  In distributed classification, each learner observes its environment and
deduces a classifier. As a learner has only a local view of its environment,
classifiers can be exchanged among the learners and integrated, or merged, to
improve accuracy. However, the operation of merging is not defined for most
classifiers. Furthermore, the classifiers that have to be merged may be of
different types in settings such as ad-hoc networks in which several
generations of sensors may be creating classifiers. We introduce decision
spaces as a framework for merging possibly different classifiers. We formally
study the merging operation as an algebra, and prove that it satisfies a
desirable set of properties. The impact of time is discussed for the two main
data mining settings. Firstly, decision spaces can naturally be used with
non-stationary distributions, such as the data collected by sensor networks, as
the impact of a model decays over time. Secondly, we introduce an approach for
stationary distributions, such as homogeneous databases partitioned over
different learners, which ensures that all models have the same impact. We also
present a method that uses storage flexibly to achieve different types of decay
for non-stationary distributions. Finally, we show that the algebraic approach
developed for merging can also be used to analyze the behaviour of other
operators.
