The interactive film is in the book's Companion

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Energy from Singular Values: Rebuild a Picture Layer by Layer

Chapter 8 · Mathematics for AI and Machine Learning · Beginner · 1:31

An interactive live film: a 10 × 10 smiling face rebuilt from its rank-one SVD layers; the energy ‖A‖²_F is the sum of the squared singular values, and a truncated SVD loses exactly the energy of the layers it drops.

Narration

The bars are a ten by ten matrix A, a small picture of a smiling face. Its energy is the sum of all its squared entries.

The SVD writes A as a sum of rank one layers, sigma i times u i times v i transpose, from the strongest to the weakest. This picture needs only five of them.

The rest of the narration is in the book's Companion.

More from Chapter 8

Interactive1:49SVD: Rotate, Stretch, RotateChapter 8Preview1:33Double Descent at the Interpolation ThresholdChapter 8Preview1:32The Marchenko-Pastur Law and the Escaping EigenvalueChapter 8Preview1:43Eckart-Young: the Best Low-Rank ApproximationChapter 8Preview1:46The Pseudoinverse: the Shortest SolutionChapter 8Preview1:31Polar Decomposition: Stretch, then RotateChapter 8Preview1:47Randomized SVD: Catching the Top DirectionsChapter 8