Huge amounts of data are nowadays produced by a large family of sensors, which typically measure multiple variables over time. Such information can be profitably organized as multivariate time-series. Collecting enough labelled samples to set up a supervised analysis for such kind of data is challenging. In this context, semi-supervised clustering methods represent a well suited tool to get the most out of such reduced amount of knowledge. With the aim to deal with the semi-supervised analysis of multivariate time-series data, we propose a semi-supervised (constrained) deep embedding time-series clustering framework to cope with weakly supervision in form of must- and cannot-link constraints. Experimental evaluation on real-world benchmarks has highlighted the effectiveness of our proposal.