Similarity/Diversity Indices on Incidence Matrices Containing Missing Values

Quantifying the diversity content of an incidence matrix is challenging in several scientific fields. The existing indices capture diverse facets of diversity and thus comparing their behaviour is not a straightforward task. For example, an application of diversity measures involves ensembles of classifiers which usually in real applications contain missing values. Therefore, we analysed 14 statistics and, after making them comparable and able to deal with missing values, we applied them on more than one hundred incidence matrices in order to examine the relationships among the measures themselves. In particular, we highlighted the importance of the inter-row agreement of factors, the general agreement of incident factors, as well as the influence on the indices of the proportion of missing values and matrix dimensions, the sensitivity to missing values, the uniform distribution of entries and the invariance to matrix transposition.