Multilinear rank

Multilinear rank — one retained rank per mode, for example (2, 2, 3). Spanish: rango multilineal.

This is what Tucker gives you that PCA cannot: a separate budget for each axis. The taxi tensor keeps 2 directions for pickup borough, 2 for dropoff borough, and 3 for hour of day, because the hour axis is 24 long and genuinely carries more structure than the two 5-long borough axes.

A rank is a budget, not a subset. Rank 3 on the hour mode buys three directions to describe variation across all 24 hours — it does not keep three hours and throw away 21.