The Mean Angular Distance Among Objects and Its Relationships with Kohonen Artificial Neural Networks

This job refers to classification of multidimensional objects and Kohonen artificial neural networks. A new concept is introduced, called the mean angular distance among objects (MADO). Its value can be calculated as the cosine of the mean centered vectors between objects. It can be expressed in matrix form for any number of objects. The MADO allows us to interpret the final organization of the objects in a Kohonen map. Simulated examples demonstrate the relationship between MADO and Kohonen maps and show a way to take advantage of the information present in both of them. Finally, a real analytical chemistry case is analyzed as an application on a big data set of an air quality monitoring campaign. It is possible to discover in it a subgroup of objects with different characteristics than those of the general trend. This subgroup is linked to the existence of an unidentified SO₂ source that, a priori, has not been taken into account.