Timeline for Listing applications of the SVD
Current License: CC BY-SA 4.0
40 events
| when toggle format | what | by | license | comment | |
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| Jul 16 at 20:30 | comment | added | Don Hatch | Regarding "Finding the nearest orthogonal matrix to a given matrix", aka orthogonal Procrustes problem or Wahba's problem or rigid point set registration (all minor variations on the same problem), the textbook solution is, indeed, to compute the SVD $M = U \Sigma V^T$, and throw away $\Sigma$, producing the answer $U V^T$, the orthogonal matrix closest to $M$. (Assume $M$ has positive determinant, to sidestep a mess.) But I noticed that, in the 2 dimensional case, SVD isn't needed at all. If $M = [[a,b],[c,d]]$, then the answer is simply $[[a+d,b-c],[c-b,a+d]] / \sqrt{(a+d)^2+(b-c)^2}$. | |
| Dec 13, 2021 at 5:06 | answer | added | dineshdileep | timeline score: 0 | |
| Nov 18, 2021 at 3:08 | answer | added | kkm mistrusts SE | timeline score: 2 | |
| Nov 17, 2021 at 20:09 | comment | added | Dirk | No, I haven't. I just found it musing that the OP and answerer talked past each other (if I understood correctly). | |
| Nov 17, 2021 at 15:32 | comment | added | wlad | @Dirk Sorry, I'm not sure I've understood you. Have you reconsidered your opinion that SVD is terrible for image compression or haven't you? D.W.'s last comment looks like a fairly negative assessment of it. | |
| Nov 17, 2021 at 13:54 | comment | added | Dirk | @RodrigodeAzevedo Thanks for the link - it a quite funny read. Alas, from that page it still seems like image compression by SVD may be a non-terrible idea… | |
| Nov 17, 2021 at 13:38 | answer | added | Joe | timeline score: 2 | |
| Nov 17, 2021 at 13:21 | answer | added | Dirk | timeline score: 6 | |
| Nov 17, 2021 at 13:05 | history | edited | Peter Mortensen | CC BY-SA 4.0 |
Copy edited (e.g. ref. <en.wikipedia.org/wiki/Singular_value_decomposition>, <en.wikipedia.org/wiki/Linear_algebra>, <en.wikipedia.org/wiki/Discrete_cosine_transform>, and <en.wikipedia.org/wiki/Principal_component_analysis>). Introd. abbr. "PCA". Removed meta information (this belongs in comments).
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| Nov 17, 2021 at 13:00 | answer | added | Dirk | timeline score: 6 | |
| Nov 17, 2021 at 12:50 | comment | added | Dirk | The image compression example is a toy example. SVD is not used like that in any image compression standard I am aware of. It is very inefficient for compression and the artifacts are unpleasant. | |
| Nov 17, 2021 at 11:56 | answer | added | Ander Biguri | timeline score: 7 | |
| Nov 17, 2021 at 6:35 | history | edited | Martin Sleziak |
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| Nov 17, 2021 at 0:54 | answer | added | CrabMan | timeline score: 3 | |
| Nov 16, 2021 at 21:49 | comment | added | Rodrigo de Azevedo | Somewhat related | |
| Nov 16, 2021 at 18:46 | answer | added | David E Speyer | timeline score: 5 | |
| Nov 16, 2021 at 18:40 | answer | added | David E Speyer | timeline score: 15 | |
| Nov 16, 2021 at 18:24 | answer | added | Stopple | timeline score: 4 | |
| Nov 16, 2021 at 14:50 | answer | added | kjetil b halvorsen | timeline score: 3 | |
| Nov 16, 2021 at 14:32 | answer | added | Stephan Kolassa | timeline score: 5 | |
| Nov 16, 2021 at 10:36 | answer | added | polfosol | timeline score: 6 | |
| Nov 15, 2021 at 21:01 | answer | added | Daniel Shapero | timeline score: 10 | |
| Nov 15, 2021 at 16:15 | comment | added | Timothy Chow | @ogogmad Re: toy vs. serious application, what often happens in practice is that the best algorithms are very complicated, and SVD is used as a subroutine somewhere. Or, SVD is used to analyze the algorithm or motivate it. For example, I more or less randomly Googled "compressed sensing SVD" and found A Robust and Efficient Compressed Sensing Algorithm for Wideband Acoustic Imaging, which combines orthogonal matching pursuit with SVD. For classroom purposes, there's a tradeoff. The real algorithm may be too complex for first-time students to grasp. | |
| Nov 15, 2021 at 8:47 | comment | added | wlad | @RBega2 The question is whether it's a toy or a serious application. The comparison with JPEG is needed to establish which of those it is | |
| Nov 15, 2021 at 5:27 | comment | added | usul | On low-rank approximation, I understand that one can get somewhere by simply imputing the missing values (hopefully not with zeroes, but something more clever) and then using the SVD. More generally, some of your objections seem to be over-thinking for your pedagogical purpose: maybe the pure SVD approach isn't exactly state of the art, but it seems necessary to understand SVD in order to understand the state of the art, and you're teaching linear algebra, not applied ML, so.... | |
| Nov 15, 2021 at 3:40 | comment | added | Sam Hopkins | Wikipedia actually has a fairly extensive discussion at: en.wikipedia.org/wiki/… | |
| Nov 15, 2021 at 0:06 | history | became hot network question | |||
| Nov 14, 2021 at 23:16 | comment | added | RBega2 | I've used the image compression example when I've taught the class and it was well received (some of my evaluations had wished I had started with it rather than end with it). You don't have to get into the specifics of the JPG format a simple encoding still works. I prefer greyscale for simplicity but here is an example with color timbaumann.info/svd-image-compression-demo | |
| Nov 14, 2021 at 22:23 | answer | added | eddy ardonne | timeline score: 10 | |
| Nov 14, 2021 at 22:14 | answer | added | Andrei Smolensky | timeline score: 10 | |
| Nov 14, 2021 at 21:14 | answer | added | Andrei Smolensky | timeline score: 6 | |
| Nov 14, 2021 at 18:50 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Nov 14, 2021 at 17:38 | history | edited | Martin Sleziak |
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| Nov 14, 2021 at 17:37 | history | edited | wlad | CC BY-SA 4.0 |
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| Nov 14, 2021 at 16:45 | history | edited | wlad | CC BY-SA 4.0 |
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| Nov 14, 2021 at 16:03 | history | asked | wlad | CC BY-SA 4.0 |