Dynamic clustering of interval data based on hybrid \(L_q\) distance

摘要

Dynamic clustering defines partitions within data and prototypes to each partition. Distance metrics are responsible for checking the closeness between instances and prototypes. Considering the literature about interval data, distances depend on interval bounds and the information inside the intervals is ignored. This paper proposes new distances, which explore the information inside of intervals. It also presents a mapping of intervals to points, which preserves their spatial location and internal variation. We formulate a new hybrid distance for interval data based on the well-known \(L_q\) distance for point data. This new distance allows for a weighted formulation of the hybridism. Hence, we propose a Hybrid \(L_q\) distance, a Weighted Hybrid \(L_q\) distance, as well as the adaptive version of the Hybrid \(L_q\) distance for interval data. Experiments with synthetic and real interval data sets illustrate the usefulness of the hybrid approach to improve dynamic clustering for interval data.