  Ensembles, as a widely used and effective technique in the machine learning
community, succeed within a key element -- "diversity." The relationship
between diversity and generalization, unfortunately, is not entirely understood
and remains an open research issue. To reveal the effect of diversity on the
generalization of classification ensembles, we investigate three issues on
diversity, i.e., the measurement of diversity, the relationship between the
proposed diversity and the generalization error, and the utilization of this
relationship for ensemble pruning. In the diversity measurement, we measure
diversity by error decomposition inspired by regression ensembles, which
decomposes the error of classification ensembles into accuracy and diversity.
Then we formulate the relationship between the measured diversity and ensemble
performance through the theorem of margin and generalization and observe that
the generalization error is reduced effectively only when the measured
diversity is increased in a few specific ranges, while in other ranges larger
diversity is less beneficial to increasing the generalization of an ensemble.
Besides, we propose two pruning methods based on diversity management to
utilize this relationship, which could increase diversity appropriately and
shrink the size of the ensemble without much-decreasing performance. Empirical
results validate the reasonableness of the proposed relationship between
diversity and ensemble generalization error and the effectiveness of the
proposed pruning methods.

Machine Learning;Machine Learning