Appendix A: MATLAB commands for neural networks

Transcription

1 Appendix A: MATLAB commands for neura networks 132

2 Appendix A: MATLAB commands for neura networks p=importdata('pn.xs'); t=importdata('tn.xs'); [pn,meanp,stdp,tn,meant,stdt]=prestd(p,t); for m=1:10 net=newff(minmax(pn),[m,1],{'tansig','purein'},'trainm'); net.trainparam.sow=50; net.trainparam.epocs=6000; net.trainparam.goa = 1e-5; [net,tr]=train(net,pn,tn); a=sim(net,p); a=poststd(a,meant,stdt); e= t-a; perf(n) = mse(e) end After te best idden nodes m was found, ten te foowing program was run tirty times and te best five resuts were found: p=importdata('pn.xs') t=importdata('tn.xs') [pn,meanp,stdp,tn,meant,stdt]=prestd(p,t) net=newff(minmax(pn),[m,1],{'tansig','purein'},'trainm') net.trainparam.sow=50 net.trainparam.epocs=500 net.trainparam.goa = 1e-5 [net,tr]=train(net,pn,tn) a=sim(net,p) a=poststd(a,meant,stdt) e1= t-a perf1= mse(e1) pnew=importdata('pnnew.xs') tnew=importdata('tnnew.xs') pnewn=trastd(pnew,meanp,stdp) anewn=sim(net,pnewn) anew=poststd(anewn,meant,stdt) e= tnew-anew perf= mse(e) end Te training data of input nodes and output nodes are stored in pn.xs and tn.xs fie respectivey, wie te testing data are stored in pnnew.xs and tnnew.xs respectivey. Here, n means te data of buiding A,B,C and D. 133

3 Appendix B: An overview of statistica earning teory 134

4 Appendix B: An overview of statistica earning teory Vapnik (1995) presents a te macine earning probems as te foowing: n Given a set of data points (( x y ),( x, y ),..., ( x, y )( x X R, y Y R is te 1, i i, number of data points, for regression estimation and density estimation and y i Y N for pattern recognition) randomy and independenty generated from an unknown probabiity distribution p ( x, y), find a function f ( x, tat as te minima risk function (B.1). R( f ) = L9y, f ( x, ) p( x, y) dxdy (B.1) x, y Were a is te parameter of f ( x,. R( f ) is caed te generaization error or te expected test error. It is a measure of te generaization performance of f ( x,. L( y, f (x, ) is caed te oss function. It is a measure of te deviations between te actua vaues and te estimated vaues on te data points generated from p( x, y). As p( x, y) is unknown, traditiona metods attempt to estimate f ( x, by minimizing te empirica risk function: R emp 1 ( f ) = L( yi, f ( x, ) (B.2) i= 1 R emp ( f ) is caed te empirica error. Tat is, p( x, y) is estimated by training sampes. Empirica Risk Minimization (ERM) principe is to minimize te 135

5 generaization error by minimizing te empirica error R emp ( f ). Traditiona neura networks utiizes tis principe. However, because of te imited number of, sometimes ( f ) R emp cannot estimate R( f ) we. As described in te statistica earning teory, R ( f ) and ( f ) ave R emp te foowing reationsip: R( f ) Remp ( f ) + Ω( ) (B.3) were is caed te Vapnik-Cervonenkis (VC) dimension. It is a measure of te capacity of f ( x,, wic means tat te abiity of f ( x, to earn any training data point witout error. Ω ( ) is caed te confidence interva, a decreasing function of, wic is te ration of te number of training sampes into te VC dimension of te estimator. Equation (B.3) sows tat te vaue of R ( f ) depends bot on ( f ) R emp and Ω ( ). Hence, R emp ( f ) can accuratey estimate R ( f ) ony wen Ω ( ) is sma enoug. Because of tis, Vapnik deveoped te Structura Risk Minimization (SRM) principe. Te SRM principe is: one defines a nested structure S S... S..., 1 2 m as sown in Appendix B.1, on te set of functions { f x, a } S = ( ), a Λ wit teir VCdimensions satisfying m..., and ten cooses te structure eement S k wit te minima upper bound of te generaization error R( f ). 136

6 S 1 S n Appendix B.1 A structure on te set of functions is determined by te nested subsets of functions. Te objective of SRM principe is to estimate f ( x, by minimizing bot te empirica error R emp ( f ) and te confidence interva Ω ( ), as sown in Appendix B.2. It defines a trade-off between te quaity of te approximation of te given data and te compexity of te approximating function. Risk Bound of te risk VC Confidence Empirica Risk * corresponding to S* Appendix B.2 Te bound on te risk is te sum of te empirica risk and of te confidence interva. Te smaest bound of te risk is acieved on some appropriate eement of te structure (Source: Vapnik, 1995) 137

7 Appendix C: An introduction to LIBSVM 2.6 program 138

8 Appendix C: An introduction to LIBSVM 2.6 program Libsvm is a simpe, easy-to-use, and efficient software for SVM cassification and regression. Libsvm 2.6 was deveoped by Ci-Cung Cang and Ci-Jen Lin in It can sove C-SVM cassification, nu-svm cassification, one-cass-svm, epsion-svm regression, and nu-svm regression. It aso provides an automatic mode seection too for C-SVM cassification. Libsvm 2.6 is avaiabe at ttp:// Te format of training and testing data fie is: <abe> <index1>:<vaue1> <index2>:<vaue2> <abe> is te target vaue of te training data. For cassification, it soud be an integer wic identifies a cass (muti-cass cassification= is supported). For regression, it's any rea number. For one-cass SVM, it's not used so can be any number. <index> is an integer starting from 1, <vaue> is a rea number. Te abes in te testing data fie are ony used to cacuate accuracy or error. If tey are unknown, just fi tis coumn wit a number. svm-train Usage Usage: svm-train [options] training_set_fie [mode_fie] options: 139

9 -s svm_type : set type of SVM (defaut 0) 0 -- C-SVC 1 -- nu-svc 2 -- one-cass SVM 3 -- epsion-svr 4 -- nu-svr -t kerne_type : set type of kerne function (defaut 2) 0 -- inear: u'*v 1 -- poynomia: (gamma*u'*v + coef0)^degree 2 -- radia basis function: exp(-gamma* u-v ^2) 3 -- sigmoid: tan(gamma*u'*v + coef0) -d degree : set degree in kerne function (defaut 3) -g gamma : set gamma in kerne function (defaut 1/k) -r coef0 : set coef0 in kerne function (defaut 0) -c cost : set te parameter C of C-SVC, epsion-svr, and nu-svr (defaut 1) -n nu : set te parameter nu of nu-svc, one-cass SVM, and nu-svr (defaut 0.5) -p epsion : set te epsion in oss function of epsion-svr (defaut 0.1) -m cacesize : set cace memory size in MB (defaut 40) -e epsion : set toerance of termination criterion (defaut 0.001) - srinking: weter to use te srinking euristics, 0 or 1 (defaut 1) -b probabiity_estimates: weter to train an SVC or SVR mode for probabiity estimates, 0 or 1 (defaut 0) -wi weigt: set te parameter C of cass i to weigt*c in C-SVC (defaut 1) -v n: n-fod cross vaidation mode Te k in te -g option means te number of attributes in te input data. 140

10 option -v randomy spits te data into n parts and cacuates cross vaidation accuracy/mean squared error on tem. svm-predict Usage Usage: svm-predict [options] test_fie mode_fie output_fie options: -b probabiity_estimates: weter to predict probabiity estimates, 0 or 1 (defaut 0); one-cass SVM not supported yet mode_fie is te mode fie generated by svm-train. test_fie is te test data you want to predict. svm-predict wi produce output in te output_fie. (Source: Cang and Lin, 2001) 141

11 Appendix D: Autor s pubication ist 142

12 Appendix D: Autor s pubication ist Journa papers: 1. B. Dong, S.E. Lee, M.H.Sapar, "A oistic utiity bi anaysis metod for baseining woe commercia buiding energy consumption in Singapore", Energy and Buidings, vo. 37 (2), pp , B. Dong, C.Cen, S.E. Lee, "Appying support vector macines to predict buiding energy consumption in te tropics", Energy and Buidings, in Press, Conference papers: 1. B. Dong, S.E. Lee, M.H.Saper, H.S. Sun, "Appying neura networks to predict buiding energy consumption in Singapore". Proceedings of internationa conference on Contro, Automation and Systems, Aug , 2004, Bangkok, Taiand. 2. B. Dong, S.E. Lee, "Evauating utiity bi anaysis metod for baseining woe buiding energy consumption in Singapore", Proceedings of Internationa conference on energy efficiency buidings, Apri 19-21, 2004, Frankfurt, German. 143