Transcript About a method to forecast using neural network

Application of
Back-Propagation neural
network in data forecasting
Le Hai Khoi, Tran Duc Minh
Institute Of Information Technology – VAST
Ha Noi – Viet Nam
Acknowledgement
The authors want to Express our
thankfulness to Prof. Junzo WATADA who
read and gave us worthy comments.
Authors
CONTENT
Introduction
Steps in data forecasting modeling
using neural network
Determine network’s topology
Application
Concluding remarks
Introduction
• Neural networks are “Universal Approximators”
• To find a suitable model for the data forecasting problem is very difficult and
in reality, it might be done only by trial-and-error
• We may take the data forecasting problem for a kind of data processing
problem
Data collecting and
analyzing
Pre-processing
Neural Networks
Post-processing
Figure 1: Data Processing.
Steps in data forecasting modeling using neural network
The works involved in are:
* Data pre-processing:
determining data interval: daily, weekly, monthly or quarterly; data type:
technical index or basic index; method to normalize data: max/min or
mean/standard deviation.
* Training:
determining the learning rate, momentum coefficient, stop condition, maximum
cycles, weight randomizing, and size of training set, test set and verification
set.
* Network’s topology:
determining number of inputs, hidden layers, number of neurons in each layer,
number of neurons in output layer, transformation functions for the layers and
error function
Steps in data forecasting modeling using neural network
The major steps in design the data forecasting model is as follow:
１. Choosing variables
２．Data collection
３．Data pre-processing
４．Dividing the data set into smaller sets: training, test and verification
５．Determining network’s topology: number of hidden layers, number of
neurons in each layer, number of neurons in output layer and the
transformation function.
６．Determining the error function
７．Training
８．Implementation.
In performing the above steps, it is not necessary to perform steps sequentially. We could be back to the
previous steps, especially in training and choosing variables steps. The reason is because in the designing
period, if the variables chosen gave us unexpected results then we need to choose another set of variables
and bring about the training step
Choosing variables and Data collection
Determining which variable is related directly or indirectly to the data
that we need to forecast.
• If the variable does not have any affect to the value of data that we need to
forecast then we should wipe it out of consider.
• Beside it, if the variable is concerned directly or indirectly then we should
take it on consider.
Collecting data involved with the variables that are chosen
Data pre-processing
Analysis and transform values of input and output data to emphasize the
important features, detect the trends and the distribution of data.
Normalize the input and output real values into the interval between max and
min of transformation function (usually in [0, 1] or [-1, 1] intervals). The most
popular methods are following:
SV = ((0.9 - 0.1) / (MAX_VAL - MIN_VAL)) * (OV - MIN_VAL)
Or:
SV = TFmin + ((TFmax - TFmin) / (MAX_VAL - MIN_VAL)) * (OV - MIN_VAL)
where:
SV: Scaled Value
MAX_VAL: Max value of data
MIN_VAL: Min value of data
TFmax: Max of transformation function
TFmin: Min of transformation function
OV: Original Value
Dividing patterns set
Divide the whole patterns set into the smaller sets:
(1) Training set
(2) Test set
(3) Verification set.
The training set is usually the biggest set employed in training the network.
The test set, often includes 10% to 30% of training set, is used in testing the
generalization. And the verification set is set balance between the needs of
enough patterns for verification, training, and testing.
Determining network’s topology
This step determines links between neurons, number of hidden layers,
number of neurons in each layer.
1. How neurons in network are connected to each other.
2. The number of hidden layers should not exceed two
3. There is no method to find the most optimum number of neurons used in
hidden layers.
=> Issue 2 and 3 can only be done by trial and error since it is depended on the
problem that we are dealing with.
Determining the error function
• To estimate the network’s performance before and after training process.
• Function used in evaluation is usually a mean squared errors. Other functions
may be: least absolute deviation, percentage differences, asymmetric least
squares etc.
Performance index
F(x) = E[eTe] = E [ ( t - a )T ( t - a ) ]
Approximate Performance index
F(x) = eT(k)e(k)] = (t(k) - a(k) )T ( t(k) - a(k))
• The lastest quality determination function is usually the Mean Absolute
Percentage Error - MAPE.
Training
Training tunes a neural network by adjusting the weights and biases
that is expected to give us the global minimum of performance
index or error function.
When to stop the training process ?
1. It should stop only when there is no noticeable progress of the error
function against data based on a randomly chosen parameters set?
2. It should regularly examine the generalization ability of the network by
checking the network after a pre-determined number of cycles?
3. Hybrid solution is having a monitoring tool so we can stop the training
process or let it run until there is no noticeable progress.
4. The result after examining of verification set of a neural network is most
persuadable since it is a directly obtained result of the network after
training.
Implementation
This is the last step after we determined the factors related to network’s
topology, variables choosing, etc.
1. Which environment: Electronic circuits or PC
2. The interval to re-train the network: might be depended on the times and
also other factors related to our problem.
Determine network’s topology
Multi-layer feed-forward neural networks
R1 x1
S1xR1
1
P
a1
W1
f1

n1
S1x1
f2
S1x1
S2xS1
S1x1

n2
S2x1
S2x1
1
b1
a2
W2
b2
S2x1
a2 = f2( W2 f1 (W1p + b1) + b2)
Figure 2: Multi-layer feed-forward neural networks
where:
P: input vector (column vector)
Wi: Weight matrix of neurons in layer i. (SixRi: Si rows (neurons), Ri columns
(number of inputs))
i
b : bias vector of layer i (Six1: for Si neurons)
ni: net input (Six1)
fi: transformation function (activate function)
ai: net output (Six1)
: SUM function
i = 1 .. N, N is the total number of layers.
Determine training algorithm and network’s topology
bias
x１
wij
1
wjk
bias
x2
wkl
1
Output
…
…
…
xn
…
Input layer
Hidden layers
Output layer
Figure 3: Multi-layered Feed-forward neural network layout
Transfer function is a sigmoid or any squashing function that is differentiable
1
ƒ(x) =
and ƒ’(x) = ƒ(x) { 1 - ƒ(x) }
1 + e-δx
Back-propagation algorithm
Step 1: Feed forward the inputs through networks:
a0 = p
am+1 = fm+1 (Wm+1 am + bm+1), where m = 0, 1, ..., M – 1.
a = aM
Step 2: Back-propagate the sensitive (error):
 M
M
M
 2 F
s
m
 W  s
s F n
m
n t  a
m
m 1 T
m 1
at the output layer
at the hidden layers
where m = M – 1, ..., 2, 1.
Step 3: Finally, weights and biases are updated by following formulas:

W m k  1  W m k    s m a m 1
b m k  1  b m k    s m

T
.
(Details on constructing the algorithm and other related issues should be found on text book Neural Network Design)
Using Momentum
This is a heuristic method based on the observation of training results.
The standard back-propagation algorithm will add following item to the weight as
the weight changes:
∆Wm(k) = - sm (am – 1) T,
∆bm(k) = - sm .
When using momentum coefficient, this equation will be changed as follow:
∆Wm(k) = ∆Wm(k – 1) – (1 – ) sm (am – 1)T,
∆bm(k) = ∆bm(k – 1) – (1 – ) sm .
Application
LAYER
class
Arrow: inheritance relation
Rhombic antanna arrow:
Aggregate relation
NEURAL NET class includes the
components that are the instances of
Output Layer and Hidden Layer.
Input Layer is not implemented here
since it does not do any calculation on the
input data.
friend
Output layer
Hidden layer
NEURAL NET
class
Application
Application
Application
Concluding remarks
The determination of the major works is important and realistic. It will help
develop more accuracy data forecasting systems and also give the
researchers the deeper look in implementing the solution using neural
networks
In fact, to successfully apply a neural network, it is depended on three major
factors:

First, the time to choose the variables from a numerous quantity of data as well as perform
pre-processing those data;

Second, the software should provide the functions to examine the generalization ability,
help find the optimal number of neurons for the hidden layer and verify with many input sets;

Third, the developers need to consider, examine all the possible abilities in each time
checking network’s operation with various input sets as well as the network’s topologies
so that the chosen solution will exactly described the problem as well as give us the most
accuracy forecasted data.
THANK YOU FOR
ATTENDING!
Authors
Kytakyushu 03/2004