10 · Tucker Decomposition on Real Data

Part IV, Block 6 of Tensors for Machine Learning. One practical question:

How can we compress a tensor while keeping the meaning of its different axes?

PCA compresses a matrix — two axes. Real data often has more. Tucker decomposition generalizes PCA to a tensor of any order: one factor matrix per axis, plus a small core tensor describing how the factors combine.

The tensor is real: 6,433 New York taxi trips poured into pickup borough × dropoff borough × hour of day. And the headline is not the compression ratio. It is that the decomposition found evening rush hour without being told what an hour is. That is expected rather than magic: every entry is a trip count, so the strongest pattern along the hour axis follows how busy each hour is.

Study here, then run the real thing: notebook 10 on Colab · the handbook · Kahoot 3

Built from the workshop’s own material by Ravi Kalia and Sebastian Laverde Chunza, CC BY 4.0.