The PZMI vector of order 4 for the NF cartography has 9 complex numbers that describe amplitudes and phases.
Afterwards, we determine the PZMI vector for all the NF cartographies.
The study of the PZMI vector invariance shows that with a moment order equal to 4, the PZMI can describe a dipole for different orientations with an accuracy equal to 90%.
In order to classify the radiating elements using the PZMI vector, we have chosen an algorithm usually used in pattern recognition and classification: the neural network.
To implement a neural network in our study, we have prepared a learning database including 1,158 PZMI vectors calculated from 1,158 different cartographies.
To overcome this problem, we propose to improve this method by coupling it with the PZMI and the NN, as described in Section 3 of this paper.