Dynamic clustering of interval data using a Wasserstein-based distance

Interval data allow statistical units to be described by means of intervals of values, whereas their representation by means of a single value appears to be too reductive or inconsistent. In the present paper, we present a Wasserstein-based distance for interval data, and we show its interesting properties in the context of clustering techniques. We show that the proposed distance generalizes a wide set of distances proposed for interval data by different approaches or in different contexts of analysis. An application on real data is performed to illustrate the impact of using different metrics and the proposed one using a dynamic clustering algorithm.