Multilayer feed-forward artificial neural networks for Class-modeling F. Marini, A. Magrì, R. Bucci Dept. of Chemistry - University of Rome “La Sapienza”

The starting question…. Despite literature on NNs has increased significantly, no paper considers the possibility of performing class- modeling

class modeling: what…. Class modeling considers one class at a time Any object can then belong or not to that specific class model As a consequence, any object can be assigned to only one class, to more than one class or to no class at all classificationclass modeling

…..and why Flexibility Additional information: –sensitivity: fraction of samples from category X accepted by the model of category X –specificity: fraction of samples from category Y (or Z, W….) refused by the model of category X No need to rebuild the existing models each time a new category is added. less equivocal answer to the question: “are the analytical data compatible with the product being X as declared?”

A first step forward A particular kind of NN, after suitable modifications could be used for performing class-modeling ( Anal. Chim. Acta, 544 (2005), 306 ) –Kohonen SOM –Addition of dummy random vectors to the training set –Computation of a suitable (non-parametric) probability distribution after mapping on the 2D Kohonen layer. –Definition of the category space based on this distribution

In this communication… …The possibility of using a different type of neural network (multilayer feed-forward) to operate class- modeling is studied –How to? –Examples

Just a few words about NN   Sophocles

NN: a mathematical approach From a computational point of view, ANNs represent a way to operate a non-linear functional mapping between an input and an output space. This functional relation is expressed in an implicit way (via a combination of suitably weighted non-linear functions, in the case of MLF-NN ) ANNs are usually represented as groups of elementary computational units (neurons) performing simultaneously the same operations. Types of NN differ in how neurons are grouped and how they operate

Multilayer feed-forward NN Individual processing units are organized in three types of layer: input, hidden and output All neurons within the same layer operate simultaneously output hidden input x 1 x 2 x 3 x 4 x 5 y 1 y 2 y 3 y 4

The artificial neuron f(  )  w 1k w 2k w 3k x3x3 x2x2 x1x1 zkzk hidden input x 1 x 2 x 3 x 4 x 5

The artificial neuron f(  )  w 1j w 2j w 3j z3z3 z2z2 z1z1 yjyj hidden input x 1 x 2 x 3 x 4 x 5 output y 1 y 2 y 3 y 4

Training Iterative variation of connection weights, to minimize an error criterion. Usually, backpropagation algorithm is used:

MLF class-modeling: what to do? Model for each category has to be built using only training samples from that category Suitable definition of category space

Somewhere to start from When targets are equal to input values, hidden nodes could be thought of as a sort of non-linear principal components Input Hidden Input x 1 x 2 x 3 X j x m Output value of hidden node 1 Output value of hidden node 2

… and a first ending point For each category a neural network model is computed providing the input vector also as desired target vector N inp -N hid -N inp Number of hidden layer is estimated by loo-cv (minimum reconstruction error in prediction) The optimized model is then used to predict unknown samples: –Sample is presented to the network –Vector of predicted responses (which is an estimate of the original input vector) is computed –Prediction error is calculated and compared to the average prediction error for samples belonging to the category (as in SIMCA ).

NN-CM in practice Separate category autoscaling if is lower than a predifined threshold, the sample is refused by the category model.

A couple of examples

The classical X-OR 200 training samples:200 training samples: –100 class 1 –100 class test samples:200 test samples: –100 class 1 –100 class 2 3 hidden neurons for each category

Results Sensitivity: –100% class 1, 100% class2 Specificity: –75% class1 vs class 2 –67% class2 vs class 1 Prediction ability: –87% class1 –83% class2 –85% overall These results are significantly better than with SIMCA and UNEQ ( specificities lower than 30% and classification slightly higher than 60%)

A very small data-set: honey

CM of honey samples 76 samples of honey from 6 different botanical origins (honeydew, wildflower, sulla, heather, eucalyptus and chestnut) samples per class 2 input variables: specific rotation; total acidity Despite the small number of samples, a good NN model was obtained (2 hidden neurons for each class) Possibility of drawing a Coomans’ plot

Further work and Conclusions A novel approach to class-modeling based on multilayer feed-forward NN was presented Preliminary results seem to indicate its usefulness in cases where traditional class modeling fails Effect of training set dimension should be further invetigated (our “small” data set was too good to be used for obtaining a definitive answer) We are analyzing other “exotic” data sets for classification where traditional methods fail.

Acknowledgements Prof. Jure Zupan, SloveniaProf. Jure Zupan, Slovenia