- On 4. oktober 2018
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There are two types of training used in neural networks, supervised and unsupervised training, of which supervised is the most common.
The training data contains examples of inputs together with the corresponding outputs, and the network learns to infer the relationship between the two.
Then, we set the number of input, which is 13 because out data set has 13 input attributes, and the number of outputs is 3 because of three different classes - outcomes.
We can see that this table has 16 columns, first 13 of them represents inputs, and last 3 of them represents outputs from our data set.
Standard approaches to validation of neural networks are mostly based on empirical evaluation through simulation and/or experimental testing.
It is capable of modeling complex functions, it is robust (good at ignoring irrelevant inputs and noise) ,and can adapt its weights and/or topology in response to environment changes.
Another reason we will use this type of perceptron is simply because it is very easy to use - it implements black-box point of view, and can be used with few knowledge about the relationship of the function to be modeled.
Then we click on Next, and the following window will show (but not the values inside) Problems that require more than one hidden layers are rarely encountered.
We also checked 'Use Bias Neurons' option and chosen 'Sigmoid' for transfer function (because our data set is normalized, values are between 0 and 1).
The Bias weights control shapes, orientation and steepness of all types of Sigmoid functions through data mapping space.
The idea is to stabilize the weight change by making non radical revisions using the combination of the gradient decreasing term with a fraction of the previous weight change.
After 13 iterations Total Net Error drop down to a specified level of 0.01 which means that training process was successful and that now we can
As we can see, in the first attempt we succeeded to find pretty good solution, so we can conclude that this type of neural network architecture is the good choice .
We know that the larger the learning rate is, the larger the weight changes on each epoch, and the quicker the network learns.
Even though the previous architecture gave really good results, we will try to lower the number of neurons in hidden layer in order to see what the performances of network will be like then.
It was needed 10 iteration to reach the total mean square error of 0.0036316… that is only 0.00035 lower then previous attempt.
But, if we continue to lower down the number of hidden neurons, and put only one hidden neuron and leave default Learning parameters, the network will be not able to do the training successfully.
First we create a new neural network, type will be Multy Layer Perceptron as it was in the previous attempts.
We can conclude that two hidden layers architecture is able to find the solution, but is not necessary for our problem and we can get better results using just one layer.
This is really big benefit due to the fact in real world applications developers only have a small part of all possible patterns for the generation of a neural network.
To do this, we have to divide our training set to two sets- one amount of data will remain training set, and the second one will become the test data.
We will try to see how fast and good will network learn if we lower the training set and examine the ability of a network to classify input patterns that are not in the training set.
To reach the best generalization, the data set should be split into three parts: validation, training and testing set.
In the advanced training we are going to use the architecture given in the attempt number 4, that is 13 inputs, 3 outputs, 4 hidden neurons and all other parameters used before.
In this first attempt we will choose random 40% of instances of training set for training and remain 60% for testing.
The Max Error will remain 0.01, Learning Rate 0.2 and Momentum 0.7 If we look at the graph above and compare it with the one we had in attempt 4 we will see that the function came close to wanted value after more iteration.
The individual errors are mainly good, but we have some cases where are pretty high (0.835, 0.754…) How we are going to use 30% of data set or 53 instances for training, and 70% that is 125 instances to test the network.
The function needed some time to start to fall down, it was not immediately like we have already use to it, but after 26 iteration the total error was below 0.01.
In order to verify the network, we are going to randomly take 5 instances again: The output neural network produced for this input is, respectively:
In the attempt 11 we are going to use 20% or 53 instances for training, and 80% or 125 instances to test the network.
As we can see, if the parameters remain the same, the result are 100% worse that before even though we increase the test data and decrease the training set by 10%.
Furthermore, in individuals error we have some that are really high 0.8349, 0.7167… But, knowing that we used only 17 instances to train the network, these results are not shocking at all.
What proved out to be crucial to the success of the training, is the selection of an appropriate number of hidden neurons during the creating of a new neural network.
We used 17, 4 and 2 hidden neurons, and the best results have been reached with 4 neurons in one hidden layer.
In the end, we divided original data set into two sets- training and testing in order to examine the ability of generation for the architecture with four hidden neurons.
In the first table (Table 1.) are the results obtained using standard training techniques, and in the second table (Table 2.) the results obtained by using advanced training techniques.
- On 25. september 2021
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