Cities are growing at a fast rate, and transportation networks need to adapt accordingly. To design, plan, and manage transportation networks, domain experts need data that reflect how people move from one place to another, at what times, for what purpose, and in what mode(s) of transportation. However, traditional data collection methods are not cost-effective or timely. For instance, travel surveys are very expensive, collected every ten years, a period of time that does not cope with quick city changes, and using a relatively small sample of people. In this paper, we propose an algorithmic pipeline to infer the distribution of mode of transportation usage in a city, using mobile phone network data. Our pipeline is based on a Topic-Supervised Non-Negative Matrix Factorization model, using a Weak-Labeling strategy on user trajectories with data obtained from open datasets, such as GTFS and OpenStreetMap. As a case study, we show results for the city of Santiago, Chile, which has a sophisticated intermodal public transportation system. Importantly, our pipeline delivers coherent results that are explainable, with interpretable parameters at each step. Finally, we discuss the potential applications and implications of such a system in transportation and urban planning.