MLP

A Multilayer Perceptron Neural Network implementation written in ANSI-C.

Multilayer Perceptron Implementation

This was a project for the course MYE035-CSE.UOI - Computational Intelligence during the 2018-19 winter semester.

Created by:

Nick Deligiannis
Paschalis Homondozlis

The problem

The mlp was used to solve a three class classification problem which is the following:

Given 6000 examples [points (x1,x2) at 2D space] in which:

3000 points are contained in the rectangle [0,2] x [0,2] ( 1500 for training and 1500 for validation )
3000 points are contained in the rectangle [-2,0] x [-2,0] ( 1500 for training and 1500 for validation )

Hence, there are two data sets. The training set and the testing/validation set. Finally we define the three classes/categories as following:

${\color{Red} (x_{1} - 1)^{2} +(x_{2}- 1)^{2} \leq 0.16 }$

${\color{Red} (x_{1} + 1)^{2} +(x_{2} + 1)^{2} \leq 0.16 }$
${\color{Green} \left [ (x_{1} - 1)^{2} +(x_{2} -1)^{2} > 0.16 \right ] \cap \left [ (x_{1} - 1)^{2} + ( x_{2} -1)^{2} < 0.64 \right] }$

${\color{Green} \left [ (x_{1} + 1)^{2} +(x_{2} +1)^{2} > 0.16 \right ] \cap \left [ (x_{1} + 1)^{2} + ( x_{2} +1)^{2} < 0.64 \right] }$
${\color{Cyan} ( x_{1} - 1)^{2} + ( x_{2} -1 )^{2} \geq 0.64 }$

${\color{Cyan} ( x_{1} + 1)^{2} + ( x_{2} + 1 )^{2} \geq 0.64 }$

### Visualisation

Specifications

This Neural Network has two hidden layers with customizable number of neurons in each one. The learning method implemented is gradient descent and the activation functions used are the logistic and the hyberbolic tangent.

Known Issues

There is a problem using the hyperbolic tangent as activation function. If you select the tanh function then it is being asserted to all the neurons of the network, including the output layer neurons, something that will not provide the proper results since tanh ranges from -1 to +1 and the encoding used was based on the logistic function which ranges from 0 to 1.

Usage

Generate the dataset using the “dataset_generation.c” file (compile /w gcc dataset_generation.c).
Change the path @ lines 752-754 (on mlp.c) or comment out those lines if you don’t wish to use gnuplot for visualisation
Compile the “mlp.c” file (compile /w gcc mlp.c -lm)
Run the executable file.

MLP

A Multilayer Perceptron Neural Network implementation written in ANSI-C.

Multilayer Perceptron Implementation

The problem

Specifications

Known Issues

Usage

Example

Results of a run.

Visualisation in gnuplot

Points classified correctly

Points classified wrong

Square error behavior