Figure 1.

The mutual information SBMI, conditional entropy SBCE and objective function at the center (A,B) and border (C,D) of a category of width W depending on the similarity width with triangular similarity measures. Since information and entropies are always positive, larger values of $\alpha$ always lead to lower objective functions. The right panels (B,D) are magnifications of the rectangles depicted in the left panels (A,C). Arrows indicate the maxima of the objective functions. We observe that the maximum of the objective function at the center is always larger than $W/2$ and increases slowly with trade-off parameter $\alpha$, while the maximum at the border is very small for small values of $\alpha$ and then undergoes an abrupt increase. These results are obtained for categories of width W.