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Daily traffic evolution and the Super Bowl

With an eye towards predicting traffic evolution, we begin by examining the time-dependence of the contribution from the first principal components on different days of the week. Traffic throughout the day $\vert x(t) \rangle$ can be represented in the basis of principal components; $\vert x(t) \rangle$ $= \sum_{i} c_i(t) \vert \phi_i \rangle $$^1$, where $\vert \phi_i \rangle$ is the ith principle component. The coefficients $c_i(t)$, sometimes called the “scores” of $\vert x(t) \rangle $ in the basis of principal components, carry all of the dynamics.

ModeTDependence
The largest deviations in the traffic patterns (and of the scores) are during weekday rush hours (around 8 am and 5 pm) – see plot of the scores for several modes throughout Jan. 15. (more…)

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Data reduction by PCA

evals

Here, we characterize the data compression benefits of projection onto a subset of the eigenvectors of our traffic system’s covariance matrix.  We address this compression from two different perspectives:  First, we consider the partial traces of the covariance matrix, and second we present visual comparisons of the actual vs. projected traffic plots. (more…)

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Traffic patterns of the year: 2014 edition

Mode1

Mode2

As we mentioned in the last post, there are currently over 2000 active speed loop detectors within the Bay Area highway system.  The information provided by these loops is often highly redundant because speeds at neighboring sites typically differ little from one another.  This observation suggests that a higher level, “macro” picture of traffic conditions could provide more insight:  Rather than stating the speed at each detector, we might instead offer info like “101S is rather slow right now”.   In fact, we aim to characterize traffic conditions as efficiently as possible.  To move towards this goal, we have carried out a principal component analysis (PCA)$^1$ of the full 2014 (year to date) PEMS data set. (more…)

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