London traffic analysis from real data:
- city traffic state depends on car speed on thousands of streets;
- speeds are averaged on each street during 1h intervals;
- from speed we obtain an approximate car density and thus car flow vectors;
- we define a regular grid (1km side) over the city and sum flow vectors within each cells (right figure);
- each day we have a city trajectory with 24 points;
- to plot trajectories in 2D we use a PCA to perform dimensionality reduction (left fig).

Given another unknown traffic state, it's quite easy to classify it and to forecast what's going to happen next. Notice how different weekends are from workdays.

ps: numbers in trajectories are hours of the day