Future value prediction with neural network method and right input and target format data

Hello, Could anyone explain, how to do following with matlab neural network NARX method I have six variables numbers (they depends on each other) for each day and for 10 days.

• day1 x1, x2, x3, x4, x5, x6
• day2 x1, x2, x3, x4 ,x5,x6
• ..........................
• day10 x1, x2, x3, x4, x5, x6

and I want to predict these six variables for 11th day using matlab neural network So prediction:

• day11 y1,y2,y3,y4,y5, y6

I am starting to work with neural networks, so I know that I have to use

ntstool and to select NARX method, but there I stopped with right format of data at matlab work space variables table. Could anyone please help how to enter input and target data in right format for this case at matlab work space variables table that could allow to simulate this.

[Tim Maguire]

Were you able to get an answer?

[AKHILA GOUDA]

Hello sir, If you got your ans then please help me . I have same problem that how can I predict next day data.. Thank you

[Greg Heath]

try searching

 narx greg

in both

   NEWSREADER and ANSWERS

Hope this helps

Greg

Answer 1

[Greg Heath]

Your inputs are outputs. Therefore you should be using NAR, not NARX.

How many days, weeks, months or years of data do you have?

Did you look at the output auto and cross-correlation functions to determine that you need feedback lags of 10 days ?

Hope this helps.

Greg

[Kranthi Kumar]

Sir, I have also same kind of query. I have 5 variables.I need to predict those 5 variables in future. i have some 259 data points of 259 days.What would be my input and target values? Those 5 variables are some what interrelated to each other.I am using nts tool NAR. Please help me with this.

Answer 2

[Greg Heath]

This is an example of using a double loop to choose as small a number of hidden nodes as possible to mitigate overtraining an overfit net and to mitigate the failure of random initial weights by obtaining multiple designs.

To make it easier to understand, I used 'dividetrain' which is valid for this data because the number of training equations, Neq, is much greater than the number of unknown weights that have to be estimated, Nw.

For small data sets where Neq >> Nw is not possible, regularization (see help mse and doc mse) or validation set stopping using nonrandom data division (see help divideblock and divideind) should be used. If validation stopping is used, the validation performance is used to choose the best net. A completely unbiased estimate of performance on new data is then obtained from the corresponding test set.

Hope this helps.

Greg

 close all,clear all, clc, plt=0;
 tic

 T = simplenar_dataset;
 t  = cell2mat(T);
 whos
 [ O N ] = size(T)           % [ 1 100]
 Neq     = prod(size(T))     % 100

 rng(0)
 for k = 1:100
    n                = randn(1,N);
    autocorrn        = nncorr(n,n,N-1,'biased');
    sortabsautocorrn = sort(abs(autocorrn));
    M                = floor(0.95*(2*N-1))  % 189
    thresh95(k)      = sortabsautocorrn(M);
 end
 sigthresh95 = mean(thresh95)  % 0.2194

 zt          = zscore(t,1);
 autocorrzt  = nncorr(zt,zt,N-1,'biased');
 lags        = 0:N-1;
 siglags     = -1+find(abs(autocorrzt(N:end))>sigthresh95);

 plt = plt+1, figure(plt)     % Fig 1
 hold on
 plot( zeros(1,N), 'k--', 'LineWidth', 2 )
 plot(sigthresh95*ones(1,N), 'r--', 'LineWidth', 2 )
 plot(-sigthresh95*ones(1,N), 'r--', 'LineWidth', 2 )
 plot( lags, autocorrzt(N:end), 'LineWidth', 2 )
 plot( siglags, autocorrzt(N+siglags), 'o', 'LineWidth', 2 )

 FD   = 1:2
 NFD  = length(FD)   % 2
 LDB  = max(FD)      % 2
 Ns   = N-LDB        % 98
 Nseq = Ns*O         % 98
 % Nw = (NFD*O+1)*H+(H+1)*O
 Hub     =  -1+ceil( (Nseq-O) / (NFD*O+O+1))  % 24
 Hmax    =  floor(Hub/10) %  Hmax = 2 ==>  Nseq >>Nw :
 Hmin    =  0
 dH      = 1
 Ntrials = 10

 j=0
 rng(4151941)
 for h = Hmin:dH:Hmax
    j = j+1
    if h == 0
        net = narnet( FD, [] );
        Nw =  ( NFD*O + 1)*O
    else
        net = narnet( FD, h );
        Nw =  ( NFD*O + 1)*h + ( h + 1)*O
    end
    Ndof            = Nseq-Nw
    [ Xs Xi Ai Ts ] = preparets(net,{},{},T);
    ts              = cell2mat(Ts);
    MSE00s          = mean(var(ts',1))
    MSE00as         = mean(var(ts'))
    MSEgoal         = 0.01*Ndof*MSE00as/Neq
    MinGrad         = MSEgoal/10

    net.trainParam.goal      =  MSEgoal;
    net.trainParam.min_grad  =  MinGrad;
    net.divideFcn            =  'dividetrain';

    for i = 1:Ntrials

        net            =  configure(net,Xs,Ts);
        [ net tr Ys ]  =  train(net,Xs,Ts,Xi,Ai);
        ys             =  cell2mat(Ys);

        stopcrit{i,j}  = tr.stop;
        bestepoch(i,j) = tr.best_epoch;
        MSE            = mse(ts-ys);
        MSEa           = Nseq*MSE/Ndof;
        R2(i,j)        = 1-MSE/MSE00s; 
        R2a(i,j)       = 1-MSEa/MSE00as;

    end
 end

 stopcrit   =  stopcrit    %Min grad reached (for all).
 bestepoch  =  bestepoch
 R2         =  R2
 R2a        =  R2a
 Totaltime  =  toc

 %  H =                   0    1     2

 %
 % bestepoch =              1     7    16
 %                          1     7     7
 %                          1     7     4
 %                          1     5     8
 %                          1     6     5
 %                          1     5    11
 %                          1     8     5
 %                          1     4    16
 %                          1     5     6
 %                          1     3     6
 % 
 % R2 =                0.8885    0.9948    0.9951
 %                     0.8885    0.9954    0.9968
 %                     0.8885    0.9950    0.9983
 %                     0.8885    0.9946    0.9958
 %                     0.8885    0.9951    0.9951
 %                     0.8885    0.9929    0.9915
 %                     0.8885    0.9908    0.9956
 %                     0.8885    0.9926    0.9914
 %                     0.8885    0.9922    0.9972
 %                     0.8885   -0.0000    0.9934
 % 
 % R2a =               0.8861    0.9945    0.9947
 %                     0.8861    0.9952    0.9965
 %                     0.8861    0.9947    0.9981
 %                     0.8861    0.9944    0.9955
 %                     0.8861    0.9949    0.9946
 %                     0.8861    0.9926    0.9908
 %                     0.8861    0.9904    0.9952
 %                     0.8861    0.9923    0.9907
 %                     0.8861    0.9919    0.9969
 %                     0.8861   -0.0430    0.9928

[phuong]

Based this result, which number that you choice?

[Greg Heath]

My goal was to minimize H subject to the constraint R2a >= 0.99. Since Ntrneq >> Nw, any, some, or all (e.g., a 9 net ensemble) of the 9 nets satisfying the goal should be acceptable for unseen data.

[Greg Heath]

I don't understand the meaning of these code lines. Please explain Hoang Pham Truc Phuong

95% of the autocorrelation values for a random Gaussian signal are below sigthresh95. Using 100 random trials to estimate it yields

 for k = 1:100
    n                = randn(1,N);
    autocorrn        = nncorr(n,n,N-1,'biased');
    sortabsautocorrn = sort(abs(autocorrn));
    M                = floor(0.95*(2*N-1))  % 189
    thresh95(k)      = sortabsautocorrn(M);
 end

 sigthresh95 = mean(thresh95)

Now if you calculate the autocorrelation function of a time series prediction target function, you can estimate the significant feedback lags as those where the absolute value of its acf exceeds sigthresh95.

Search NEWSGROUP and ANSWERS using

 greg sigthrsh95

and

 greg sigthresh95.

A more exact estimate uses the "partial" autocorrelation. I've never used it. If you are interested see Wikipedia.

[Tomas Simonson]

Mr. Heath, I have created a zscore function of my own since I don't have the statistics toolbox yet. I have duplicated the above function and it runs, but my bestepoch outputs are not the same as what you posted. I verified that the rng is the same. The output values are: % bestepoch =

     2     6     3
     2     4     6
     2     6     5
     2     3    11
     2     6     5
     2    11     9
     2     4    11
     2     6     3
     2     4     4
     2     4     4

Could you provide the output of your variable "zt" so I can troubleshoot my created zscore function? Of note the first first column of the R2 and R2a matricies are the same and the second and third columns deviate at the second and third digits. Thank you for your time. -Tomas

[Tomas Simonson]

Mr. Heath, I am also getting a different number for the value of sigthresh95. I am using matlab 2015a, is it possible that the random number generator I am using is different than when if was tested? I tried it with rng(o,'v4') and the result was still not what was posted in the comments. Any help is greatly appreciated. -Tomas

[Greg Heath]

 T = simplenar_dataset;
t  = cell2mat(T);
[I N ]     = size(t)
meant      = mean(t)
stdtb      = std(t,1)   % biased( div by N)
ztb        = (t-meant)/stdtb;
minmaxdztb = minmax(ztb-zscore(t,1))

 stdtu      = std(t,0)   % unbiased( div by N-1)
ztu        = (t-meant)/stdtu;
minmaxdztu = minmax(ztu-zscore(t,0))

 I         =  1
N          =  100
meant      =  0.72345
stdtb      =  0.25161
minmaxdztb =  [  0  0 ]
stdtu      =  0.25287
minmaxdztu =  [  0  0 ]

Answer 3

[Povi Nike]

Hello thanks for answer. I have data for 1 year , it is 212 sets of x1, x2, x3, x4, x5, x6. My purpose is to predict next date future values of number set and correlation functions of sets 212 of values.

Ok I shall use NAR method by using ntstool. AS I understood I enter targets and NAR method perform calculations and saved output file gives predicted values? I entered 13 sets and it calculated 11 sets of output values Why less than targets sets?

[Greg Heath]

Please do not use the answer box for comments. Use the comment box.

13 input examples - 2 delays = 11 output examples

Answer 4

[Greg Heath]

Your comments are not clear.

You have data for N = 212 consecutive days of the same year?

You want to calculate the O=6 autocorrelation functions and 6*5/2= 15 cross-correlation functions to find a good range of delays to use?

To avoid confusion, I suggest first concentrating on the positive lags of the 6 autocorrelation functions. If final results need improvement take a look at the cross-correlation functions of the worst predicted variables.

Apparently you used the NAR defaults FD = 1:2 (ND = 2 delays) and H = 10 (hidden nodes); With O = 6 outputs, there are

 Nw = (ND*O+1)*H+(H+1)*O = 130+66 = 196

unknown weights weights to estimate with

 Ntrneq = Ntrn*O = 6*Ntrn

training equations. For Ntrneq >> Nw, you need

 Ntrn >> ~33

However, you only had the default Ntrn = 13-2*round(0.15*13)= 9.

Therefore I suggest

1. Use all of the data Ntrn = 221-(0.3*221)=155

2. Replace dividerand with divideblock

3. Design 10 nets to mitigate the random weight initialization.

If you need more help, please post your code.

Hope this helps.

Greg

[Povi Nike]

Thanks for answer. I built a code.

Where and how I should to replace dividerand with divideblock. How to indicate 10 nets to mitigate the random weight initialization at code?

% Solve an Autoregression Time-Series Problem with a NAR Neural Network % Script generated by NTSTOOL % Created Mon Jun 03 13:58:06 EEST 2013 % % This script assumes this variable is defined: % % unnamed - feedback time series.

targetSeries = tonndata(unnamed,false,false);

% Create a Nonlinear Autoregressive Network feedbackDelays = 1:2; hiddenLayerSize = 10; net = narnet(feedbackDelays,hiddenLayerSize);

% Choose Feedback Pre/Post-Processing Functions % Settings for feedback input are automatically applied to feedback output % For a list of all processing functions type: help nnprocess net.inputs{1}.processFcns = {'removeconstantrows','mapminmax'};

% Prepare the Data for Training and Simulation % The function PREPARETS prepares timeseries data for a particular network, % shifting time by the minimum amount to fill input states and layer states. % Using PREPARETS allows you to keep your original time series data unchanged, while % easily customizing it for networks with differing numbers of delays, with % open loop or closed loop feedback modes. [inputs,inputStates,layerStates,targets] = preparets(net,{},{},targetSeries);

% Setup Division of Data for Training, Validation, Testing % For a list of all data division functions type: help nndivide net.divideFcn = 'dividerand'; % Divide data randomly net.divideMode = 'time'; % Divide up every value net.divideParam.trainRatio = 70/100; net.divideParam.valRatio = 15/100; net.divideParam.testRatio = 15/100;

% Choose a Training Function % For a list of all training functions type: help nntrain net.trainFcn = 'trainlm'; % Levenberg-Marquardt

% Choose a Performance Function % For a list of all performance functions type: help nnperformance net.performFcn = 'mse'; % Mean squared error

% Choose Plot Functions % For a list of all plot functions type: help nnplot net.plotFcns = {'plotperform','plottrainstate','plotresponse', ... 'ploterrcorr', 'plotinerrcorr'};

% Train the Network [net,tr] = train(net,inputs,targets,inputStates,layerStates);

% Test the Network outputs = net(inputs,inputStates,layerStates); errors = gsubtract(targets,outputs); performance = perform(net,targets,outputs)

% Recalculate Training, Validation and Test Performance trainTargets = gmultiply(targets,tr.trainMask); valTargets = gmultiply(targets,tr.valMask); testTargets = gmultiply(targets,tr.testMask); trainPerformance = perform(net,trainTargets,outputs) valPerformance = perform(net,valTargets,outputs) testPerformance = perform(net,testTargets,outputs)

% View the Network view(net)

% Plots % Uncomment these lines to enable various plots. %figure, plotperform(tr) %figure, plottrainstate(tr) %figure, plotresponse(targets,outputs) %figure, ploterrcorr(errors) %figure, plotinerrcorr(inputs,errors)

% Closed Loop Network % Use this network to do multi-step prediction. % The function CLOSELOOP replaces the feedback input with a direct % connection from the outout layer. netc = closeloop(net); [xc,xic,aic,tc] = preparets(netc,{},{},targetSeries); yc = netc(xc,xic,aic); perfc = perform(net,tc,yc)

% Early Prediction Network % For some applications it helps to get the prediction a timestep early. % The original network returns predicted y(t+1) at the same time it is given y(t+1). % For some applications such as decision making, it would help to have predicted % y(t+1) once y(t) is available, but before the actual y(t+1) occurs. % The network can be made to return its output a timestep early by removing one delay % so that its minimal tap delay is now 0 instead of 1. The new network returns the % same outputs as the original network, but outputs are shifted left one timestep. nets = removedelay(net); [xs,xis,ais,ts] = preparets(nets,{},{},targetSeries); ys = nets(xs,xis,ais); closedLoopPerformance = perform(net,tc,yc)

Answer 5

[Greg Heath]

%Where and how I should to replace dividerand with divideblock.

net = narnet % No semicolon

See the entry for net.divideFcn? To change it use

net.divideFcn = 'divideblock';

Similarly for any other property of the net that you wish to change.

%How to indicate 10 nets to mitigate the random weight initialization at code?

Search for my double loop codes using

greg Ntrials

I did not look at the rest of your post.

Come back with specifics if you have problems.

You might want to search for more info using

greg narnet

Hope this helps.

Greg

Answer 6

[Povi Nike]

OK I changed: net = narnet % No semicolon; net.divideFcn = 'divideblock'; For undestanding clearly results Are saved output my future predicted values?

I searched for greg Ntrials. is that code right for my case on this link : http://www.mathworks.se/matlabcentral/answers/62625-how-can-i-improve-the-performance-of-a-closed-loop-narx-neural-network

Answer 7

[Povi Nike]

Thanks for example. Ok I adapt this double loop model to my model. I have general question. When NAR method is used , neural network is trained, I get results, where to find predicted values of next steps? First I thought that saved output values are predicted values but after some examples I understood that is not.

[Greg Heath]

Yes, the outputs are predicted values.

However, if you wish to continue the predictions beyond the current data,

1. Make sure the current output with target feedback yields a very low error rate

2. Convert to a closeloop configuration.

3. Test to see if the closeloop configuration with output (not target) feedback also yields a sufficiently low error.

4. If the closeloop configuration doesn't measure up, use train to modify the weights and improve performance.

5. Finally, run the closeloop net beyond the original data.

Answer 8

[Greg Heath]

help closeloop

doc closeloop

help removedelay

doc removedelay

Also search for these terms in NEWSGROUP and ANSWERS.

Greg

Answer 9

[akhilesh]

Using Time series toolbox I have generated a network model and it takes 4 delay input and gives 4 delay output. Confusion is, what 4 delay output values represent. Is they are 4 predicted values, if so then which one is more accurate. Please clear.