1. Artificial Neural Networks
Davide Ballabio
Milano Chemometrics and QSAR Research Group
Università Milano - Bicocca
Kohonen Maps and
Counterpropagation
Artificial Neural Networks
Toolbox for MATLAB

2. Kohonen and CPANN Toolbox for MATLAB
Kohonen Maps (or Self Organizing Maps) and Counterpropagation Artificial Neural Networks (CPANNs) are two of the most popular Neural Networks (algorithms that simulate the human learning).
can handle both supervised and unsupervised problems
Kohonen and CP-ANN toolbox is a collection of MATLAB modules freely available via internet:

3. Kohonen maps
Kohonen Maps (or Self Organizing Maps) can handle unsupervised problems
SOM are made of neurons and need time (iterations) to learn to describe the data.
The time (number of iterations) and the size (number of neurons) must be defined by the user

4. Kohonen maps
Kohonen Maps (or Self Organizing Maps) can handle unsupervised problems
TOP MAP A x1 x2 x3 x4
Kohonen layers
p Kohonen layers
(p = number of variables)

5. Kohonen maps
Kohonen Maps (or Self Organizing Maps) can handle unsupervised problems
Toroidal geometry X

6. CPANN
Counterpropagation Artificial neural Networks can handle supervised problems (in this case classification problems)
CPANNs are an evolution of Kohonen Maps

7. CPANN
Class unfolding: transform the class vector in a matrix of zeros and ones
Class (n x 1)
Multi-y (n x G) 1 2 3 .. G
… … … 0
… … … 0
… … … 0
… … … 1
unfolding

8. CPANN
Counterpropagation Artificial neural Networks can handle supervised problems (in this case classification problems) A x1 x2 x3 x4
TOP MAP
Kohonen layers y1 y2 y3
Output layers

9. CPANN
Counterpropagation Artificial neural Networks can handle supervised problems (in this case classification problems):
For each sample,
for each epoch:
1) Find the winning neuron

10. CPANN
Counterpropagation Artificial neural Networks can handle supervised problems (in this case classification problems):
For each sample,
for each epoch:
2) Update the Kohonen weights
learning rate
topological distance

11. CPANN
Counterpropagation Artificial neural Networks can handle supervised problems (in this case classification problems):
For each sample,
for each epoch:
3) Update the output weights

12. Kohonen Maps and CPANN
In order to better understand how variables can characterize the data, we can do Principal Component Analysis on the Kohonen weights:
variables
1. Eigenvalues:
decide how many
component we can retain
PCA W
Weights matrix
N x p
neurons
2. Eigenvectors (loadings)
analyse the variables
3. Scores
analyse the neurons
relate neurons (and samples placed in neurons) and variables in a global way

13. Kohonen Maps and CPANN toolbox
Features of the toolbox:
user defined data scaling + automatic range scaling
modules for fitting and validating models
main available settings:
size and epochs (required)
boundary condition
learning rates can be modified
missing values are handled
visualize top map with Graphical User Interface
visualize PCA on weights with Graphical User Interface
The toolbox is based on the algorithm explained in:
Zupan J, Novic M, Ruisánchez I. Chemometrics and Intelligent Laboratory Systems (1997)

14. Kohonen Maps and CPANN toolbox
Example of application on the ITAOILS dataset:
572 olive oil samples,
each sample is described by the percentage composition of 8 fatty acids (variables)
samples belong to 9 different Italian areas of productions (classes)
the final aim of the classification model is the geographical origin determination of the samples.
Data reference:
M. Forina, C. Armanino, S. Lanteri, E. Tiscornia, in: Food Research and Data Analysis, Classification of olive oils from their fatty acid composition, Applied Science Publishers, London, 1983.

15. Kohonen Maps and CPANN toolbox
Principal Component Analysis for data structure evaluation

16. Thanks for your attention !
Davide Ballabio
Milano Chemometrics and QSAR Research Group
Department of Environmental Sciences
Università Milano – Bicocca
You can download the Kohonen and CP-ANN toolbox 1.0 here:
Version 2.0 will be available soon…
Paper in preparation, to be submitted to Chemometrics
and Intelligent Laboratory Systems
Thanks for your attention !