This paper proposes the sky-signature model, an extension of the signature model Gautrais et al. (in: Proceedings of the Pacific-Asia conference on knowledge discovery and data mining (PAKDD), Springer, 2017b) to multi-objective optimization. The signature approach considers a sequence of itemsets, and given a number k it returns a segmentation of the sequence in k segments such that the number of items occuring in all segments is maximized. The limitation of this approach is that it requires to manually set k, and thus fixes the temporal granularity at which the data is analyzed. The sky-signature model proposed in this paper removes this requirement, and allows to examine the results at multiple levels of granularity, while keeping a compact output. This paper also proposes efficient algorithms to mine sky-signatures, as well as an experimental validation both real data both from the retail domain and from natural language processing (political speeches).