Reconstructing Missing Traffic Data with Tensor Mathematics
This tensor-based data imputation method was developed and tested as part of FEDORA Deliverable D3.1 – Integrated Cross-Sectoral Data Space.
Traffic sensors fail. Induction loops drop out, communication links go down, and entire stretches of a city’s traffic network can go dark for hours, days, or longer. Yet the analytics, forecasting and traffic-management tools that cities rely on need continuous, complete data to work properly. The question FEDORA set out to answer is a practical one: when the data has holes in it, how do you reliably fill them back in?
The answer draws on a mathematical structure called a tensor — essentially a multi-dimensional generalisation of the tables and matrices most data tools use. Traffic data naturally has several dimensions at once: it varies by location, by day, and by time of day, and all of these dimensions are correlated — a traffic jam on one street tends to be linked to conditions nearby and to what happened at the same time yesterday. A technique known as low-rank tensor learning uses exactly this structure, treating the network’s spatial layout and its recurring temporal patterns as built-in clues that guide how missing values should be reconstructed.
Two specific methods were put to the test. One, called ST-LRTC, builds in the physical logic of how traffic actually flows through a network — respecting the continuity and daily rhythm of traffic and the way congestion propagates spatially between locations. The other, GLSKF, is tuned to capture both the big-picture, long-range patterns across the network and the short, sudden fluctuations — like a rush-hour spike — that a smoother model might miss.
Both were tested against real-world data: a month of vehicle-flow readings from 339 induction loops in a northern Spanish city, recorded every minute — over 44,000 data points per sensor location. The team then deliberately introduced six different patterns of missing data, from random single dropouts to entire sensors or entire days going silent, at severities ranging from a light 10% gap to a severe 90% blackout, and measured how accurately and how quickly each method could reconstruct the missing values.
The results give city operators and data teams something genuinely useful: an evidence-based comparison of how each method performs under different real-world failure scenarios, not just in theory. That matters because the type of data gap — a single faulty sensor versus a whole network outage — calls for different reconstruction strategies, and now there’s a documented basis for choosing between them.
It’s unglamorous, behind-the-scenes work, but it’s exactly the kind of engineering that keeps mobility data usable when the real world doesn’t cooperate — and it’s a foundation piece for any traffic-management or simulation tool built on top of incomplete, real-world sensor networks.
Learn more: The full methodology, algorithm details and results tables are available in FEDORA Deliverable D3.1 – Integrated Cross-Sectoral Data Space, Section 5.3.2.1.