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Re: Neural Network Building Energy Forecast
Posted:
Feb 15, 2013 6:40 AM


"Subodh Paudel" <subodhpaudel@gmail.com> wrote in message <kfitfe$8hi$1@newscl01ah.mathworks.com>... > Hai All, > I want to forecast the building energy demand: input parameters: outside temperature and solar radiation, and output parameter: energy consumption > > I am choosing 2 layered network. I have a 1826 samples. My R2 value is in negative and i am not finding the solution of it? Please, could you help me. > > The data size consists all inputs and targets in column vector.
[ I N ] = size( input ) % [ 2 1826 ] [ O N ] = size( target ) % [ 1 1826 ]
>I have used 70% samples for the generalization and 30% for prediction.
Terminology:
total = design + test design = train + validation
> The souce code is given: > > data=xlsread('z:\testdata.xlsx','Sheet1') > %Size of input and Target Layers I:Input Layer, O:Output Layer,
Official Terminology: 2 layers of Hidden and Output neurons. Input elements are fanin units and NOT neurons. The unmodifed term 'layer' does not apply to inputs. The typical MLP is a 2layer FFNN. I don't like this at all. Therefore I only refer to (3) layers of nodes (NOT neurons!). Consequently, since the typical MLP always has a layer of input nodes and a layer of output nodes, I refer to the typical topology as a MLP or FFNN with one hidden layer (of nodes or neurons).
dN=size of > %the data > [dN I]=size(data);
Please remove the "d" it is unnecessary and confusing.
> dNt=round(0.7*dN); %70% of Data Used for the Training and Generalization
Not standard terminology or proceedure Design = Training and Validation Use Validation set iteratively to determine training parameters and choose best of multiple designs. Need a nondesign subset (Test) to predict generalization error. If results are unsatisfactory, need to repeat with a new trn/val/tst data split (i.e., Test set is only used ONCE!)
> input_sample= data((1:dNt),1:2)'; > target_sample=data((1:dNt),3)'; > validation_inputsample=data(((dNt+1):dN),1:2)'; > validation_targetsample=data(((dNt+1):dN),3)'; > > %DataProcessing of Training Sample (normalization with mean 0.1 and 0.9) > [pn,ps]=mapstd(input_sample,0.1,0.9); > [tn,ts]=mapstd(target_sample,0.1,0.9);
No! There is absolutely no good reason to do that! Standarization means zeromean/unitvariance.
> %Apply Normalization to the Validation Input Sample > an=mapstd('apply',validation_inputsample,ps); > > %Iterative Optimization wrt to RMSE to determine Hidden Neurons:hidden_node,
Use dimensionless NMSE = MSE/MSE00 (MSE00 = mean(var(target',1)) ) instead of scale dependent RMSE. Then coefficient of determination (i.e., R^2) is given by R2 =1NMSE.
> %Learning Rate:lr_rate and Momentum:mc_rate > sbmin=99999999; > hidden_node=0; > mc_rate=0; > lr_rate=0; > mm=1;
?? Always begin with the MATLAB defaults.
> %MLP (211 Network)with tangent hyperbolic transfer function in the hidden layer and > %Linear Activation Function in the Output Layer
TERMINOLOGY: 2H1 node topology
> %Initial Hidden Neuron Size Varies from 5 to 10
Ntrneq = Ntrn*O % No. of training equations Nw = (I+1)*H+(H+1)*O % No. of unknown weights
To mitigate noise and measurement error when not using regularization(msereg) or validation stopping, require Ntrneq >= Nw but desire Ntrneq >> Nw. This yields an upperbound for H
Hub = 1 + ceil( (NtrneqO)/(I+O+1)) % 319
%Hub = 1 + ceil( ( 0.7*18261)/(2+1+1) ) = 319 %Hmax ~ round(Hub/8) = 40
> for i=1:1:40; How about starting with a coarse search 1:5:40 > net=newff(minmax(pn),[i 1],{'tansig','purelin'},'trainlm') > net.performFcn='mse'; > net.performParam=[]; > net.trainParam.goal=0.01*var(tn); > net.trainParam.epochs=1000; > net.trainParam.show=30; > net.trainParam.mu_max=1e10; > net.trainParam.min_grad=0.000001;
Too complicated. To start, use as many defaults as possible For example
net=newff(minmax(pn),[i 1]); net.trainParam.goal=0.01*var(tn); net.trainParam.show=30;
> net.trainParam.max_fail=20;
Too high for val stopping. Just delete and accept the default of 6.
> for k=1:1:4 %Learning Rate Varies from 0.25 to 1 > lr=0.25+(k1)*.25; > net.trainParam.lr=lr; > for m=1:1:4 %Momentum Varies from 0.25 to 1 > mc=0.25+(m1)*0.25; > net.trainParam.m=mc; > net=init(net);%Assume 0 weight > net=train(net,pn,tn); > yn=sim(net,pn); > y=mapstd('reverse',yn,ts); > error=ytarget_sample; > RMSE(i,k,m)=sqrt(mse(error));%RMSE Value Check for the Minimum Root Mean Square > if RMSE(i,k,m)<sbmin > sbmin=RMSE(i,k,m); > hidden_node=i; > mc_rate=mc; > lr_rate=lr; > IW_initial=net.IW{1,1}; > LW_initial=net.IW{2,1}; > hidden_bias_initial=net.b{1}; > output_bias_initial=net.b{2}; > end > end > end > end
??? Life is already hard enough, why not accept most defaults and just search over H and initial weights?
NOTE: minmax version of newff automatically configures the initial weights.
I'll stop here. Basically, start simple and gradually make improvements. Your current code will probably take hours and not give you any insight.
Hope this helps.
Greg
> parameters =[hidden_node mc_rate lr_rate] > net=newff(minmax(pn),[hidden_node 1],{'tansig','purelin'},'trainlm') > net.performFcn='mse'; > net.performParam=[]; > net.trainParam.goal=0.01*var(tn); > net.trainParam.epochs=1000; > net.trainParam.show=30; > net.trainParam.mu_max=1e10; > net.trainParam.max_fail=20; > net.trainParam.min_grad=0.000001; > net.trainParam.lr=lr_rate; > net.trainParam.m=mc_rate; > > MSE_initial=mean(var(target_sample)); %Approximate MSE for a constant output model > net.IW{1,1}=IW_initial; > net.IW{2,1}=LW_initial; > net.b{1}=hidden_bias_initial; > net.b{2}=output_bias_initial; > > net=train(net,pn,tn); > yn=sim(net,an); > y=mapstd('reverse',yn,ts); > %Error Calculation > error=yvalidation_targetsample; > percentage_error=abs(error)./y*100; %Percentage of Error > RMSE=sqrt(mse(error)); %Root Mean Square Error > NMSE= mse(error)/MSE_initial; % Normalized Mean Square Error > R2=1NMSE; %R^2 Statistics for the Regression Analysis > MAE=mean(abs(error)); %Mean Absolute Error > MAPE = mean(percentage_error); % Mean Absolute Percentage Error > %Analysis of Predicted and Target Values > performance_error=[RMSE R2] > pp=[validation_targetsample y]; > figure(1) > plot(y,'g') > hold > plot(validation_targetsample,'r') > title('comparision between actual targets and predictions'



