Complex Aggregates over Clusters of Elements

Complex aggregates have been proposed as a way to bridge the gap between approaches that handle sets by imposing conditions on specific elements, and approaches that handle them by imposing conditions on aggregated values. A complex aggregate summarises a subset of the elements in a set, where this subset is defined by conditions on the attribute values. In this paper, we present a new type of complex aggregate, where this subset is defined to be a cluster of the set. This is useful if subsets that are relevant for the task at hand are difficult to describe in terms of attribute conditions. This work is motivated from the analysis of flow cytometry data, where the sets are cells, and the subsets are cell populations. We describe two approaches to aggregate over clusters on an abstract level, and validate one of them empirically, motivating future research in this direction