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mml-book / mml-book.github.io

Companion webpage to the book "Mathematics For Machine Learning"
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Example 4.14 #686

Open vnrajapakse opened 3 years ago

vnrajapakse commented 3 years ago

In Example 4.14 (page 127), it is written:

"We interpret the left-singular vectors u_i as stereotypical movies and the right-singular vectors v_j as stereotypical viewers."

Shouldn't the left singular vectors u_i be interpreted as stereotypical viewers, and the right singular vectors v_j as stereotypical movies?

It is stated that "We then make the assumption that any viewer’s specific movie preferences can be expressed as a linear combination of the v_j". But the viewer preference vectors are 4-dimensional, while the v_j are 3-dimensional.

WenqingZong commented 2 years ago

I have some questions about this example, too.

  1. The explanation mentions the red and green shadings in Figure 4.10 but says nothing about the purple and the yellow shadings, probably the authors changed the text and forgot to update the figure? (I'm reading the 2021-7-29 version)

  2. I've read this example 7 times, and I'm still struggling to understand it. To me, it is like: Bob's weight is 70kg=2*5*7kg. The decomposition makes no practical sense, it is merely equivalent numerically.

I'm really hoping someone can explain it more clearly to me.