (0.000000)(0.376619)(0.775270)Ackley2000000.0000001.68364912.365417 (0.000000)(1.317866)(1.265322)The parameters of both the CPSO and the SPSO are set as those in Ref.[8]. For the FA,the parameters were selected by some preliminary experiments.We found that the FA worked quite well at the setting:n=5,m=50,a=0.04, b=0.8,ˆA=40,andˆm=5,which is applied in all the comparison experiments.Table2depicts the optimization accuracy of the three algorithms on nine benchmark functions,which are averaged over20independent runs.It can be seen that the proposed FA clearly outperforms both the CPSO and SPSO on all the functions.In addition,the FA canﬁnd optimal solutions on most benchmark functions in less than10000function evaluations,as shown in Table3.However, the optimization accuracy of the CPSO and the SPSO is unacceptable within 10000function evaluations.Besides optimization accuracy,convergence speed is quite essential to an opti-mizer.To validate the convergence speed of the FA,we conducted more thorough experiments.Fig.3depicts the convergence curves of the FA,the CPSO and the SPSO on eight benchmark functions averaged over20independent runs.From these results,we can arrive at a conclusion that the proposed FA has a much faster speed than the CPSO and the SPSO.From Table3,we canﬁnd that the FA canﬁnd excellent solutions with only10000times of function evaluations. This also reﬂects the fast convergence speed of the proposed FA.362Y.Tan and Y.C.Zhu(a)Sphere(b)Rosenbrock(c)Rastrigin(d)Griewank(e)Ellipse(f)Cigar(g)Tablet(h)SchwefelFig.3.Convergence curves of the F A,the CPSO and the SPSO on eight benchmark functions.The function ﬁtness are averaged over 20independent runs.Fireworks Algorithm for Optimization363 Table3.Statistical mean and standard deviation of solutions found by the F A,the CPSO and the SPSO on nine benchmark functions over20independent runs of10000 function evaluationsFunction F A’s mean CPSO’s mean SPSO’s mean(StD)(StD)(StD)Sphere0.00000011857.42578124919.099609 (0.000000)(3305.973067)(3383.241523)Rosenbrock19.383302750997504.0000005571942400.000000 (11.94373)(1741747548.420642)(960421617.568024)Rastrigrin0.00000010940.14843824013.001953 (0.000000)(3663.484331)(4246.961530)Griewank0.0000003.4572737.125976 (0.000000)(0.911027)(0.965788)Ellipse0.0000002493945.5000005305106.500000 (0.000000)(1199024.648305)(1117954.409340)Cigar0.000000122527168.000000149600864.000000 (0.000000)(28596381.089661)(13093322.778560)Tablet0.00000015595.10742242547.488281 (0.000000)(8086.792234)(8232.221882)Schwefel4.3537338775860.0000006743699.000000 (1.479332)(1217609.288290)(597770.084232)Ackley0.00000015.90766518.423347 (0.000000)(1.196082)(0.503372)3.3DiscussionAs shown in the experiments,the FA has a faster convergence speed and a better optimization accuracy,compared to the PSO.We consider the success of the FA lies in the following two aspects.–In the FA,sparks suﬀer the power of explosion from z dimensions simul-taneously,and the z dimensions are randomly selected for each spark˜x i.Thus,there is a probability that the diﬀerences between theﬁrework and the target location happen to lie in these z dimensions.In this scenario,the sparks of theﬁrework can move towards the target location from z directions simultaneously,which endues the FA with a fast convergence speed.–Two types of sparks are generated to keep the diversity of sparks,and the speciﬁc selection process for locations is a mechanism for keeping diversity.Therefore,the FA has the capability of avoiding premature convergence.4ConclusionsMimicking the explosion process ofﬁreworks,the so-called FA is proposed and implemented for function optimization.The experiments among the FA,the CPSO and the SPSO have shown that the proposed FA has a promising per-formance.It clearly outperforms the CPSO and the SPSO on nine benchmark364Y.Tan and Y.C.Zhufunctions in terms of both optimization accuracy and convergence speed,which endues the FA with a promising prospect of application and extension.In future work,we will seek a deep theoretical analysis on the FA and try to apply the FA to some practical engineering applications.Finally,we intend to discuss the relationship between the FA and other general-purpose optimization algorithms. Acknowlegements.This work was supported by National Natural Science Foundation of China(NSFC),under Grant No.60875080and60673020,and partially supported by the National High Technology Research and Develop-ment Program of China(863Program),with Grant No.2007AA01Z453.Authors appreciate Mr.Chao Rui for his facility with the early phase of the experiments. 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土地市场化的经济增长效应及传导机制——理论机制与实证检验

第 40 卷，第 4 期 2023 年8 月15 日国土资源科技管理Vol. 40，No.4Aug. 15，2023 Scientific and Technological Management of Land and Resourcesdoi：10.3969/j.issn.1009-4210.2023.04.009土地市场化的经济增长效应及传导机制——理论机制与实证检验邓郴宜，万　勇（上海社会科学院　应用经济研究所，上海　200235）摘　要：土地要素在中国式现代化过程中起到了重要作用。

在市场化改革背景下，运用数理模型演绎法、面板数据固定效应模型、系统GMM模型、中介效应模型以及bootstrap检验考察土地出让市场化影响城市经济增长的效果及影响渠道。

研究结果表明：（1）土地出让市场化每提高一个单位，城市经济增长提高0.132个百分点；（2）二者之间通过提高资源配置效率、提高城市创新水平以及提高城市土地融资水平三条路径产生作用。

（3）资源配置、城市创新、土地融资中介效应大小分别为0.081、0.052、0.314。

因此，中国应继续深化土地要素市场化改革，加强法规建设，充分考虑地区差异性，将政府与市场相结合。

关键词：土地市场化；城市经济增长；统一大市场中图分类号：F290 文献标志码：Ａ文章编号：1009-4210-（2023）04-091-15Land allocation and urban economic growth in the market oriented reform: theoretical mechanism and empirical testDENG Chen-yi，WAN Yong（Institute of Applied Economics，Shanghai Academy of Social Sciences，Shanghai 200235，China）Abstract: Land plays an important role in Chinese path to modernization. In the context of market-oriented reform，panel data fixed effect model，system GMM model，mesomeric effect model and bootstrap test are applied to investigate the effect and influence of land marketization on urban economic growth. The research results are as follows：(1) For each unit of land marketization increase，urban economic growth increases by 0.132 percentage points；(2) The two play a role by improving the efficiency of resource allocation，the level of urban innovation and improving the level of urban land financing.(3) The intermediary effects of resource allocation，urban innovation and land financing are 0.081，0.052 and 0.314 respectively. It is concluded that China should continue to deepen the market-based allocation of factors of land，strengthen the construction of laws and regulations，give full consideration to regional differences，and combine the government with the market.Key words: Land marketization，urban economic growth，unified market收稿日期：2023-04-07；改回日期：2023-05-16基金项目：国家社科基金重点项目（19AZS018）作者简介：邓郴宜（1993—），女，博士研究生，从事城市规划与城市经济学研究。

C.parvum全基因组序列

DOI: 10.1126/science.1094786, 441 (2004);304Science et al.Mitchell S. Abrahamsen,Cryptosporidium parvum Complete Genome Sequence of the Apicomplexan, (this information is current as of October 7, 2009 ):The following resources related to this article are available online at/cgi/content/full/304/5669/441version of this article at:including high-resolution figures, can be found in the online Updated information and services,/cgi/content/full/1094786/DC1 can be found at:Supporting Online Material/cgi/content/full/304/5669/441#otherarticles , 9 of which can be accessed for free: cites 25 articles This article 239 article(s) on the ISI Web of Science. cited by This article has been /cgi/content/full/304/5669/441#otherarticles 53 articles hosted by HighWire Press; see: cited by This article has been/cgi/collection/genetics Genetics: subject collections This article appears in the following/about/permissions.dtl in whole or in part can be found at: this article permission to reproduce of this article or about obtaining reprints Information about obtaining registered trademark of AAAS.is a Science 2004 by the American Association for the Advancement of Science; all rights reserved. The title Copyright American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. 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asynchronyof600ms.While subjects were readingthe sentences,their EEG was recorded and ampliﬁed with a high-cut-off frequency of70Hz,a time constant of8s,and asamplingfrequency of200Hz.14.Materials and methods are available as supportingmaterial on Science Online.15.M.Kutas,S.A.Hillyard,Science207,203(1980).16.C.Brown,P.Hagoort,J.Cognit.Neurosci.5,34(1993).17.C.M.Brown,P.Hagoort,in Architectures and Mech-anisms for Language Processing,M.W.Crocker,M.Pickering,C.Clifton Jr.,Eds.(Cambridge Univ.Press,Cambridge,1999),pp.213–237.18.F.Varela et al.,Nature Rev.Neurosci.2,229(2001).19.We obtained TFRs of the single-trial EEG data by con-volvingcomplex Morlet wavelets with the EEG data andcomputingthe squared norm for the result of theconvolution.We used wavelets with a7-cycle width,with frequencies ranging from1to70Hz,in1-Hz steps.Power values thus obtained were expressed as a per-centage change relative to the power in a baselineinterval,which was taken from150to0ms before theonset of the critical word.This was done in order tonormalize for individual differences in EEG power anddifferences in baseline power between different fre-quency bands.Two relevant time-frequency compo-nents were identiﬁed:(i)a theta component,rangingfrom4to7Hz and from300to800ms after wordonset,and(ii)a gamma component,ranging from35to45Hz and from400to600ms after word onset.20.C.Tallon-Baudry,O.Bertrand,Trends Cognit.Sci.3,151(1999).tner et al.,Nature397,434(1999).22.M.Bastiaansen,P.Hagoort,Cortex39(2003).23.O.Jensen,C.D.Tesche,Eur.J.Neurosci.15,1395(2002).24.Whole brain T2*-weighted echo planar imaging bloodoxygen level–dependent(EPI-BOLD)fMRI data wereacquired with a Siemens Sonata1.5-T magnetic reso-nance scanner with interleaved slice ordering,a volumerepetition time of2.48s,an echo time of40ms,a90°ﬂip angle,31horizontal slices,a64ϫ64slice matrix,and isotropic voxel size of3.5ϫ3.5ϫ3.5mm.For thestructural magnetic resonance image,we used a high-resolution(isotropic voxels of1mm3)T1-weightedmagnetization-prepared rapid gradient-echo pulse se-quence.The fMRI data were preprocessed and analyzedby statistical parametric mappingwith SPM99software(http://www.ﬁ/spm99).25.S.E.Petersen et al.,Nature331,585(1988).26.B.T.Gold,R.L.Buckner,Neuron35,803(2002).27.E.Halgren et al.,J.Psychophysiol.88,1(1994).28.E.Halgren et al.,Neuroimage17,1101(2002).29.M.K.Tanenhaus et al.,Science268,1632(1995).30.J.J.A.van Berkum et al.,J.Cognit.Neurosci.11,657(1999).31.P.A.M.Seuren,Discourse Semantics(Basil Blackwell,Oxford,1985).32.We thank P.Indefrey,P.Fries,P.A.M.Seuren,and M.van Turennout for helpful discussions.Supported bythe Netherlands Organization for Scientiﬁc Research,grant no.400-56-384(P.H.).Supporting Online Material/cgi/content/full/1095455/DC1Materials and MethodsFig.S1References and Notes8January2004;accepted9March2004Published online18March2004;10.1126/science.1095455Include this information when citingthis paper.Complete Genome Sequence ofthe Apicomplexan,Cryptosporidium parvumMitchell S.Abrahamsen,1,2*†Thomas J.Templeton,3†Shinichiro Enomoto,1Juan E.Abrahante,1Guan Zhu,4 Cheryl ncto,1Mingqi Deng,1Chang Liu,1‡Giovanni Widmer,5Saul Tzipori,5GregoryA.Buck,6Ping Xu,6 Alan T.Bankier,7Paul H.Dear,7Bernard A.Konfortov,7 Helen F.Spriggs,7Lakshminarayan Iyer,8Vivek Anantharaman,8L.Aravind,8Vivek Kapur2,9The apicomplexan Cryptosporidium parvum is an intestinal parasite that affects healthy humans and animals,and causes an unrelenting infection in immuno-compromised individuals such as AIDS patients.We report the complete ge-nome sequence of C.parvum,type II isolate.Genome analysis identiﬁes ex-tremely streamlined metabolic pathways and a reliance on the host for nu-trients.In contrast to Plasmodium and Toxoplasma,the parasite lacks an api-coplast and its genome,and possesses a degenerate mitochondrion that has lost its genome.Several novel classes of cell-surface and secreted proteins with a potential role in host interactions and pathogenesis were also detected.Elu-cidation of the core metabolism,including enzymes with high similarities to bacterial and plant counterparts,opens new avenues for drug development.Cryptosporidium parvum is a globally impor-tant intracellular pathogen of humans and animals.The duration of infection and patho-genesis of cryptosporidiosis depends on host immune status,ranging from a severe but self-limiting diarrhea in immunocompetent individuals to a life-threatening,prolonged infection in immunocompromised patients.Asubstantial degree of morbidity and mortalityis associated with infections in AIDS pa-tients.Despite intensive efforts over the past20years,there is currently no effective ther-apy for treating or preventing C.parvuminfection in humans.Cryptosporidium belongs to the phylumApicomplexa,whose members share a com-mon apical secretory apparatus mediating lo-comotion and tissue or cellular invasion.Many apicomplexans are of medical or vet-erinary importance,including Plasmodium,Babesia,Toxoplasma,Neosprora,Sarcocys-tis,Cyclospora,and Eimeria.The life cycle ofC.parvum is similar to that of other cyst-forming apicomplexans(e.g.,Eimeria and Tox-oplasma),resulting in the formation of oocysts1Department of Veterinary and Biomedical Science,College of Veterinary Medicine,2Biomedical Genom-ics Center,University of Minnesota,St.Paul,MN55108,USA.3Department of Microbiology and Immu-nology,Weill Medical College and Program in Immu-nology,Weill Graduate School of Medical Sciences ofCornell University,New York,NY10021,USA.4De-partment of Veterinary Pathobiology,College of Vet-erinary Medicine,Texas A&M University,College Sta-tion,TX77843,USA.5Division of Infectious Diseases,Tufts University School of Veterinary Medicine,NorthGrafton,MA01536,USA.6Center for the Study ofBiological Complexity and Department of Microbiol-ogy and Immunology,Virginia Commonwealth Uni-versity,Richmond,VA23198,USA.7MRC Laboratoryof Molecular Biology,Hills Road,Cambridge CB22QH,UK.8National Center for Biotechnology Infor-mation,National Library of Medicine,National Insti-tutes of Health,Bethesda,MD20894,USA.9Depart-ment of Microbiology,University of Minnesota,Min-neapolis,MN55455,USA.*To whom correspondence should be addressed.E-mail:abe@†These authors contributed equally to this work.‡Present address:Bioinformatics Division,Genetic Re-search,GlaxoSmithKline Pharmaceuticals,5MooreDrive,Research Triangle Park,NC27009,USA.R E P O R T S SCIENCE VOL30416APRIL2004441o n O c t o b e r 7 , 2 0 0 9 w w w . s c i e n c e m a g . o r g D o w n l o a d e d f r o mthat are shed in the feces of infected hosts.C.parvum oocysts are highly resistant to environ-mental stresses,including chlorine treatment of community water supplies;hence,the parasite is an important water-and food-borne pathogen (1).The obligate intracellular nature of the par-asite ’s life cycle and the inability to culture the parasite continuously in vitro greatly impair researchers ’ability to obtain purified samples of the different developmental stages.The par-asite cannot be genetically manipulated,and transformation methodologies are currently un-available.To begin to address these limitations,we have obtained the complete C.parvum ge-nome sequence and its predicted protein com-plement.(This whole-genome shotgun project has been deposited at DDBJ/EMBL/GenBank under the project accession AAEE00000000.The version described in this paper is the first version,AAEE01000000.)The random shotgun approach was used to obtain the complete DNA sequence (2)of the Iowa “type II ”isolate of C.parvum .This isolate readily transmits disease among numerous mammals,including humans.The resulting ge-nome sequence has roughly 13ϫgenome cov-erage containing five gaps and 9.1Mb of totalDNA sequence within eight chromosomes.The C.parvum genome is thus quite compact rela-tive to the 23-Mb,14-chromosome genome of Plasmodium falciparum (3);this size difference is predominantly the result of shorter intergenic regions,fewer introns,and a smaller number of genes (Table 1).Comparison of the assembled sequence of chromosome VI to that of the recently published sequence of chromosome VI (4)revealed that our assembly contains an ad-ditional 160kb of sequence and a single gap versus two,with the common sequences dis-playing a 99.993%sequence identity (2).The relative paucity of introns greatly simplified gene predictions and facilitated an-notation (2)of predicted open reading frames (ORFs).These analyses provided an estimate of 3807protein-encoding genes for the C.parvum genome,far fewer than the estimated 5300genes predicted for the Plasmodium genome (3).This difference is primarily due to the absence of an apicoplast and mitochondrial genome,as well as the pres-ence of fewer genes encoding metabolic functions and variant surface proteins,such as the P.falciparum var and rifin molecules (Table 2).An analysis of the encoded pro-tein sequences with the program SEG (5)shows that these protein-encoding genes are not enriched in low-complexity se-quences (34%)to the extent observed in the proteins from Plasmodium (70%).Our sequence analysis indicates that Cryptosporidium ,unlike Plasmodium and Toxoplasma ,lacks both mitochondrion and apicoplast genomes.The overall complete-ness of the genome sequence,together with the fact that similar DNA extraction proce-dures used to isolate total genomic DNA from C.parvum efficiently yielded mito-chondrion and apicoplast genomes from Ei-meria sp.and Toxoplasma (6,7),indicates that the absence of organellar genomes was unlikely to have been the result of method-ological error.These conclusions are con-sistent with the absence of nuclear genes for the DNA replication and translation machinery characteristic of mitochondria and apicoplasts,and with the lack of mito-chondrial or apicoplast targeting signals for tRNA synthetases.A number of putative mitochondrial pro-teins were identified,including components of a mitochondrial protein import apparatus,chaperones,uncoupling proteins,and solute translocators (table S1).However,the ge-nome does not encode any Krebs cycle en-zymes,nor the components constituting the mitochondrial complexes I to IV;this finding indicates that the parasite does not rely on complete oxidation and respiratory chains for synthesizing adenosine triphosphate (ATP).Similar to Plasmodium ,no orthologs for the ␥,␦,or εsubunits or the c subunit of the F 0proton channel were detected (whereas all subunits were found for a V-type ATPase).Cryptosporidium ,like Eimeria (8)and Plas-modium ,possesses a pyridine nucleotide tran-shydrogenase integral membrane protein that may couple reduced nicotinamide adenine dinucleotide (NADH)and reduced nico-tinamide adenine dinucleotide phosphate (NADPH)redox to proton translocation across the inner mitochondrial membrane.Unlike Plasmodium ,the parasite has two copies of the pyridine nucleotide transhydrogenase gene.Also present is a likely mitochondrial membrane –associated,cyanide-resistant alter-native oxidase (AOX )that catalyzes the reduction of molecular oxygen by ubiquinol to produce H 2O,but not superoxide or H 2O 2.Several genes were identified as involved in biogenesis of iron-sulfur [Fe-S]complexes with potential mitochondrial targeting signals (e.g.,nifS,nifU,frataxin,and ferredoxin),supporting the presence of a limited electron flux in the mitochondrial remnant (table S2).Our sequence analysis confirms the absence of a plastid genome (7)and,additionally,the loss of plastid-associated metabolic pathways including the type II fatty acid synthases (FASs)and isoprenoid synthetic enzymes thatTable 1.General features of the C.parvum genome and comparison with other single-celled eukaryotes.Values are derived from respective genome project summaries (3,26–28).ND,not determined.FeatureC.parvum P.falciparum S.pombe S.cerevisiae E.cuniculiSize (Mbp)9.122.912.512.5 2.5(G ϩC)content (%)3019.43638.347No.of genes 38075268492957701997Mean gene length (bp)excluding introns 1795228314261424ND Gene density (bp per gene)23824338252820881256Percent coding75.352.657.570.590Genes with introns (%)553.9435ND Intergenic regions (G ϩC)content %23.913.632.435.145Mean length (bp)5661694952515129RNAsNo.of tRNA genes 454317429944No.of 5S rRNA genes 6330100–2003No.of 5.8S ,18S ,and 28S rRNA units 57200–400100–20022Table parison between predicted C.parvum and P.falciparum proteins.FeatureC.parvum P.falciparum *Common †Total predicted proteins380752681883Mitochondrial targeted/encoded 17(0.45%)246(4.7%)15Apicoplast targeted/encoded 0581(11.0%)0var/rif/stevor ‡0236(4.5%)0Annotated as protease §50(1.3%)31(0.59%)27Annotated as transporter ࿣69(1.8%)34(0.65%)34Assigned EC function ¶167(4.4%)389(7.4%)113Hypothetical proteins925(24.3%)3208(60.9%)126*Values indicated for P.falciparum are as reported (3)with the exception of those for proteins annotated as protease or transporter.†TBLASTN hits (e Ͻ–5)between C.parvum and P.falciparum .‡As reported in (3).§Pre-dicted proteins annotated as “protease or peptidase”for C.parvum (CryptoGenome database,)and P.falciparum (PlasmoDB database,).࿣Predicted proteins annotated as “trans-porter,permease of P-type ATPase”for C.parvum (CryptoGenome)and P.falciparum (PlasmoDB).¶Bidirectional BLAST hit (e Ͻ–15)to orthologs with assigned Enzyme Commission (EC)numbers.Does not include EC assignment numbers for protein kinases or protein phosphatases (due to inconsistent annotation across genomes),or DNA polymerases or RNA polymerases,as a result of issues related to subunit inclusion.(For consistency,46proteins were excluded from the reported P.falciparum values.)R E P O R T S16APRIL 2004VOL 304SCIENCE 442 o n O c t o b e r 7, 2009w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o mare otherwise localized to the plastid in other apicomplexans.C.parvum fatty acid biosynthe-sis appears to be cytoplasmic,conducted by a large(8252amino acids)modular type I FAS (9)and possibly by another large enzyme that is related to the multidomain bacterial polyketide synthase(10).Comprehensive screening of the C.parvum genome sequence also did not detect orthologs of Plasmodium nuclear-encoded genes that contain apicoplast-targeting and transit sequences(11).C.parvum metabolism is greatly stream-lined relative to that of Plasmodium,and in certain ways it is reminiscent of that of another obligate eukaryotic parasite,the microsporidian Encephalitozoon.The degeneration of the mi-tochondrion and associated metabolic capabili-ties suggests that the parasite largely relies on glycolysis for energy production.The parasite is capable of uptake and catabolism of mono-sugars(e.g.,glucose and fructose)as well as synthesis,storage,and catabolism of polysac-charides such as trehalose and amylopectin. Like many anaerobic organisms,it economizes ATP through the use of pyrophosphate-dependent phosphofructokinases.The conver-sion of pyruvate to acetyl–coenzyme A(CoA) is catalyzed by an atypical pyruvate-NADPH oxidoreductase(Cp PNO)that contains an N-terminal pyruvate–ferredoxin oxidoreductase (PFO)domain fused with a C-terminal NADPH–cytochrome P450reductase domain (CPR).Such a PFO-CPR fusion has previously been observed only in the euglenozoan protist Euglena gracilis(12).Acetyl-CoA can be con-verted to malonyl-CoA,an important precursor for fatty acid and polyketide biosynthesis.Gly-colysis leads to several possible organic end products,including lactate,acetate,and ethanol. The production of acetate from acetyl-CoA may be economically beneficial to the parasite via coupling with ATP production.Ethanol is potentially produced via two in-dependent pathways:(i)from the combination of pyruvate decarboxylase and alcohol dehy-drogenase,or(ii)from acetyl-CoA by means of a bifunctional dehydrogenase(adhE)with ac-etaldehyde and alcohol dehydrogenase activi-ties;adhE first converts acetyl-CoA to acetal-dehyde and then reduces the latter to ethanol. AdhE predominantly occurs in bacteria but has recently been identified in several protozoans, including vertebrate gut parasites such as Enta-moeba and Giardia(13,14).Adjacent to the adhE gene resides a second gene encoding only the AdhE C-terminal Fe-dependent alcohol de-hydrogenase domain.This gene product may form a multisubunit complex with AdhE,or it may function as an alternative alcohol dehydro-genase that is specific to certain growth condi-tions.C.parvum has a glycerol3-phosphate dehydrogenase similar to those of plants,fungi, and the kinetoplastid Trypanosoma,but(unlike trypanosomes)the parasite lacks an ortholog of glycerol kinase and thus this pathway does not yield glycerol production.In addition to themodular fatty acid synthase(Cp FAS1)andpolyketide synthase homolog(Cp PKS1), C.parvum possesses several fatty acyl–CoA syn-thases and a fatty acyl elongase that may partici-pate in fatty acid metabolism.Further,enzymesfor the metabolism of complex lipids(e.g.,glyc-erolipid and inositol phosphate)were identified inthe genome.Fatty acids are apparently not anenergy source,because enzymes of the fatty acidoxidative pathway are absent,with the exceptionof a3-hydroxyacyl-CoA dehydrogenase.C.parvum purine metabolism is greatlysimplified,retaining only an adenosine ki-nase and enzymes catalyzing conversionsof adenosine5Ј-monophosphate(AMP)toinosine,xanthosine,and guanosine5Ј-monophosphates(IMP,XMP,and GMP).Among these enzymes,IMP dehydrogenase(IMPDH)is phylogenetically related toε-proteobacterial IMPDH and is strikinglydifferent from its counterparts in both thehost and other apicomplexans(15).In con-trast to other apicomplexans such as Toxo-plasma gondii and P.falciparum,no geneencoding hypoxanthine-xanthineguaninephosphoribosyltransferase(HXGPRT)is de-tected,in contrast to a previous report on theactivity of this enzyme in C.parvum sporo-zoites(16).The absence of HXGPRT sug-gests that the parasite may rely solely on asingle enzyme system including IMPDH toproduce GMP from AMP.In contrast to otherapicomplexans,the parasite appears to relyon adenosine for purine salvage,a modelsupported by the identification of an adeno-sine transporter.Unlike other apicomplexansand many parasitic protists that can synthe-size pyrimidines de novo,C.parvum relies onpyrimidine salvage and retains the ability forinterconversions among uridine and cytidine5Ј-monophosphates(UMP and CMP),theirdeoxy forms(dUMP and dCMP),and dAMP,as well as their corresponding di-and triphos-phonucleotides.The parasite has also largelyshed the ability to synthesize amino acids denovo,although it retains the ability to convertselect amino acids,and instead appears torely on amino acid uptake from the host bymeans of a set of at least11amino acidtransporters(table S2).Most of the Cryptosporidium core pro-cesses involved in DNA replication,repair,transcription,and translation conform to thebasic eukaryotic blueprint(2).The transcrip-tional apparatus resembles Plasmodium interms of basal transcription machinery.How-ever,a striking numerical difference is seenin the complements of two RNA bindingdomains,Sm and RRM,between P.falcipa-rum(17and71domains,respectively)and C.parvum(9and51domains).This reductionresults in part from the loss of conservedproteins belonging to the spliceosomal ma-chinery,including all genes encoding Smdomain proteins belonging to the U6spliceo-somal particle,which suggests that this par-ticle activity is degenerate or entirely lost.This reduction in spliceosomal machinery isconsistent with the reduced number of pre-dicted introns in Cryptosporidium(5%)rela-tive to Plasmodium(Ͼ50%).In addition,keycomponents of the small RNA–mediatedposttranscriptional gene silencing system aremissing,such as the RNA-dependent RNApolymerase,Argonaute,and Dicer orthologs;hence,RNA interference–related technolo-gies are unlikely to be of much value intargeted disruption of genes in C.parvum.Cryptosporidium invasion of columnarbrush border epithelial cells has been de-scribed as“intracellular,but extracytoplas-mic,”as the parasite resides on the surface ofthe intestinal epithelium but lies underneaththe host cell membrane.This niche may al-low the parasite to evade immune surveil-lance but take advantage of solute transportacross the host microvillus membrane or theextensively convoluted parasitophorous vac-uole.Indeed,Cryptosporidium has numerousgenes(table S2)encoding families of putativesugar transporters(up to9genes)and aminoacid transporters(11genes).This is in starkcontrast to Plasmodium,which has fewersugar transporters and only one putative ami-no acid transporter(GenBank identificationnumber23612372).As a first step toward identification ofmulti–drug-resistant pumps,the genome se-quence was analyzed for all occurrences ofgenes encoding multitransmembrane proteins.Notable are a set of four paralogous proteinsthat belong to the sbmA family(table S2)thatare involved in the transport of peptide antibi-otics in bacteria.A putative ortholog of thePlasmodium chloroquine resistance–linkedgene Pf CRT(17)was also identified,althoughthe parasite does not possess a food vacuole likethe one seen in Plasmodium.Unlike Plasmodium,C.parvum does notpossess extensive subtelomeric clusters of anti-genically variant proteins(exemplified by thelarge families of var and rif/stevor genes)thatare involved in immune evasion.In contrast,more than20genes were identified that encodemucin-like proteins(18,19)having hallmarksof extensive Thr or Ser stretches suggestive ofglycosylation and signal peptide sequences sug-gesting secretion(table S2).One notable exam-ple is an11,700–amino acid protein with anuninterrupted stretch of308Thr residues(cgd3_720).Although large families of secretedproteins analogous to the Plasmodium multi-gene families were not found,several smallermultigene clusters were observed that encodepredicted secreted proteins,with no detectablesimilarity to proteins from other organisms(Fig.1,A and B).Within this group,at leastfour distinct families appear to have emergedthrough gene expansions specific to the Cryp-R E P O R T S SCIENCE VOL30416APRIL2004443o n O c t o b e r 7 , 2 0 0 9 w w w . s c i e n c e m a g . o r g D o w n l o a d e d f r o mtosporidium clade.These families —SKSR,MEDLE,WYLE,FGLN,and GGC —were named after well-conserved sequence motifs (table S2).Reverse transcription polymerase chain reaction (RT-PCR)expression analysis (20)of one cluster,a locus of seven adjacent CpLSP genes (Fig.1B),shows coexpression during the course of in vitro development (Fig.1C).An additional eight genes were identified that encode proteins having a periodic cysteine structure similar to the Cryptosporidium oocyst wall protein;these eight genes are similarly expressed during the onset of oocyst formation and likely participate in the formation of the coccidian rigid oocyst wall in both Cryptospo-ridium and Toxoplasma (21).Whereas the extracellular proteins described above are of apparent apicomplexan or lineage-specific in-vention,Cryptosporidium possesses many genesencodingsecretedproteinshavinglineage-specific multidomain architectures composed of animal-and bacterial-like extracellular adhe-sive domains (fig.S1).Lineage-specific expansions were ob-served for several proteases (table S2),in-cluding an aspartyl protease (six genes),a subtilisin-like protease,a cryptopain-like cys-teine protease (five genes),and a Plas-modium falcilysin-like (insulin degrading enzyme –like)protease (19genes).Nine of the Cryptosporidium falcilysin genes lack the Zn-chelating “HXXEH ”active site motif and are likely to be catalytically inactive copies that may have been reused for specific protein-protein interactions on the cell sur-face.In contrast to the Plasmodium falcilysin,the Cryptosporidium genes possess signal peptide sequences and are likely trafficked to a secretory pathway.The expansion of this family suggests either that the proteins have distinct cleavage specificities or that their diversity may be related to evasion of a host immune response.Completion of the C.parvum genome se-quence has highlighted the lack of conven-tional drug targets currently pursued for the control and treatment of other parasitic protists.On the basis of molecular and bio-chemical studies and drug screening of other apicomplexans,several putative Cryptospo-ridium metabolic pathways or enzymes have been erroneously proposed to be potential drug targets (22),including the apicoplast and its associated metabolic pathways,the shikimate pathway,the mannitol cycle,the electron transport chain,and HXGPRT.Nonetheless,complete genome sequence analysis identifies a number of classic and novel molecular candidates for drug explora-tion,including numerous plant-like and bacterial-like enzymes (tables S3and S4).Although the C.parvum genome lacks HXGPRT,a potent drug target in other api-complexans,it has only the single pathway dependent on IMPDH to convert AMP to GMP.The bacterial-type IMPDH may be a promising target because it differs substan-tially from that of eukaryotic enzymes (15).Because of the lack of de novo biosynthetic capacity for purines,pyrimidines,and amino acids,C.parvum relies solely on scavenge from the host via a series of transporters,which may be exploited for chemotherapy.C.parvum possesses a bacterial-type thymidine kinase,and the role of this enzyme in pyrim-idine metabolism and its drug target candida-cy should be pursued.The presence of an alternative oxidase,likely targeted to the remnant mitochondrion,gives promise to the study of salicylhydroxamic acid (SHAM),as-cofuranone,and their analogs as inhibitors of energy metabolism in the parasite (23).Cryptosporidium possesses at least 15“plant-like ”enzymes that are either absent in or highly divergent from those typically found in mammals (table S3).Within the glycolytic pathway,the plant-like PPi-PFK has been shown to be a potential target in other parasites including T.gondii ,and PEPCL and PGI ap-pear to be plant-type enzymes in C.parvum .Another example is a trehalose-6-phosphate synthase/phosphatase catalyzing trehalose bio-synthesis from glucose-6-phosphate and uridine diphosphate –glucose.Trehalose may serve as a sugar storage source or may function as an antidesiccant,antioxidant,or protein stability agent in oocysts,playing a role similar to that of mannitol in Eimeria oocysts (24).Orthologs of putative Eimeria mannitol synthesis enzymes were not found.However,two oxidoreductases (table S2)were identified in C.parvum ,one of which belongs to the same families as the plant mannose dehydrogenases (25)and the other to the plant cinnamyl alcohol dehydrogenases.In principle,these enzymes could synthesize protective polyol compounds,and the former enzyme could use host-derived mannose to syn-thesize mannitol.References and Notes1.D.G.Korich et al .,Appl.Environ.Microbiol.56,1423(1990).2.See supportingdata on Science Online.3.M.J.Gardner et al .,Nature 419,498(2002).4.A.T.Bankier et al .,Genome Res.13,1787(2003).5.J.C.Wootton,Comput.Chem.18,269(1994).Fig.1.(A )Schematic showing the chromosomal locations of clusters of potentially secreted proteins.Numbers of adjacent genes are indicated in paren-theses.Arrows indicate direc-tion of clusters containinguni-directional genes (encoded on the same strand);squares indi-cate clusters containingg enes encoded on both strands.Non-paralogous genes are indicated by solid gray squares or direc-tional triangles;SKSR (green triangles),FGLN (red trian-gles),and MEDLE (blue trian-gles)indicate three C.parvum –speciﬁc families of paralogous genes predominantly located at telomeres.Insl (yellow tri-angles)indicates an insulinase/falcilysin-like paralogous gene family.Cp LSP (white square)indicates the location of a clus-ter of adjacent large secreted proteins (table S2)that are cotranscriptionally regulated.Identiﬁed anchored telomeric repeat sequences are indicated by circles.(B )Schematic show-inga select locus containinga cluster of coexpressed large secreted proteins (Cp LSP).Genes and intergenic regions (regions between identiﬁed genes)are drawn to scale at the nucleotide level.The length of the intergenic re-gions is indicated above or be-low the locus.(C )Relative ex-pression levels of CpLSP (red lines)and,as a control,C.parvum Hedgehog-type HINT domain gene (blue line)duringin vitro development,as determined by semiquantitative RT-PCR usingg ene-speciﬁc primers correspondingto the seven adjacent g enes within the CpLSP locus as shown in (B).Expression levels from three independent time-course experiments are represented as the ratio of the expression of each gene to that of C.parvum 18S rRNA present in each of the infected samples (20).R E P O R T S16APRIL 2004VOL 304SCIENCE 444 o n O c t o b e r 7, 2009w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o m。

基于代价敏感XGBoost的企业信用评估模型

文章编号： 1009 − 444X（2022）02 − 0218 − 06基于代价敏感XGBoost的企业信用评估模型

张田华，张　怡，谢晓金（上海工程技术大学数理与统计学院，上海 201620）摘要：我国信用不良的企业数量远小于信用良好的企业数量，样本类别的极端不平衡导致传统的信用评估模型在训练时无法充分学习信用不良企业的特征. 为提高极端梯度提升算法(Extreme Gradient Boosting, XGBoost)在企业信用评估这种不平衡分类问题中的准确率，提出一种基于代价敏感XGBoost的企业信用评估模型. 在XGBoost算法拟合过程中，加入代价敏感损失函数迫使模型更加关注少数类的特征，并引入贝叶斯优化调整模型的重要超参数. 以我国A股市场中小板块企业2016—2020年数据为样本，实证结果表明，基于代价敏感XGBoost的企业信用评估模型能够在保证总体识别精度的情况下提高对信用不良企业的识别准确率.关键词：损失函数；极端梯度提升算法；代价敏感；企业信用评估中图分类号： TP391 文献标志码： A

Enterprise credit evaluation model based oncost sensitive XGBoost

ZHANG Tianhua ，ZHANG Yi ，XIE Xiaojin（ School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China）Abstract：In China, the number of enterprises with bad credit is much smaller than that of enterprises withgood credit. The extreme imbalance of sample categories results in the traditional credit evaluation modelunable to fully learn the characteristics of bad credit enterprises during training. In order to improve theaccuracy of extreme gradient boosting (XGBoost) in unbalanced classification problems such as enterprisecredit evaluation, an enterprise credit evaluation model based on cost sensitive XGBoost was proposed. In theprocess of XGBoost algorithm fitting, the cost sensitive loss function was added to force the model to pay moreattention to the characteristics of minority classes, and the bayesian optimization was introduced to adjust thehyperparameters of the model. Taking the datas of small and medium-sized enterprises in China's A-sharemarket from 2016 to 2020 as the sample, the experimental results show that the enterprise credit evaluationmodel based on cost sensitive XGBoost can improve the identification accuracy of bad credit enterprises whileensuring the overall identification accuracy.Key words：loss function；extreme gradient boosting (XGBoost)；cost sensitivity；enterprise credit evaluation

基于TLS_辅助的长白落叶松一级枝条生物量模型构建

第４７卷㊀第２期２０２３年３月南京林业大学学报（自然科学版）ＪｏｕｒｎａｌｏｆＮａｎｊｉｎｇＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ（ＮａｔｕｒａｌＳｃｉｅｎｃｅｓＥｄｉｔｉｏｎ）Ｖｏｌ．４７，Ｎｏ．２Ｍａｒ．，２０２３㊀收稿日期Ｒｅｃｅｉｖｅｄ：２０２２⁃０４⁃１５㊀㊀㊀㊀修回日期Ａｃｃｅｐｔｅｄ：２０２２⁃０６⁃１３㊀基金项目：国家自然科学基金区域联合基金项目（Ｕ２１Ａ２０２４４）㊂㊀第一作者：唐依人（２９５９０１７５５１＠ｑｑ．ｃｏｍ）㊂∗通信作者：贾炜玮（ｊｉａｗｗ２００２＠１６３．ｃｏｍ），教授㊂㊀引文格式：唐依人，贾炜玮，王帆，等．基于ＴＬＳ辅助的长白落叶松一级枝条生物量模型构建［Ｊ］．南京林业大学学报（自然科学版），２０２３，４７（２）：１３０－１４０．ＴＡＮＧＹＲ，ＪＩＡＷＷ，ＷＡＮＧＦｅｔａｌ．ＣｏｎｓｔｒｕｃｔｉｎｇａｂｉｏｍａｓｓｍｏｄｅｌｏｆＬａｒｉｘｏｌｇｅｎｓｉｓｐｒｉｍａｒｙｂｒａｎｃｈｅｓｂａｓｅｄｏｎＴＬＳ［Ｊ］．ＪｏｕｒｎａｌｏｆＮａｎｊｉｎｇＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ（ＮａｔｕｒａｌＳｃｉｅｎｃｅｓＥｄｉｔｉｏｎ），２０２３，４７（２）：１３０－１４０．ＤＯＩ：１０．１２３０２／ｊ．ｉｓｓｎ．１０００－２００６．２０２２０４０３７．基于ＴＬＳ辅助的长白落叶松一级枝条生物量模型构建唐依人１，贾炜玮１，２∗，王㊀帆１，孙毓蔓１，张㊀颖１（１．东北林业大学林学院，黑龙江㊀哈尔滨㊀１５００４０；２．东北林业大学森林生态系统可持续经营教育部重点实验室，黑龙江㊀哈尔滨㊀１５００４０）摘要：ʌ目的ɔ探究利用地基激光雷达（ｔｅｒｒｅｓｔｒｉａｌｌａｓｅｒｓｃａｎｎｉｎｇ，ＴＬＳ）点云数据估测枝条生物量的可行性，构建预测长白落叶松（黄花落叶松）枝条生物量的最优模型㊂ʌ方法ɔ以利用孟家岗林场２６株长白落叶松点云数据提取出的７３３个一级枝条的特征因子［枝长（ＬＢＬ）㊁弦长（ＬＢＣＬ）㊁基径（ｄＢ）㊁着枝角度（ＡＢ）㊁弓高（ＨＢＡＨ）㊁枝条基部断面积（ＳＢＡＢ）㊁相对着枝深度（ｄＲＤＩＮＣ）］和对应的实测数据为数据源，分别建立枝条水平上的一级枝条生物量基础模型，通过对比基础模型之间的差异来分析利用ＴＬＳ数据建立枝条生物量模型的可行性㊂最后利用ＴＬＳ数据分别对比基础模型㊁混合效应模型和随机森林模型的预测效果㊂ʌ结果ɔ基础模型中最终选定的自变量为ＳＢＡＢ和ＬＢＣＬ㊂利用ＴＬＳ数据建立的枝条生物量基础模型具有更好的预测精度㊂对比３种模型预测能力结果显示，随机森林模型无论在训练集还是测试集上都表现出最好的效果，具体顺序为：随机森林模型＞混合效应模型＞基础模型㊂其中随机森林模型的决定系数（Ｒ２）相较于混合模型和基础模型分别提高了１．３２％和４．８９％，均方根误差（ＲＭＳＥ）分别降低了１１．２３％和１３．６０％㊂ʌ结论ɔ基于ＴＬＳ利用随机森林算法能够准确对枝条生物量进行估测，不仅为随机森林算法在林分生长模型上的应用奠定了一定的实践基础，也为ＴＬＳ在树冠结构研究中的应用提供了重要的参考价值㊂关键词：长白落叶松（黄花落叶松）；点云数据；枝条特征因子；枝条生物量；混合模型；随机森林中图分类号：Ｓ７５８㊀㊀㊀㊀㊀㊀㊀文献标志码：Ａ开放科学（资源服务）标识码（ＯＳＩＤ）：文章编号：１０００－２００６（２０２３）０２－０１３０－１１ＣｏｎｓｔｒｕｃｔｉｎｇａｂｉｏｍａｓｓｍｏｄｅｌｏｆＬａｒｉｘｏｌｇｅｎｓｉｓｐｒｉｍａｒｙｂｒａｎｃｈｅｓｂａｓｅｄｏｎＴＬＳＴＡＮＧＹｉｒｅｎ１，ＪＩＡＷｅｉｗｅｉ１，２∗，ＷＡＮＧＦａｎ１，ＳＵＮＹｕｍａｎ１，ＺＨＡＮＧＹｉｎｇ１（１．ＳｃｈｏｏｌｏｆＦｏｒｅｓｔｒｙ，ＮｏｒｔｈｅａｓｔＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ，Ｈａｒｂｉｎ１５００４０，Ｃｈｉｎａ；２．ＫｅｙＬａｂｏｒａｔｏｒｙｏｆＳｕｓｔａｉｎａｂｌｅＦｏｒｅｓｔＥｃｏｓｙｓｔｅｍＭａｎａｇｅｍｅｎｔ，ＭｉｎｉｓｔｒｙｏｆＥｄｕｃａｔｉｏｎ，ＮｏｒｔｈｅａｓｔＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ，Ｈａｒｂｉｎ１５００４０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：ʌＯｂｊｅｃｔｉｖｅɔＴｏｅｘｐｌｏｒｅｔｈｅｆｅａｓｉｂｉｌｉｔｙｏｆｕｓｉｎｇｔｅｒｒｅｓｔｒｉａｌｌａｓｅｒｓｃａｎｎｉｎｇ（ＴＬＳ）ｐｏｉｎｔｃｌｏｕｄｄａｔａｔｏｅｓｔｉｍａｔｅｂｒａｎｃｈｂｉｏｍａｓｓａｎｄｆｉｎｄｔｈｅｏｐｔｉｍｕｍｍｏｄｅｌｔｏｐｒｅｄｉｃｔｔｈｅｂｒａｎｃｈｂｉｏｍａｓｓｏｆＬａｒｉｘｏｌｇｅｎｓｉｓ．ʌＭｅｔｈｏｄɔＴｈｅｃｈａｒａｃｔｅｒｉｓｔｉｃｆａｃｔｏｒｓ（ｂｒａｎｃｈｌｅｎｇｔｈ（ＬＢＬ），ｂｒａｎｃｈｃｈｏｒｄｌｅｎｇｔｈ（ＬＢＣＬ），ｂｒａｎｃｈｄｉａｍｅｔｅｒ（ｄＢ），ｂｒａｎｃｈａｎｇｌｅ（ＡＢ），ｂｒａｎｃｈａｒｃｈｈｅｉｇｈｔ（ＨＢＡＨ），ｂａｓａｌａｒｅａｏｆｂｒａｎｃｈｅｓ（ＳＢＡＢ），ａｎｄｒｅｌａｔｉｖｅｄｅｐｔｈｗｉｔｈｉｎｔｈｅｃｒｏｗｎ（ｄＲＤＩＮＣ））ｏｆ７３３ｆｉｒｓｔ⁃ｏｒｄｅｒｂｒａｎｃｈｅｓｅｘｔｒａｃｔｅｄｕｓｉｎｇｐｏｉｎｔｃｌｏｕｄｄａｔａｏｆ２６ａｒｔｉｆｉｃｉａｌｌａｒｃｈｐｌａｎｔｓａｎｄｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇｍｅａｓｕｒｅｄｄａｔａｆｒｏｍＭｅｎｇｊｉａｇａｎｇＦｏｒｅｓｔｒｙＦａｒｍｗｅｒｅｕｓｅｄａｓｄａｔａｓｏｕｒｃｅｓｔｏｅｓｔａｂｌｉｓｈｆｉｒｓｔ⁃ｌｅｖｅｌｂｒａｎｃｈｂｉｏｍａｓｓｂａｓｅｍｏｄｅｌｓａｔｔｈｅｂｒａｎｃｈｌｅｖｅｌ．Ａｄｄｉｔｉｏｎａｌｌｙ，ｔｈｅｆｅａｓｉｂｉｌｉｔｙｏｆｕｓｉｎｇＴＬＳｄａｔａｔｏｅｓｔａｂｌｉｓｈｂｒａｎｃｈｂｉｏｍａｓｓｍｏｄｅｌｓｂｙｃｏｍｐａｒｉｎｇｔｈｅｄｉｆｆｅｒｅｎｃｅｓｂｅｔｗｅｅｎｂａｓｅｍｏｄｅｌｓｗｅｒｅａｎａｌｙｚｅｄ．Ｆｉｎａｌｌｙ，ｔｈｅｐｒｅｄｉｃｔｉｏｎｅｆｆｅｃｔｓｏｆｔｈｅｂａｓｅｍｏｄｅｌ，ｍｉｘｅｄ⁃ｅｆｆｅｃｔｓｍｏｄｅｌ，ａｎｄｒａｎｄｏｍｆｏｒｅｓｔｍｏｄｅｌｗｅｒｅｃｏｍｐａｒｅｄｓｅｐａｒａｔｅｌｙｕｓｉｎｇＴＬＳｄａｔａ．ʌＲｅｓｕｌｔɔＴｈｅｉｎｄｅｐｅｎｄｅｎｔｖａｒｉａｂｌｅｓｓｅｌｅｃｔｅｄｉｎｔｈｅｂａｓｅｍｏｄｅｌｗｅｒｅＳＢＡＢａｎｄＬＢＣＬ．ＵｓｉｎｇＴＬＳｄａｔａｔｏｂｕｉｌｄｔｈｅｂｒａｎｃｈｂｉｏｍａｓｓｂａｓｅｍｏｄｅｌｈａｄａｂｅｔｔｅｒｐｒｅｄｉｃｔｉｏｎａｃｃｕｒａｃｙ．Ｃｏｍｐａｒｉｎｇｔｈｅｒｅｓｕｌｔｓｏｆｔｈｅｔｈｒｅｅｍｏｄｅｌｓｓｈｏｗｅｄｔｈａｔｔｈｅｒａｎｄｏｍｆｏｒｅｓｔｍｏｄｅｌｓｈｏｗｅｄｔｈｅｂｅｓｔｒｅｓｕｌｔｓｂｏｔｈｏｎｔｈｅｔｒａｉｎｉｎｇａｎｄｔｅｓｔ㊀第２期唐依人，等：基于ＴＬＳ辅助的长白落叶松一级枝条生物量模型构建ｓｅｔｓ，ｉｎｔｈｅｆｏｌｌｏｗｉｎｇｏｒｄｅｒ：ｒａｎｄｏｍｆｏｒｅｓｔｍｏｄｅｌ＞ｍｉｘｅｄ⁃ｅｆｆｅｃｔｓｍｏｄｅｌ＞ｂａｓｅｍｏｄｅｌ．ＴｈｅＲ２ｏｆｔｈｅｒａｎｄｏｍｆｏｒｅｓｔｍｏｄｅｌｉｍｐｒｏｖｅｄｂｙ１．３２％ａｎｄ４．８９％，ａｎｄｔｈｅＲＭＳＥｄｅｃｒｅａｓｅｄｂｙ１１．２３％ａｎｄ１３．６０％，ｒｅｓｐｅｃｔｉｖｅｌｙ，ｃｏｍｐａｒｅｄｔｏｔｈｅｍｉｘｅｄｍｏｄｅｌａｎｄｔｈｅｂａｓｅｍｏｄｅｌ．ʌＣｏｎｃｌｕｓｉｏｎɔＴｈｅｒｅｓｕｌｔｓｏｆｔｈｉｓｐａｐｅｒｐｒｏｖｅｄｔｈａｔｔｈｅｂｒａｎｃｈｂｉｏｍａｓｓｃａｎｂｅｅｓｔｉｍａｔｅｄａｃｃｕｒａｔｅｌｙｂａｓｅｄｏｎＴＬＳｕｓｉｎｇｔｈｅｒａｎｄｏｍｆｏｒｅｓｔａｌｇｏｒｉｔｈｍ，ｗｈｉｃｈｎｏｔｏｎｌｙｌａｉｄａｐｒａｃｔｉｃａｌｆｏｕｎｄａｔｉｏｎｆｏｒｔｈｅａｐｐｌｉｃａｔｉｏｎｏｆｔｈｅｒａｎｄｏｍｆｏｒｅｓｔａｌｇｏｒｉｔｈｍｏｎｓｔａｎｄｇｒｏｗｔｈｍｏｄｅｌｓ，ｂｕｔａｌｓｏｐｒｏｖｉｄｅｄａｎｉｍｐｏｒｔａｎｔｒｅｆｅｒｅｎｃｅｖａｌｕｅｆｏｒｔｈｅａｐｐｌｉｃａｔｉｏｎｏｆＴＬＳｉｎｔｈｅｓｔｕｄｙｏｆｃｒｏｗｎｓｔｒｕｃｔｕｒｅ．Ｋｅｙｗｏｒｄｓ：Ｌａｒｉｘｏｌｇｅｎｓｉｓ；ｐｏｉｎｔｃｌｏｕｄｄａｔａ；ｂｒａｎｃｈｃｈａｒａｃｔｅｒｉｚａｔｉｏｎｆａｃｔｏｒ；ｂｒａｎｃｈｂｉｏｍａｓｓ；ｍｉｘｅｄ⁃ｅｆｆｅｃｔｓｍｏｄｅｌ；ｒａｎｄｏｍｆｏｒｅｓｔ㊀㊀树木生物量的估计对于模拟林分的总初级生产和理解森林在全球碳循环中的作用至关重要，能否对森林生物量进行准确估计是森林经营管理与评价过程中的关键一环［１］㊂树枝生物量是树木地上生物量的重要组成部分，可以帮助反映气候变化如何影响碳分配模式［２］㊂另一方面，单个树枝可以反映树冠生物量的垂直分布，或通过节子对木材质量产生影响［３－４］，这对于确定采伐作业和优化可持续森林管理的疏伐战略至关重要㊂传统上，建立和模拟树木结构㊁生物量和生长需要进行破坏性测量㊂由于野外工作费时费力，地面激光扫描（ｔｅｒ⁃ｒｅｓｔｒｉａｌｌａｓｅｒｓｃａｎｎｉｎｇ，ＴＬＳ）为快速㊁无损地测量树木结构提供了一种解决方案㊂已有研究表明，利用ＴＬＳ可以成功地获取各种树木结构变量，在弥补森林研究中破坏性测量的缺点方面显示出巨大的潜力［５－１０］㊂以往的研究都是采用模型估计法，即通过异速生长或基于理论方程估计森林生物量，这些方程的变量可以从容易测量的因子（如胸径㊁树高㊁冠长）中推导得出［１１－１４］，能有效估测森林生态系统内的生物量和生产力㊂有研究者采用模型估计法进行了枝条生物量的预测［１５－１６］，这些学者主要采用胸径和树高因子为自变量研究枝条生物量，模型预测精度通常较低㊂因此，开始关注构建枝条水平上的高精度枝条生物量模型研究［１，１７］，并进行混合模型技术的应用［１８－２０］㊂在枝条水平上建立的枝条生物量模型预测精度明显提高，但是往往需要通过破坏性手段来获取所需要的枝条因子，而ＴＬＳ的出现完美弥补了这一缺点，使得无损高效测量树木生物量成为可能㊂一些研究者基于异速生长模型与ＴＬＳ衍生出的参数来进行枝条生物量的无损估计［２１－２２］，或者使用从树木定量结构模型（ＴｒｅｅＱＳＭｓ）得到的枝条体积乘以枝条木材密度来获取枝条生物量［２３－２４］㊂这两种估测方法只能在单木水平上估计总体枝条的生物量，而对于单个分枝的生物量估计，目前还鲜有报道㊂线性㊁非线性㊁混合模型［１，１７，２５］等传统的参数模型在森林生物量的研究中已被广泛应用㊂但是，参数模型在使用时往往需满足一些基本的统计假设条件，例如数据需符合正态分布㊁等方差等；由于林木生长数据需要进行连续观测，通常难以满足以上条件［２６］，因此必须寻找新的方法㊂随机森林是基于集成学习的决策树模型［２７］，这种决策树模型能有效处理各种类型（如分类㊁连续和偏态）的预测变量，不需要对数据进行任何形式的分布假设，还能很好地克服数据中可能存在的噪音㊁缺失㊁异方差和共线性等问题［２８］，已成为一种主流的非参数模型㊂目前，随机森林法已用于分析林木生长的适应性［２９］㊁林木生物量转换和扩展因子的影响因素［３０］，并在预测单木胸径生长［３１］㊁森林蓄积量［３２］方面有了很好的应用㊂综合以上分析可知，目前基于ＴＬＳ数据建立的枝条生物量模型主要是单木水平上的总体枝条生物量；利用随机森林模型预测枝条生物量的研究目前还未见报道㊂鉴于此，本研究以利用ＴＬＳ数据提取的７３３个一级枝条的特征因子及其对应的实测数据为数据源，分析对比两种数据类型下基础模型之间的差异，证明利用ＴＬＳ数据构建枝条生物量模型的可行性㊂随后采用混合模型技术建立预测单个分枝生物量的传统数学模型，采用随机森林算法建立估测单个分枝生物量的新型机器学习模型㊂对比分析传统数学模型与新型机器学习模型的优劣性，找出精确估测单个分枝生物量的最优模型㊂１㊀材料与方法１．１㊀研究区概况研究区位于黑龙江省佳木斯市孟家岗镇林场境内（１３０ʎ３２ᶄ １３０ʎ５２ᶄＥ，４６ʎ２０ᶄ ４６ʎ３０ᶄＮ）㊂孟家岗林场属完达山西麓余脉，主要地貌为低山丘陵；坡度１０ʎ ２０ʎ，平均海拔２５０ｍ，主要属于东亚大陆性季风气候，春季降雨量少；秋季易产生霜冻；夏季短暂，雨量充足；冬季漫长，寒冷干燥㊂最高温与最低温分别约３５．６ħ和－３４．７ħ，年均温度１３１南京林业大学学报（自然科学版）第４７卷２．７ħ左右；无霜期１２０ｄ，年均降水量５５０６７０ｍｍ㊂林场内主要土壤类型是典型暗棕壤，还分布着少量草甸暗棕壤㊁潜育暗棕壤和原始暗棕壤等；此外还存在着草甸土㊁沼泽土，以及泥炭土㊂林场内人工林面积约占林分总面积的２／３，天然次生林面积约为１／３，森林覆盖率为８１．７％㊂１．２㊀数据来源本研究所使用的数据于２０１９年１１月在孟家岗林场进行采集，主要包括地基激光雷达扫描数据和伐倒解析木的地面实测数据㊂枝条生物量采集过程：在孟家岗林场的６块黄花落叶松（Ｌａｒｉｘｏｌｇｅｎｓｉｓ，俗名长白落叶松）人工林标准样地中按等断面积法将树木分成５个等级，每个等级分别选出１株树木用来进行枝条解析，共选出３０株解析木㊂解析木伐倒后对各轮的一级枝条编号，在每轮中再选取１个长势均匀的枝条作为标准枝条，测量该枝条的鲜质量，然后对所有标准枝条进行取样，用烘箱在１０５ħ条件下对样品进行烘干㊂最后利用各标准枝条的鲜质量与干质量推导计算出解析木各枝条的生物量（Ｗｂ）㊂有４株解析木由于树冠遮挡严重导致点云质量较差，将该数据剔除，最终在２６株解析木上进行了枝条因子的提取，包括枝长（ＬＢＬ）㊁基径（ｄＢ）㊁弦长（ＬＢＣＬ）㊁着枝角度（ＡＢ）㊁弓高（ＨＢＡＨ）和着枝高度（ＨＢＨ），通过与实测数据进行对比，结果显示ＬＢＬ㊁ＬＢＣＬ㊁ｄＢ㊁ＡＢ㊁ＨＢＡＨ㊁ＨＢＨ平均提取精度分别为：９０％㊁９０６％㊁７１５％㊁８２５％㊁７０７％㊁９８６％㊂枝条因子提取示意图如图１，具体提取方法参见文献［９］㊂本研究根据上述因子额外计算了相对着枝深度（ｄＲＤＩＮＣ）和枝条基部断面积（ＳＢＡＢ）㊂ｄＲＤＩＮＣ＝（Ｈ－ＨＢＨ）／ｌ；（１）ＳＢＡＢ＝π㊃（ｄＢ／２）２㊂（２）式中：Ｈ为树高，ｌ为冠长㊂对数据进行整理，剔除异常值之后最终获得２６株单木的７３３个枝条的特征因子㊂按照随机抽样的方式以４ʒ１的比例分为训练集和测试集，具体数据见表１㊂表１㊀单木因子与枝条因子统计表Ｔａｂｌｅ１㊀Ｔｈｅｓｔａｔｉｓｔｉｃａｌｔａｂｌｅｏｆｔｒｅｅｆａｃｔｏｒａｎｄｂｒａｎｃｈｆａｃｔｏｒｓ数据ｄａｔａ变量ｖａｒｉａｂｌｅ训练集ｔｒａｉｎ测试集ｔｅｓｔ平均值ｍｅａｎ最大值ｍａｘ最小值ｍｉｎ标准差ＳＤ平均值ｍｅａｎ最大值ｍａｘ最小值ｍｉｎ标准差ＳＤＴＬＳ数据ＴＬＳｄａｔａ单木因子ｔｒｅｅｆａｃｔｏｒｎ＝２０ｎ＝６树高／ｍ（Ｈ）１８．６９２５．８２１３．１２３．８５１９．７４２３．０５１４．０５３．５６胸径／ｃｍ（ＤＢＨ）１９．２２３１．１０９．０６５．８１１８．３１２６．３５１２．３２５．５３枝条因子ｂｒａｎｃｈｆａｃｔｏｒｎ＝６０１ｎ＝１３２枝长／ｃｍ（ＬＢＬ）２１７．４０５２５．００１５．８０９１．２８１９８．７１５３０．５９１７．８７９３．５４弦长／ｃｍ（ＬＢＣＬ）２０１．２０４９３．００１４．８０８４．２１１８６．１９５００．３０１５．０３８５．１５弓高／ｃｍ（ＨＢＡＨ）２６．００８０．０００．００１２．９４１９．９７７８．４３１．００１４．８０基径／ｍｍ（ｄＢ）２６．６０６９．４９１１．１０１３．１５２８．１０６１．５６１２．００１３．０２枝条基部断面积／ｃｍ２（ＳＢＡＢ）６．８１３７．９３１．０４８．０５７．５２２９．７６１．１４７．１４着枝角度／（ʎ）（ＡＢ）６０．００１５０．００１５．００１６．０２５３．００１０４．００１９．００１５．００相对着枝深度（ｄＲＤＩＮＣ）０．６１１．０００．１００．２００．６２１．０００．１００．２０实测数据ｒｅａｌｄａｔａ单木因子ｔｒｅｅｆａｃｔｏｒｎ＝２０ｎ＝６树高／ｍ（Ｈ）１８．７５２６．００１３．１７３．９２１９．６０２３．２２１３．９８３．２６胸径／ｃｍ（ＤＢＨ）１９．４０３１．００９．００５．４９１８．５８２６．１２１２．０８５．１３枝条因子ｂｒａｎｃｈｆａｃｔｏｒｎ＝６０１ｎ＝１３２枝长／ｃｍ（ＬＢＬ）２１０．００５３２．００１０．００９９．５１１８２．００５１５．００１３．００９２．１８弦长／ｃｍ（ＬＢＣＬ）２００．００５１８．００８８２．００１８０．００４９６．００１０．００８３．００弓高／ｃｍ（ＨＢＡＨ）２３．００７０．０００．００１２．００１９．００８１．００１．００１５．００基径／ｍｍ（ｄＢ）２７．３２７０．１２６．２８１４．５５２９．４８６５．７４８．５１１３．７４枝条基部断面积／ｃｍ２（ＳＢＡＢ）７．０３３８．０９０．８５８．８８７．７３３１．２９０．９２７．８５着枝角度／（ʎ）（ＡＢ）５６．００１３５．００１０．００１８．００５９．００１１５．００１６．００１７．００相对着枝深度（ｄＲＤＩＮＣ）０．６２１．０００．１４０．２１０．６２１．０００．１１０．２０枝条生物量／ｇ（Ｗｂ）４１６．９３４３０３．３２３．２６５３９．９７４６０．３４３０７５．５９４．７１５７２．８８２３１㊀第２期唐依人，等：基于ＴＬＳ辅助的长白落叶松一级枝条生物量模型构建Ａ．枝长ｂｒａｎｃｈｌｅｎｇｔｈ；Ｂ．弦长ｂｒａｎｃｈｃｈｏｒｄｌｅｎｇｔｈ；Ｃ．弓高ｂｒａｎｃｈａｒｃｈｈｅｉｇｈｔ；Ｄ．着枝角度ｂｒａｎｃｈａｎｇｌｅ；Ｅ．基径ｂｒａｎｃｈｄｉａｍｅｔｅｒ㊂图１㊀提取枝条因子示意图Ｆｉｇ．１㊀Ｔｈｅｄｉａｇｒａｍｏｆｅｘｔｒａｃｔｉｎｇｂｒａｎｃｈｆａｃｔｏｒｓ１．３㊀基础模型根据以往的研究，枝条生物量与枝条因子之间存在着密切的联系［１，１７］，因此本研究决定通过分析枝条因子与枝条生物量之间的相关性，并考虑各因子之间的共线性问题，选择相关性最高且无共线性的枝条因子作为自变量，进行枝条生物量基础模型的构建㊂模型形式如下：Ｗｂ＝ａ１ｘａ２１ｘａ３２ｘａｎ＋１ｎ㊂（３）式中：Ｗｂ代表枝条生物量；ｘ１，ｘ２，．．．，ｘｎ代表枝条因子；ａ１，ａ２，．．．，ａｎ＋１代表方程参数㊂１．４㊀混合模型混合效应模型是一种新的统计方法，模型中分为固定效应和随机效应两部分，其中固定效应用来描述样本总体的趋势，而随机效应用来描述总体样本中的个体变化，因此混合效应模型拥有十分灵活的优点㊂为了研究单木对枝条生物量的随机干扰，本研究在方程（３）的基础上加入随机效应建立样木水平的枝条生物量非线性混合模型，具体的模型形式如下所示：㊀Ｗｉｊ＝ｆ（δｉｊ，ｖｉｊ）＋εｉｊ，ｉ＝１，，Ｍ，ｊ＝１，，ｎｉ；δｉｊ＝Ａｉｊχ＋Ｂｉｊβｉ；βｉＮ（０，Ｄ），εｉｊＮ（０，σ２Ｒｉ）；Ｒｉ＝σ２Ｇ０．５ｉΓｉＧ０．５ｉ㊂ìîíïïïïïï（４）式中：Ｗｉｊ表示第ｉ株样木中第ｊ个枝条的生物量观测值；ｖｉｊ为函数ｆ的自变量；εｉｊ是模型的误差项；Ｍ代表划分的组别即样木数量；ｎｉ代表各组内的观测值数量；Ａｉｊ㊁Ｂｉｊ为已知的设计矩阵；βｉ为（ｑˑ１）维随机效应向量；χ为（ｐˑ１）维固定效应向量；Ｄ为随机效应的方差⁃协方差矩阵；σ２是方差；Ｇｉ为描述方差异质性的对角矩阵；Ｒｉ为分组内方差⁃协方差矩阵；Γｉ是样木内误差的相关性结构㊂构建混合效应模型首先需要确定参数效应，本研究利用赤池信息准则（ＡＩＣ）㊁对数似然值（ＬｏｇＬｉｋｅｌｉｌｏｏｄ）㊁贝叶斯准则（ＢＩＣ）作为评价指标，将所有可能的参数组合作为随机效应对模型进行拟合㊂ＡＩＣ与ＢＩＣ越小，对数似然值越大，模型的拟合效果越好㊂同时对参数个数不同的模型进行似然比（ＬＲＴ）检验，以避免模型过参数化，最后选择参数少而显著性好的模型作为最优模型㊂随机效应方差⁃协方差矩阵能反映个体随机效应间的差异，例如引入样木层次的随机效应，体现的是样木间的差异㊂从复合对称矩阵（ＣＳ）㊁对角矩阵［ＵＮ（１）］和广义正定矩阵（ＵＮ）中进行选择，将ＡＩＣ㊁ＢＩＣ值最小和对数似然值最大时的矩阵作为最优矩阵形式㊂从一阶自回归结构［ＡＲ（１）］㊁一阶自回归与移动平均结构［ＡＲＭＡ（１，１）］和复合对称矩阵（ＣＳ）中来选择最佳误差项方差⁃协方差矩阵㊂为了解决生物量模型中普遍存在的异方差问题，本研究采用指数函数对其进行校正［１９］㊂混合模型的建立是基于Ｒ软件的ｎｌｍｅ包完成的㊂１．５㊀随机森林回归模型随机森林（ＲａｎｄｏｍＦｏｒｅｓｔ，ＲＦ）是以决策树为基学习器的集成式算法㊂利用有放回的随机重采样方式构造出一系列的基学习器（如ｎ个），这一系列的决策树即构成了森林，最后将这些基学习器预测的结果组合起来进行输出㊂在构建基学习器的过程中，ＲＦ通过节点分裂从全部Ｑ个变量中随机选择ｍ个（１ɤｍɤＱ），再从ｍ中找出最优的划分变量作为分裂节点㊂对于回归问题，ＲＦ模型将所有决策树预测得到的结果进行加权平均来输出最终的结果［３１］㊂在每次抽样过程中约有１／３的样本未被选中，这部分样本称为袋外数据（ｏｕｔ⁃ｏｆ⁃ｂａｇ，ＯＯＢ），利用这些样本计算可得袋外错误率（ＯＯＢｅｒｒｏｒｒａｔｅ）㊂为避免训练出的模型出现过拟合的现象，可以利用袋外错误率验证模型的泛化能力㊂ＲＦ模型可以通过提供自变量的相对重要性以及因变量受自变量影响的偏依赖图来提高ＲＦ模型的可解释性㊂通过偏依赖图有助于将因变量对自变量的依赖关系进行可视化㊂在此需要强调，计算依赖关系时不能忽略其他变量对因变量的影响，应该考虑所有变量对因变量影响的平均效果㊂本研究以７个枝条因子（ＬＢＬ㊁ＬＢＣＬ㊁ＨＢＡＨ㊁ｄＢ㊁ＳＢＡＢ㊁ＡＢ㊁ｄＲＤＩＮＣ）和２个单木因子（ＤＢＨ㊁Ｈ）为自变量，采用随机森林回归算法构建人工长白落叶松枝条生物量预测模型㊂在ＲＦ模型的构建过程中，超参数的设置十分重要，本研究采用Ｐｙｔｈｏｎ软件３３１南京林业大学学报（自然科学版）第４７卷ｓｋｌｅａｒｎ库中的ＲａｎｄｏｍｉｚｅｄＳｅａｒｃｈＣＶ和ＧｒｉｄＳｅａｒｃｈＣＶ函数对ＲＦ算法中比较重要的４个超参数进行自动寻优：决策树个数（ｎ＿ｅｓｔｉｍａｔｏｒｓ）㊁最小分离样本数（ｍｉｎ＿ｓａｍｐｌｅｓ＿ｓｐｌｉｔ）㊁最小叶子节点样本数（ｍｉｎ＿ｓａｍｐｌｅｓ＿ｌｅａｆ）㊁最大分离特征数（ｍａｘ＿ｆｅａｔｕｒｅｓ），超参数的自动寻优过程基于全部的训练集㊂寻优结束后利用最优模型做出自变量对因变量影响的相对重要性和偏依赖关系图㊂１．６㊀模型检验与评价本研究在独立的测试集上进行模型拟合和预测能力的评价，评价指标为决定系数（Ｒ２）㊁平均相对偏差绝对值（ＲＭＡＥ）㊁均方根误差（ＲＭＳＥ）㊁预估精度（Ｆｐ）和平均绝对偏差（ＭＡＥ）等㊂各指标公式如下所示：决定系数（Ｒ２）Ｒ２＝１－ðｎｉ＝１（ｙｉ－ｙ＾ｉ）２ðｎｉ＝１（ｙｉ－ｙ－ｉ）２éëêêùûúú；（５）均方根误差［ＲＭＳＥ，式中记为σ（ＲＭＳＥ）］σ（ＲＭＳＥ）＝ðｎｉ＝１（ｙｉ－ｙ＾ｉ）２ｎ－ｐ；（６）平均绝对偏差［ＭＡＥ，式中记为σ（ＭＡＥ）］σ（ＭＡＥ）＝ðｎｉ＝１ｙｉ－ｙ＾ｉｎ；（７）平均相对偏差绝对值［ＲＭＡＥ，式中记为σ（ＲＭＡＥ）］σ（ＲＭＡＥ）＝１ｎðｎｉ＝１ｙｉ－ｙ＾ｉｙｉˑ１００％；（８）预估精度（Ｆｐ）Ｆｐ＝１－ｔ０．０５ｙｉ㊃ð（ｙｉ－ｙ＾）２ｎ（ｎ－ｐ）æèççöø÷÷ˑ１００％㊂（９）式中：ｙｉ为观测值；ｙ＾为预测值；ｎ为样本个数；ｙｉ为所有观测值的平均值；ｐ为模型参数个数㊂非线性混合模型中的固定效应部分可以采用传统方式进行检验，而随机效应参数的计算需利用下述公式［１］㊂β＾ｋ＝Ｄ＾Ｚ＾Ｔｋ（Ｚ＾ｋＤ＾Ｚ＾Ｔｋ＋Ｒ＾ｋ）－１ε＾ｋ㊂（１０）式中：β＾ｋ为随机效应参数；Ｄ＾为随机效应参数的方差⁃协方差矩阵；Ｚ＾ｋ为设计矩阵；Ｒ＾ｋ为组内方差⁃协方差矩阵；ε＾ｋ是观测值与固定效应参数计算的预测值的差值㊂２㊀结果与分析２．１㊀基础模型的建立枝条生物量与枝条特征因子之间的相关性结果如图２所示㊂图２㊀枝条生物量与枝条因子相关性热图Ｆｉｇ．２㊀Ｔｈｅｈｅａｔｍａｐｏｆｃｏｒｒｅｌａｔｉｏｎｂｅｔｗｅｅｎｂｒａｎｃｈｂｉｏｍａｓｓａｎｄｂｒａｎｃｈｆａｃｔｏｒ㊀㊀从图２中可以看出两种数据类型下都显示ＳＢＡＢ㊁ｄＢ㊁ＬＢＣＬ和ＬＢＬ与枝条生物量的相关性最高，但同时引入这４个因子会造成模型难以收敛的问题，并且ＳＢＡＢ和ｄＢ㊁ＬＢＣＬ和ＬＢＬ之间分别存在明显的共线性，因此本研究最终选择了枝条基部断面积（ＳＢＡＢ）和弦长（ＬＢＣＬ）两个因子作为枝条生物量建模的自变量㊂模型的拟合结果见表２，模型的最终表达式如式（１１）㊁（１２）所示㊂从表２中可以看出两种数据类型下模型参数的预测值十分接近，利用ＴＬＳ数据构建的基础模型具有更好的拟合优度与预测精度㊂因此可以利用ＴＬＳ数据对枝条生物量模型进行更加深入的研究㊂Ｗｂ实＝０．０６９７７㊃Ｓ０．７２０１４ＢＡＢ㊃Ｌ１．３５０２６ＢＣＬ；（１１）ＷｂＴＬＳ＝０．０４９５６㊃Ｓ０．７８８７１ＢＡＢ㊃Ｌ１．３４２０１ＢＣＬ㊂（１２）式中：Ｗｂ实和ＷｂＴＬＳ分别代表枝条的实测生物量和基于ＴＬＳ计算的生物量；ＳＢＡＢ代表枝条基部断面积；ＬＢＣＬ代表弦长㊂４３１㊀第２期唐依人，等：基于ＴＬＳ辅助的长白落叶松一级枝条生物量模型构建表２㊀基础模型的拟合与检验结果Ｔａｂｌｅ２㊀Ｔｈｅｆｉｔｔｉｎｇａｎｄｔｅｓｔｒｅｓｕｌｔｓｏｆｂａｓｅｍｏｄｅｌ数据ｄａｔａ参数ｐａｒａｍｅｔｅｒ预测值ｅｓｔｉｍａｔｅ标准误ＳＥｔＰ拟合优度ｇｏｏｄｎｅｓｓ⁃ｏｆ⁃ｆｉｔｓｔａｔｉｓｔｉｃ检验结果ｖａｌｉｄａｔｉｏｎｒｅｓｕｌｔＲ２ＲＭＳＥ／ｇＭＡＥ／ｇＲＭＡＥ／％Ｆｐ／％实测数据ｒｅａｌｄａｔａａ００．０６９７７０．０２５７７９．９５１＜０．０００１ａ１０．７２０１４０．０３４７４１５．１８４＜０．０００１０．８４９６１７１．７９９７．６６３９．５６９５．７１ａ２１．３５０２６０．０８４０６１２．９７５＜０．０００１ＴＬＳ数据ＴＬＳｄａｔａａ００．０４９５６０．０１７０１１２．９１４＜０．０００１ａ１０．７８８７１０．０３３２７２３．７０８＜０．０００１０．８８０８１５６．９３９０．０７３５．６６９６．８４ａ２１．３４２０１０．０６９３１１９．３６３＜０．０００１２．２㊀枝条生物量非线性混合模型的建立２．２．１㊀随机参数的确定以公式（１２）为基础模型，利用Ｒ软件的ｎｌｍｅ包对公式（１２）不同随机效应参数组合形式进行了拟合㊂利用ＡＩＣ㊁ＢＩＣ㊁ＬｏｇＬｉｋｅｌｉｈｏｏｄ㊁Ｒ２对各模型的拟合优度进行对比，选出最佳的随机参数组合形式㊂同时，对模型（１２）㊁模型（１２．２）和模型（１２．６）进行似然比（ＬＲＴ）检验，避免模型出现过参数化的问题，当Ｐ＜０．０５时表示模型间差异显著㊂具体拟合结果见表３㊂表３㊀基于不同随机效应参数组合的枝条ＡＧＢ模型拟合结果Ｔａｂｌｅ３㊀ＦｉｔｔｉｎｇｒｅｓｕｌｔｓｏｆＡＧＢｍｏｄｅｌｆｏｒｂｒａｎｃｈｅｓｂａｓｅｄｏｎｄｉｆｆｅｒｅｎｔｃｏｍｂｉｎａｔｉｏｎｓｏｆｒａｎｄｏｍｅｆｆｅｃｔｐａｒａｍｅｔｅｒｓ模型ｍｏｄｅｌ随机效应参数ｒａｎｄｏｍｅｆｆｅｃｔｐａｒａｍｅｔｅｒ参数个数ｎｕｍｂｅｒｏｆｐａｒａｍｅｔｅｒＲ２赤池信息准则ＡＩＣ贝叶斯准则ＢＩＣ对数似然值ＬｏｇＬｉｋｅｌｉｈｏｏｄ似然比ＬＲＴＰ１２无３０．８７９８４５５．５６２８５０９．３７８－４２１７．５６１２．１ａ０５０．８８７８４３３．５８８８４５５．８２５－４２１１．７９１２．２ａ１５０．９０４８３６４．２９０８３８６．５２７－４１７７．１５６６．０４４＜０．０００１１２．３ａ２５０．９０４８３６７．５４４８３８９．７８０－４１７８．７７１２．４ａ０㊁ａ１７０．９０５８４３７．５８８８４６８．７１９－４２１１．７９１２．５ａ０㊁ａ２７０．９０４８３７１．５４４８４０２．６７５－４１７８．７７１２．６ａ１㊁ａ２７０．９１３８３３８．７４１８３６９．８７２－４１６２．３７２９．５４９＜０．０００１１２．７ａ０㊁ａ１㊁ａ２１０不收敛㊀㊀从表３中可知，加入混合效应之后，模型的ＡＩＣ和ＢＩＣ相较于基础模型（１２）均有所降低，Ｒ２有所提高，说明混合模型的拟合效果更佳㊂当随机效应参数个数为１时，模型（１２．２）的拟合效果明显优于模型（１２．３）和模型（１２．１）；当随机效应参数个数为２时，模型（１２６）的拟合效果明显优于模型（１２．４）和模型（１２．５）；当随机效应参数个数为３时，模型（１２７）不收敛㊂模型的ＬＲＴ检验结果表明：基础模型（１２）和模型（１２．２）之间差异极显著；模型（１２．２）和模型（１２．６）之间差异极显著，并且模型（１２．６）的Ｒ２和ＬｏｇＬｉｋｅｌｉｈｏｏｄ最高，ＡＩＣ和ＢＩＣ最低，因此将模型（１２．６）作为枝条生物量的最优非线性混合模型㊂２．２．２㊀方差⁃协方差矩阵的确定在模型（１２．６）的基础上分析对角矩阵ＵＮ（１）㊁复合对称矩阵ＣＳ和广义正定矩阵对混合模型拟合效果的差异，见表４㊂根据表４可知，以复合对称结构ＣＳ作为随机效应方差⁃协方差矩阵时模型不收敛，而广义正定矩阵显示了最好的拟合效果，并且与对角矩阵ＵＮ（１）显示出显著的差异，因此将广义正定矩阵作为模型（１２．６）的最佳随机效应方差⁃协方差矩阵㊂将林业上常用的３种自相关结构矩阵引入混合模型（１２．６），结果见表４㊂从表中可以看出：复合对称矩阵ＣＳ依然不收敛；一阶自回归矩阵ＡＲ（１）和一阶自回归与移动平均矩阵ＡＲＭＡ（１，１）虽然收敛，但是两者之间的差异并不显著，且模型的拟合优度并无明显提升，因此可以不考虑模型（１２６）误差项的方差⁃协方差结构㊂５３１南京林业大学学报（自然科学版）第４７卷表４㊀不同随机效应方差⁃协方差矩阵和自相关结构矩阵混合模型拟合结果比较Ｔａｂｌｅ４㊀Ｃｏｍｐａｒｉｓｏｎｓｏｆｆｉｔｔｉｎｇｒｅｓｕｌｔｓｏｆｄｉｆｆｅｒｅｎｔｒａｎｄｏｍｅｆｆｅｃｔｓｖａｒｉａｎｃｅ⁃ｃｏｖａｒｉａｎｃｅｍａｔｒｉｘａｎｄａｕｔｏｃｏｒｒｅｌａｔｉｏｎｓｔｒｕｃｔｕｒｅｍｉｘｅｄ⁃ｅｆｆｅｃｔｓｍｏｄｅｌｓ类型ｔｙｐｅ矩阵ｍａｔｒｉｘ参数个数ｐａｒａｍｅｔｅｒｓｎｕｍｂｅｒ赤池信息准则ＡＩＣ贝叶斯准则ＢＩＣ对数似然值ＬｏｇＬｉｋｅｌｉｈｏｏｄ似然比ＬＲＴＰ方差⁃协方差ｖａｒｉａｎｃｅ⁃ｃｏｖａｒｉａｎｃｅ复合对称矩阵ＣＳ６不收敛对角矩阵ＵＮ（１）６８３６４．８３２８３９１．５１６－４１７６．４２广义正定矩阵７８３３８．７４１８３６９．８７２－４１６２．３７２８．０９０７＜０．０００１自相关ａｕｔｏｃｏｒｒｅｌａｔｉｏｎ复合对称矩阵ＣＳ８不收敛一阶自回归矩阵ＡＲ（１）８８３４０．１９４８３７５．７７３－４１６２．１０一阶自回归与移动平均矩阵ＡＲＭＡ（１，１）９８３４２．１３３８３８２．１５９－４１６２．０７０．０６０７０．８０５４２．３㊀随机森林模型的建立２．３．１㊀最优超参数的确定本研究采用ＲａｎｄｏｍｉｚｅｄＳｅａｒｃｈＣＶ和Ｇｒｉｄ⁃ＳｅａｒｃｈＣＶ组合的方式来自动寻找最优超参数组合㊂ＲａｎｄｏｍｉｚｅｄＳｅａｒｃｈＣＶ由随机搜索和ＣＶ交叉验证组成，通过随机搜索超参数不同的组合形式来对模型进行训练，将交叉验证结果最好的超参数组合作为最佳的超参数组合㊂ＧｒｉｄＳｅａｒｃｈＣＶ由网格搜索和ＣＶ交叉验证组成，通过遍历所有的超参数组合对模型进行训练，然后选择交叉验证结果最好的超参数组合作为最佳超参数㊂本研究先给定每个超参数一个较大的范围，利用ＲａｎｄｏｍｉｚｅｄＳｅａｒｃｈＣＶ选出一个最优超参数组合㊂再以此最优参数组合为中心，建立小范围超参数组合，随后利用ＧｒｉｄＳｅａｒｃｈＣＶ遍历所有的超参数组合，以此来确定最终的最优超参数㊂为了验证最优超参数组合结果的准确性，采用控制变量法的方式，对每一个超参数的拟合结果进行了可视化，如图３㊂图３㊀不同参数下随机森林的ＯＯＢ误差曲线图Ｆｉｇ．３㊀ＰｌｏｔｓｏｆＯＯＢｅｒｒｏｒｓｆｏｒｒａｎｄｏｍｆｏｒｅｓｔｗｉｔｈｄｉｆｆｅｒｅｎｔｐａｒａｍｅｔｅｒｓ㊀㊀图３Ａ表示的是ｎ＿ｅｓｔｉｍａｔｏｒｓ对袋外误差的影响，从图中可以看出当ｎ＿ｅｓｔｉｍａｔｏｒｓ数量为３４０时，模型的袋外误差最小；图３Ｂ㊁３Ｃ㊁３Ｄ分别表示ｍｉｎ＿ｓａｍｐｌｅｓ＿ｓｐｌｉｔ㊁ｍｉｎ＿ｓａｍｐｌｅｓ＿ｌｅａｆ㊁ｍａｘ＿ｆｅａｔｕｒｅｓ对袋外误差的影响，当ｍｉｎ＿ｓａｍｐｌｅｓ＿ｓｐｌｉｔ为４，ｍｉｎ＿ｓａｍ⁃ｐｌｅｓ＿ｌｅａｆ为１，ｍａｘ＿ｆｅａｔｕｒｅｓ为３时模型的袋外误差分别达到最小，并且最小值均出现在ｎ＿ｅｓｔｉｍａｔｏｒｓ为３４０时，因此最终选择随机森林模型的最优超参数分别是：ｎ＿ｅｓｔｉｍａｔｏｒｓ为３４０，ｍｉｎ＿ｓａｍｐｌｅｓ＿ｓｐｌｉｔ为４，ｍｉｎ＿ｓａｍｐｌｅｓ＿ｌｅａｆ为１，ｍａｘ＿ｆｅａｔｕｒｅｓ为３㊂２．３．２㊀相对重要性与偏依赖关系各个自变量因子对枝条生物量影响的相对重６３１㊀第２期唐依人，等：基于ＴＬＳ辅助的长白落叶松一级枝条生物量模型构建要性见图４㊂图４㊀各自变量对枝条生物量影响的相对重要性得分Ｆｉｇ．４㊀Ｒｅｌａｔｉｖｅｉｍｐｏｒｔａｎｃｅｓｃｏｒｅｓｏｆｔｈｅｅｆｆｅｃｔｓｏｆｅａｃｈｉｎｄｅｐｅｎｄｅｎｔｖａｒｉａｂｌｅｏｎｂｒａｎｃｈｂｉｏｍａｓｓ㊀㊀从图４可以看出，枝条因子是影响枝条生物量的主要因素，单木因子对枝条生物量的影响较小㊂７个枝条因子对枝条生物量影响的相对重要性共计９３．４％，其中重要性排在前４位的分别是枝条基部断面积（ＳＢＡＢ）２５．７％㊁弦长（ＬＢＣＬ）２４３％㊁基径（ｄＢ）２２６％和枝长（ＬＢＬ）１６６％㊂相对着枝深度（ｄＲＤＩＮＣ）㊁弓高（ＨＢＡＨ）和角度（ＡＢ）对枝条生物量的影响最小，分别为１５％㊁１４％和１３％㊂两个单木因子胸径（ＤＢＨ）和树高（Ｈ）对枝条生物量影响的相对重要性分别为３９％和２８％㊂枝条生物量受各自变量影响的偏依赖关系见图５㊂图５㊀枝条生物量受各自变量影响的偏依赖关系图Ｆｉｇ．５㊀Ｐｌｏｔｓｏｆｂｉａｓｄｅｐｅｎｄｅｎｃｅｏｆｂｒａｎｃｈｂｉｏｍａｓｓａｆｆｅｃｔｅｄｂｙｒｅｓｐｅｃｔｉｖｅｖａｒｉａｂｌｅｓ㊀㊀从总体上看枝条生物量对ＬＢＣＬ㊁ＬＢＬ㊁ｄＢ和ＳＢＡＢ的偏依赖性很强，而对Ｈ㊁ＤＢＨ㊁ｄＲＤＩＮＣ㊁ＡＢ㊁ＨＢＡＨ的偏依赖性较小㊂枝条生物量随着枝长的增加逐渐增大到一定程度后开始趋于稳定；随着基径和枝条基部断面积的增大先缓慢增加至一定程度，随后开始快速增加最后趋于平缓；而枝条生物量随弦长的增大呈幂函数形式的状态增长㊂２．４㊀模型检验结果基础模型和混合模型的标准化残差图见图６，从图６可以看出，基础模型存在较为明显的异方差现象，在混合模型中用指数函数对异方差进行矫正后模型的异方差现象被明显消除㊂分别采用各最优模型在训练集上进行训练，在独立的测试集上验证模型的预测能力，结果见表５㊂从表中可以看出各模型在训练集上的拟合效果表现良好，模型拟合效果排序为随机森林模型＞混合模型＞基础模型㊂利用训练好的模型在测试集上检验模型的预测能力，各模型的Ｒ２均高于０．８８㊂其中随机森林模型的预测能力最佳，相较于基础模型和混合模型，Ｒ２分别提高了４．８９％和１．３２％；ＲＭＳＥ分别降低了１３．６０％和１１．２３％；ＭＡＥ分别降低了１５．２５％和１２．１２％；ＲＭＡＥ分别降低了２０．０２％７３１南京林业大学学报（自然科学版）第４７卷和１２．４９％㊂各模型的预测能力排序为：随机森林模型＞混合模型＞基础模型㊂综合上述结果可以看出，随机森林模型可以作为预测一级枝条生物量的最优模型㊂图６㊀基础模型与混合模型的标准化残差图Ｆｉｇ．６㊀Ｎｏｒｍａｌｉｚｅｄｒｅｓｉｄｕａｌｐｌｏｔｓｏｆｔｈｅｂａｓｅｍｏｄｅｌａｎｄｔｈｅｍｉｘｅｄ⁃ｅｆｆｅｃｔｓｍｏｄｅｌ表５㊀最优模型拟合与预测能力评价表Ｔａｂｌｅ５㊀Ｔｈｅｅｖａｌｕａｔｉｏｎｔａｂｌｅｏｆｏｐｔｉｍａｌｍｏｄｅｌｆｉｔｔｉｎｇａｎｄｐｒｅｄｉｃｔｉｏｎｃａｐａｂｉｌｉｔｙ模型ｍｏｄｅｌ数据集ｄａｔａＲ２ＲＭＳＥ／ｇＭＡＥ／ｇＲＭＡＥ／％Ｆｐ／％基础模型ｂａｓｅｍｏｄｅｌ训练集ｔｒａｉｎ０．８７９１６２．１４９３．５１３８．１３９６．５１测试集ｔｅｓｔ０．８８０１５６．９３９０．０７３５．６６９６．８４混合模型ｍｉｘｅｄｍｏｄｅｌ训练集ｔｒａｉｎ０．９１３１５０．４９８３．６５３１．５８９７．０２测试集ｔｅｓｔ０．９１１１５２．７５８６．８６３２．５９９６．９９随机森林模型ｒａｎｄｏｍｆｏｒｅｓｔｍｏｄｅｌ训练集ｔｒａｉｎ０．９３０１３０．２３６７．２３２４．３０９７．８３测试集ｔｅｓｔ０．９２３１３５．５９７６．３３２８．５２９７．６５３㊀讨㊀论通过对枝条生物量与枝条因子进行相关性分析，发现与枝条生物量相关性较高的因子分别为枝条基部断面积（ＳＢＡＢ）㊁枝条基径（ｄＢ）㊁弦长（ＬＢＣＬ）和枝长（ＬＢＬ），由于这４个变量之间存在共线性，最终选择将相关性更高的ＳＢＡＢ和ＬＢＣＬ作为基础模型的自变量㊂利用ＴＬＳ数据建立的枝条生物量模型相较于实测数据模型参数差异不大，但ＴＬＳ数据模型的预测效果更好，证明可以利用ＴＬＳ数据进行枝条生物量模型的研究㊂基于样木效应的混合模型拟合效果明显优于基础模型，广义正定矩阵可以作为随机效应的最优方差⁃协方差矩阵㊂当随机效应分别加在ＳＢＡＢ和ＬＢＣＬ上时，模型有最佳的拟合优度㊂指数函数为校正模型异方差的最佳权函数形式，可明显校正模型的异方差现象㊂随机森林模型作为一种非参数模型可以很好地对枝条生物量进行预测㊂通过分析各自变量对枝条生物量影响的相对重要性，发现重要性排在前４位的分别为ＳＢＡＢ㊁ＬＢＣＬ㊁ｄＢ和ＬＢＬ，这与传统参数模型中分析相关性得出的结论几乎一致，证明了非参数模型也具有一定的解释性㊂３个模型的拟合效果排序为：随机森林模型＞混合模型＞基础模型㊂以往关于枝条生物量模型的研究大都是采用参数方程的方法，这些方程中采用的变量一般为单木的易测因子如胸径㊁树高［１５－１６］等㊂这些方程虽然用起来十分简便，但是对于枝条生物量的预测能力较低，难以满足在树冠水平上对枝条属性的研究㊂本研究利用点云数据提取出的枝条特征因子在枝条水平上建立了人工长白落叶松枝条生物量非线性混合模型，采用的自变量为ＳＢＡＢ和ＬＢＣＬ，模型Ｒ２较高，大大提高了枝条生物量的预测精度㊂董利虎等［１］㊁许昊等［１７］分别利用枝条特征因子在枝条水平进行了人工林红松和人工林杉木枝条生物量的研究，通过对非线性模型进行对数转换来消除生物量模型中普遍存在的异方差现象，建立了枝条生物量线性混合效应模型，最后通过校正系数对所得结果进行校正以获得生物量的无偏估计㊂而本研究直接以枝条基部断面积和弦长为自变量建立了枝条生物量非线性混合模型，并利用指数函数对模型的异方差进行校正，取得了良好的效果㊂传统上基于枝条特征因子建立枝条生物量模型时往往需要伐倒树木进行枝条解析［１，１７－２０，２５］以获得枝条特征因子数据㊂随着激光雷达技术的发展，利用点云数据重现树木三维结构［６，８－９，２４］已成为现实㊂本研究利用点云数据提取出的枝条特征因子及其实测数据分别建立了长白落叶松枝条生物量基础模型，证明了利用ＴＬＳ数据进行枝条生物量研究的可行性，为利用无损化测量得到的枝条因子的实际应用奠定了一定的实践基础㊂８３１。

2012第四届全国大学生数学竞赛四川赛区获奖名单

2012第四届全国大学生数学竞赛四川赛区获奖名单更新时间：2012-11-6 16:55:252012第四届全国大学生数学竞赛四川赛区评奖工作已经结束，经过全国大学生数学竞赛四川赛区组委会专家评审，现将四川赛区本次获奖名单公布如下：第四届全国大学生数学竞赛四川赛区数学类奖名单赛区一等奖编号姓名性别学校名称学院名称参赛类型准考证1周超男四川大学应用数学数学专业201202王宇男四川大学应用数学数学专业201203陈攀男电子科技大学数学数学专业201204周世奇男电子科技大学数学数学专业201205戴烜中男四川大学吴玉章学院数学专业201206邓田娟女四川大学数学基地班数学专业201207杨爽女乐山师范学院数学与应用数学数学专业201208任偲骐男四川大学应用数学数学专业201209李昊天男四川大学数学大类数学专业2012010李波男乐山师范学院数学与应用数学数学专业2012011傅费思男四川大学应用数学数学专业20120赛区二等奖编号姓名性别学校名称学院名称参赛类型准考证1李姗蔓女宜宾学院数学与应用数学数学专业201202李佑铭男四川大学数学与应用数学(基础) 数学专业201203孔祥飞男电子科技大学数学数学专业201204石云鹏男四川大学数学大类数学专业201205佘睿男四川大学基地班数学专业201206郭汝驰男四川大学应用数学数学专业201207常建龙男电子科技大学数学数学专业2012010402 16 8鲁东男西南交通大学数学数学专业2012010803 16 9雷文超男四川大学信息与计算科学数学专业2012010807 20 10岳阳男西南交通大学计算数学专业2012010703 21 11罗开宝男内江师范学院数学与应用数学专业数学专业2012010905 22 12胡方涛男电子科技大学数学数学专业2012010730 23 13余东洲男四川大学数学大类数学专业2012010401 24 14涂代源男四川大学应用数学数学专业2012010422 24 15何俊材男四川大学应用数学数学专业2012010427 24 16孙硕男电子科技大学数学数学专业2012010829 24 17钟友林男四川大学应用数学数学专业2012011027 24 赛区三等奖编号姓名性别学校名称学院名称参赛类型准考证号名次1唐浩耘男四川大学应用数学数学专业2012010127 29 2谭大超男乐山师范学院数学与应用数学数学专业2012010214 29 3纪圣塨男西南交通大学数学数学专业2012010710 29 4赵威男四川大学数学大类数学专业2012011003 29 5胡留春男西南交通大学统计数学专业2012011119 29 6张瑞梅女内江师范学院数学与应用数学专业数学专业2012011224 29 7周义满男电子科技大学数学数学专业2012010129 35 8李艳晶女四川师范大学数学与应用数学数学专业2012010228 35 9夏王洋男四川大学应用数学数学专业2012010706 35 10王玖玮男四川大学应用数学数学专业2012010801 35 11杨红明男电子科技大学数学数学专业2012010808 35 12王琦男四川大学数学基地班数学专业2012010310 40 13周玲女四川大学数学大类数学专业2012010330 40 14李福团男西南交通大学计算数学专业2012010906 40 15唐志骥男四川大学数学与应用数学（金融）数学专业2012011129 40 16刘春燕女西华师范大学数学与应用数学数学专业2012010221 44 17王世莉女乐山师范学院数学与应用数学数学专业2012010413 4418胡又壬女四川大学基地班数学专业2012010816 4419阳密女四川师范大学数学与应用数学数学专业2012011107 4420刘连林男西南交通大学数学数学专业2012010105 4821侯振铎男四川大学数学基地班数学专业2012010202 4822张鹏成男四川大学吴玉章学院数学专业2012010227 4823王凯男四川大学数学大类数学专业2012011202 4824李洋洋男中国民航飞行学院信息0902 数学专业2012011221 4825郭凯迪女四川大学数学与经济创新班数学专业2012010120 4826王豪男四川民族学院数学与应用数学专业数学专业2012010404 48第四届全国大学生数学竞赛四川赛区非数学类获名单赛区一等奖编号姓名性别学校名称学院名称参赛类型准考证号名1 姚青松男西南交通大学经济学非数学专业2012023420 12 刘同科男电子科技大学计算机非数学专业2012023715 23 郑飞洋男电子科技大学物电非数学专业2012023214 34 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融合Albert_模型的珍稀濒危植物知识图谱的构建

湖南农业大学学报(自然科学版) 2023，49(5)：616–623．DOI：10.13331/j.cnki.jhau.2023.05.017 Journal of Hunan Agricultural University(Natural Sciences)

引用格式：田梦晖，陈明，席晓桃．融合Albert模型的珍稀濒危植物知识图谱的构建[J]．湖南农业大学学报(自然科学版)，2023，49(5)：616–623． TIAN M H，CHEN M， XI X T．Construction of the knowledge graph for the rare and endangered plants based on Albert model[J]．Journal of Hunan Agricultural University(Natural Sciences)，2023，49(5)：616–623．投稿网址：http://xb.hunau.edu.cn

融合Albert模型的珍稀濒危植物知识图谱的构建田梦晖1,2，陈明1,2*，席晓桃1,2

(1.上海海洋大学信息学院，上海 201306；2.农业农村部渔业信息重点实验室，上海 201306) 摘要：针对珍稀濒危植物形态特征、分类等级、濒危系数、保护措施等知识不明确的问题，设计了文本融合轻量

级双向转换编码表示模型(Albert)的知识抽取模型框架，实现批量抽取珍稀濒危植物知识，从而构建珍稀濒危植物知识图谱：1) 在现存一般性植物本体的基础上，采用自顶向下的方式构建珍稀濒危植物本体，得到5个体系，即物种分类体系、生长形态特征体系、命名体系、保护现状体系和生态习性体系；2) 采取Albert预训练模型来增强下游任务模型输入向量的珍稀濒危植物属性描述文本语义的表征能力；3) 利用BiLSTM–CRF模型和BiGRU–Attention模型分别实现命名实体识别和关系抽取。在珍稀濒危植物数据测试集上对模型的有效性进行验证，结果表明，命名实体识别模型和关系抽取模型的召回率和准确率的调和平均值(F1)值分别达到98.07%和93.76%，将得到的大量的实体和关系所形成的三元组存储在图数据库Neo4j中，完成珍稀濒危植物知识图谱的可视化展示。关键词：珍稀濒危植物；Albert模型；知识图谱；本体；命名实体识别；关系抽取

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交通银行2010年大学生招聘笔试名单

李颖琦
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交通银行2010年大学生招聘笔试名单
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JYZ1001201001

2011年国家自然基金获得者名录——国防科学技术大学

F020808 F020809 F020705 F020601 F010202 F010907 F020208 F010304 A040403 E020401 A040204 E050402 E050401 F030301 F010408 F020302 F020701 F040407 A011701 F020503 F050804 E051002 F020502 F010304 F020301 A040204 E051202 F010602 F050304 F010408
ห้องสมุดไป่ตู้
金额 64 70 24 56 20 25 25 23 20 20 22 22 28 17 58 25 20 23 56 24 22 26 56 28 23 25 23 24 48
61170287 11172326 61170048 61170286 61120106005 11102229 71102004 51105369 11172322 61171019 61171016 61170049 11172329 51175500 61171017 51105365 61175015 61170083 71101150 31171266 61174002 61174206 11172327 11104350 11172324 11173068 11174369 61170045 51173202 61108089
F020805 A020403 F020203 F020805 F0203 A020207 G0214 E050601 A020205 F010502 F010602 F020305 A020602 E050201 F010505 E050202 F030403 F0203 G0104 C060702 F030301 F030301 A020413 A040302 A020401 A030802 A040406 F0203 E030301 F0513

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