Kohonen nets in visualizing multivariate data
نویسنده
چکیده
We consider n = 49 Polish voivodeships (administrative units), each characterized by p = 9 traits (features) expressing social, demographic, and environmental characteristics of the given units. Exemplary traits are: use of fertilizers, natural increase, divorce rate, education, number of medical doctors. The data were formerly analyzed with the goal of nding association between the mentioned traits and mortality rates of men and women recorded in each of the voivodeship (Bartkowiak and Kup s c 1997). Our goal is to nd a graphical representation of all the n = 49 voivodeships showing their similarities (i.e. which ones are similar) and dissimilarities (i.e. which ones di er much from the others and exhibit some atypical patterns) with respect to the considered traits. From the plethora of methods we have chosen: Kohonen SOMs, i.e. Self Organizing Maps (Kohonen, 1997). It seems to us that just that method permits to use more information of the among{units relationship, compared to the traditional cluster analysis methods. In the considered case of the Polish epidemiological data it was possible to confront the results (con guration of points-voivodeships in the obtained SOM) with their true con guration in the 9{dimensional features space R. It happens, that the entire data cloud may by quite safely reproduced by the rst 3 PC-s. We retain then 84% of the total inertia. The reproduction for the individual inertia (variance) of subsequent features amounts (in percentages): 1 81; 2 95; 3 72; 4 97; 5 64; 6 87; 7 88; 8 79; 9 90: Thus the true spatial con guration of our data can be seen in a spin-plot.
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