Learning. Generate models from data Enhance models using training data. SAMT-Tutorial p.1/21

Transcription

1 Learning Generate models from data Enhance models using training data SAMT-Tutorial p.1/21

2 Lets start with a fuzzy model again Precision agriculture: we have soil and yield data; we need a robust model to control the fertilization as function of soil type for every location within the field (GPS controlled) gwd: ground water distance from surface (5 classes) rise: capillary rise (5 classes) ufc: plant available field capacity relyield: measured yield as training target Open the project training and play with it (Compare the model output of the fuzzy model with the target). Use the splatter plot with gwd, rise, ufc, relyield as input! SAMT-Tutorial p.2/21

3 Feed forward neural networks error=target Output Output Layer Hidden Layer b1 b b3 w11 w33 Input Layer I1 I2 I3 SAMT-Tutorial p.3/21

4 Training of feed forward networks N (target i output i ) 2 Min! i=0 There are three training algorithm in SAMT Back propagation algorithm (simple but useful) Back propagation with momentum Levenberg-Marquardt (default) Options: Number of hidden nodes Number of training steps Flag for shuffle of training data SAMT-Tutorial p.4/21

5 The SAMT NN within SAMT SAMT_NN can handle up to 30 inputs and 50 nodes in hidden layer (but together with SAMT the number of inputs is restricted to 3) SAMT_NN can read csv files with different separators and header lines SAMT_NN contains some graphical analysis techniques The trained models can export to SAMT SAMT-Tutorial p.5/21

6 Example for SAMT NN Problem: How can we generate training data for SAMT_NN? Pack all grids in one hdf (gwd, rise, ufc, reyield) Use GEN_NN3 to generate a training data set Start SAMT_NN and open this data set Train it and check the result in SAMT_NN Store the trained net and load it into SAMT Use the network in SAMT and check the result against the target Compare the result with the fuzzy model SAMT-Tutorial p.6/21

7 Alternative neural network architectures There is a radial basis function network in SAMT (RBF) based on cluster algorithm (kmeans and kohonen feature map) SAMT-Tutorial p.7/21

8 Kohonen feature map The kohonen feature map realizes an un-supervised learning: Kohonen map A S v Ws Ws V The training procedure produces a map from the input space V to the kohonen map. SAMT-Tutorial p.8/21

9 Training of a kohonen feature map Initialization: every node of the kohonen map gets a random starting vector w rl = rand() Select a vector v randomly from V Response: determine the winner w r with: v w r v w r r A Adaptation: w neu r h rr = exp( (r r )2 2σ 2 ) = w alt r + ǫh rr ( v w alt r ) with: A trained kohonen feature map can reproduce the statistics of V into the map A SAMT-Tutorial p.9/21

10 Example kohonen feature map Open the project training Construct a Kohonen with 3 inputs and 6 x 6 nodes Train the kohonen map and visualize it (histogram?) SAMT-Tutorial p.10/21

11 A kohonen map comes seldom alone Problem: we need a model for the yield from the inputs Define a rbf with P1=1 (kohonen) and P2=3 (inputs) Start the training Show the result Investigate the result Compare the result with the neural network and the fuzzy model SAMT-Tutorial p.11/21

12 Radial basis function network (RBF) RBF can be considered as a special fuzzy membership function: f( x, w i ) = exp( scale x w i ) y( x) = M i=0 a i f( x, w i ) SAMT-Tutorial p.12/21

13 Parameter-fit for a RBF f( x 1, w 1 )... f( x 1, w m ) f( x 2, w 1 )... f( x 2, w m )... f( x n, w 1 )... f( x n, w m ) a 1 a 2. a m = y 1 y 2. y n Remark: m is the number of kohonen nodes; n is the number of samples (about 2000); solved using QR-factorization SAMT-Tutorial p.13/21

14 Training of fuzzy models Problem: how can we enhance fuzzy models with measured data? Adapt the fuzzy membership functions Adapt the fuzzy rules Adapt the fuzzy outputs SAMT-Tutorial p.14/21

15 Adaptation of the inputs triangular function µ A (x) = trapezoid function µ A (x) = 0 : x x 1 (x x 1 )/(x 2 x 1 ) : x > x 1 x x 2 (x 3 x)/(x 3 x 2 ) : x > x 2 x < x 3 0 : x x 3 0 : x x 1 (x x 1 )/(x 2 x 1 ) : x > x 1 x < x 2 1 : x x 2 x x 3 (x 4 x)/(x 4 x 3 ) : x > x 3 x < x 4 0 : x x 4 SAMT-Tutorial p.15/21

16 Simulation of input adaptation Conclusion: input adaptation is slow SAMT-Tutorial p.16/21

17 Adaptation of rules Rule can be easily adapted by changing a pointer But a rule is a stable part of expert knowledge But a change of a rule is a global change in the model Conclusion: leave the rules as they are (unchanged) SAMT-Tutorial p.17/21

18 Adaptation of outputs Outputs as crisp values: o = k a k o k k a k (1) SAMT-Tutorial p.18/21

19 Algorithm for adaptation of outputs error of a output of active rule: step δ k : error = y i fuzzy(x 1i,x 2i,x 3i ) adaptation of the outputs: δ k = a k o k error gain o k = o k + δ k SAMT-Tutorial p.19/21

20 Example using fuzzy training Open the project training Open SAMT_Fuzzy Open in SAMT_Fuzzy the model yield_train Use the data for the neural network as training set Discuss the results, compare it to the neural network and rbf SAMT-Tutorial p.20/21

21 Conclusion learning Use the neural network if you have reliable data to train Try alternative to the feed forward a rbf network Drawback: all neural networks are used as black box models Use fuzzy model if you have expert knowledge (you have to find the best expert) Train the fuzzy model to enhance it Drawback: a fuzzy model must be carefully designed SAMT-Tutorial p.21/21