16 · PCA from a Tensors Perspective

Deep dive 16 of Tensors for Machine Learning. Plato’s prisoners see shadows. PCA asks which projection preserves the most variation:

Retained variance is not retained information. Whether the shadow keeps what a task needs is something you measure.

One real satellite dataset, followed two ways: as a sample × feature matrix and as a patch × row × column × band tensor. Connect covariance, correlation, eigendecomposition and SVD; measure what PCA does to classification and clustering with training-only preprocessing; then meet two different things called tensor PCA — multilinear PCA, which keeps the sample axis, and spiked-tensor recovery of a hidden direction.

A take-home deep dive of about 90 minutes, not one of the live labs of the six-hour workshop.

Study here, then run the real thing: notebook 16 on Colab · all the notebooks

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