Can we predict England's traffic?

- 6 mins

In September 2014, we presented a poster on some of the ancillary research I am doing as part of my latest project supported by the Centre for Sustainable Road Freight. A PDF of the poster is available to download for those that are interested. The source for the poster is hosted on the University git service.

Overview

The poster focusses on a single part of our wider research project on gathering traffic flow data. Part A of the project aims to infer traffic flow directly from video streams but knowing the current state of the world is only one part of the problem; we are also investigating what techniques can be used to predict the near future.

Data wrangling

In a previous post I outlined some of the basic steps required to get hold of the UK Highways Agency’s real time data feed and wrangling it in Python. I recommend reading that post if you’re interested in the details of how the data is fetched and parsed.

What data is available?

The UK Highways Agency publish an XML document four times an hour which gives the latest measurements for stretches of roads (or links) in England. A link has a direction; each carriageway of a road will appear as a separate link but a link may have multiple lanes. This information includes the current traffic flow (vehicles/hour), mean speed (km/hour) and occupancy (%). An occupancy of 100% means that the road is fully occupied, nose-to-tail, on each lane.

How do you get it?

The XML document itself is available via a public URL which may simply be fetched. We have developed an automated system based in the Cloud which fetches this document every 15 minutes, parses the XML and strips the information we currently do not use. The XML stream itself is 120MB an hour and so this “data reduction” step is important. We have a full archive of the XML stream for around six months which is nearly 150GB in size even when compressed.

How do you store it?

Our system in the cloud does two things. Firstly it provides an archive of the day’s traffic flows, occupancies and speeds which is downloaded and integrated into a local SQLite database on our site. This database is the source for the time-series data for individual links. The cloud based system also translate the current state of England’s traffic into a JSON-formatted document which can easily be consumed by our web-based visualisation tool (XML, despite its web-heritage, is rather inconvenient as a file format for today’s web.) On a more technical note, our cloud service also supports CORS (Cross-Origin Resource Sharing) which is again a technical requirement for making use of the data in our visualisation platform.

Analysis

Our central assumption is that all links exhibit similar patterns over the course of a day. This matches our intuition that we expect morning, evening, daytime and night time behaviours to be different for any given link but all links will have some degree of, for example, “morning rush hour”.

Traditionally this data reduction step would be performed by taking a large number of “training” samples of daily traffic behaviour and using some projection-based technique such as Principal Component Analysis to extract a small set of “basis vectors” or “components” which can be scaled and summed together to approximate any of the training samples with minimal error.

These techniques are well known and often very useful as initial data reduction step. The problem is that the basis vectors produced are not guaranteed to be positive. Usually this is not a problem but in traffic analysis one of the few things we can say with certainty is that speeds, occupancies and traffic flows are positive.

Taking a naïve PCA of 40,000 traffic flow daily samples results in these components:

The only directly interpretable component is the first cone which corresponds to the normalised mean of all traffic flows. The rest are not very illuminating. In the case of traffic analysis one has a lot of prior knowledge available which does not obviously map onto these components.

Instead of PCA, we can make use of a relatively novel technique: non-negative matrix factorisation. In this technique one forces all of the components to be positive. The downside is that the factorisation is no-longer unique. To combat this, one usually factorises while minimising some “sparseness measure”. In our case we factorise while trying to keep the components as “peak-like” as possible. Fortunately the NMF implementation we are using, scikit-learn, directly supports this. The non-negative fundamental components look like this:

It is now far easier to directly interpret these components in terms of “morning rush hour”, “night time flow”, etc.

By resolving our training flows onto these components we end up with 5 components which describe the flow on one link over an entire day rather than one number for each quarter hour sample. This is around a 5% data reduction.

We may now reason using these components to derive “typical” component values for each flow for each weekday. Typical results from this projection are shown in the poster.

Prediction

Data reduction is all well and good but it is all for naught if the reduced data doesn’t represent the actual data. To this end we investigated how well our “typical week” will predict a new week which wasn’t present in our training data. To add some challenge, the new week included a Bank Holiday Monday which wasn’t present in the training set.

Reconstructing our “typical week” for each link resulted in surprisingly good performance. Remember that this is the simplest form of prediction; we assume that each week is like the typical week. Even with such a simple model our prediction has a median relative error of only 7%. Plotting a scatter chart of predicted flow versus actual flow showed a tight adherence to the perfect 1:1 correspondence line. The bank holiday was clearly visible in the predicted output.

Summary

We investigated whether non-negative matrix factorisation of traffic flows in England could provide large scale data reduction with low error while providing basis components which retained interpretable. We showed that even reducing data to 0.25% of the original we could predict future flows with a median relative error of 7%.

Given these results we intend to proceed with traffic prediction working directly on the reduced traffic data which we believe to be a more tractable problem than dealing with the full dataset directly.

References

Rich Wareham

Rich Wareham

You know, programming is fun!

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