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mml-book / mml-book.github.io

Companion webpage to the book "Mathematics For Machine Learning"
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vector reference issue #570

Open mhfwx opened 4 years ago

mhfwx commented 4 years ago

Describe the mistake

I have a question about example 4.14.

The last few sentence in first paragraph refer Ali and Beatrix using right-singular v1. Also, Chandra is referred by v2.

Please correct me if i misunderstand. the column (vector) of left-singular metric refers to the movie type, such as science fiction movies mentioned in the example and row refers to listed movies. On the contrary, the row of right-singular metric refers movie preference and the column of right-singular metric refers to ALi, Beatrix and Chandra.

Location Please provide the

  1. version (bottom of page) : 2020-07-01
  2. Chapter 4.5 Matrix Decompositions
  3. page 128
  4. line number/equation number: 21 & 24

Proposed solution Could we be more clear about the vector v is a row vector. adding a prime sign v' can solve some confusion. Additional context Add any other context about the problem here. Could we add the axis title in the metric so that it's easier to follow.

mpd37 commented 4 years ago

The v-vectors are column vectors. However, in the SVD, we multiply with V^T, i.e., the v-vectors will be row vectors in Figure 4.10.

Agree that there's some room for improvement. If we added this information to Figure 4.10 again, i.e., A = U\Sigma V^T, would this make a substantial difference? I'm not sure I have a good way to change text without opening new questions.

balan777 commented 3 years ago

Sorry I didn't understand how You got the matrix [[2 1][1 2]] for the matrix A in (4.57)? Can You give me a hint please?

mpd37 commented 3 years ago

sorry --- that's a typo in (4.57). That matrix should not be [[2 1][1 2]], but "A". I'll fix that now.