Towards improving data presentation in the TripCheck system Rafael J. Fernández-Moctezuma

You’re about to leave… … and you’re addicted to TripCheck. So you go and check it out and see this:

What’s wrong with this picture?

Gray is not the new black!

Estimation may be better than no data on final products Data may not be displayed for various reasons –Sensor failure –Data quality May prefer to estimate the system state instead of displaying gray areas Not enough sensors – but may still be able to recover information. Must be careful with estimation – at least report a confidence factor.

System State Estimation Must carefully choose good sources of correlated data Every sensor station has its own estimator The PORTAL project does a great job at archiving data – this makes statistical regressors for state estimation a good alternative. May consider to rely on observed features from the past in addition to well-known transportation theory.

Regression Find a description of data in terms of a function Example: height (H) and weight (W) data transformed into a function F(H) = W.

Which functional family? May consider a linear family first… … which can easily be derived (Least squares). May also consider the expected value of a conditional Gaussian: A conditional Gaussian buys us statistics: The conditional mean is a linear regressor! Plus, estimating the joint is easy.

Which functional family? May also want to consider non-linear functions. A good first approach is an Artificial Neural Network

Experimental results Looked at rush hour (06:00 – 10:30) data from a “typical” Portland week, from US 26 E (Oct. 16 – Oct ) Found a segment that is typically shown gray (it is my commute, so I notice these things) Inputs: current measurements of speed at nearby stations Goal: come up with a good enough estimate to color the TripCheck map

Segment

Confusion matrices Milepost 73.62Milepost Linear ANN Prediction R Y G Observed R Y G Prediction R Y G Prediction R Y G Prediction R Y G Observed R Y G Observed R Y G Observed R Y G 80% 89%100%

Future work May still be able to recover system information with a nonlinear model from far away stations Still need to explore other segments and build a representative amount of model regressors (20% ?) to demonstrate effectiveness of the approach What keeps us from using this approach to estimate intermediate location states?

Future work May want to consider regressors with more inputs (shifted speeds, time, etc.) If nonlinear regressors are effective, we may want to use Gaussian Mixture Models (cheaper to train, statistically rich) Addressing quality in data presentation can be a sub-product of a more general problem: construct a framework for reliable system state estimation.