50 ms·
Singular Value Decomposition Tutorial
- mattrepl 17y agoFor anyone that finds the posted site painful on the eyes, here's another introduction to SVD that is all on one page by default and isn't crowded by advertisements. http://www.igvita.com/2007/01/15/svd-recommendation-system-in-ruby/ http://www.igvita.com/2007/01/15/svd-recommendation-system-i...
- codexon 17y agoOr you could just use the print version. http://www.puffinwarellc.com/index.php/news-and-articles/articles/30-singular-value-decomposition-tutorial.html?tmpl=component&print=1&layout=default&page= http://www.puffinwarellc.com/index.php/news-and-articles/art...
- gane5h 17y agoThe SVD connects the four fundamental subspaces of a linear system. I was fortunate to receive this great insight from one of Strang's lectures. I highly recommend you watch one of his videos online on this particular topic. This post doesn't do full justice to the beauty of the SVD. Intuitively, you are trying to compute a transformation that diagonalizes the covariance matrix of the data. Computing the covariance has two problems: 1) this is a O(n^2) operation and 2) can lead to big numerical errors for really small values in the matrix. By creative use of elementary matrix operations, the SVD gives you the transformation on the original matrix. If you are interested in just the first few singular vectors, certain math libraries also support an economical mode that does just this.
- ivankirigin 17y agoAfter I learned all the details in grad school, I found out how to implement it in a real world setting: [U,S,V] = svd(X)
- sprachspiel 17y agoUnless X has 17,770*480,189 elements like the netflix dataset. Then you can use something like this: http://sifter.org/~simon/journal/20061211.html http://sifter.org/~simon/journal/20061211.html The site is currently down, google chache link: http://209.85.129.132/search?q=cache:h4Ljyun3gUcJ:sifter.org/~simon/journal/20061211.html+simon+funk+try+this+at+home http://209.85.129.132/search?q=cache:h4Ljyun3gUcJ:sifter.org...
- manvsmachine 17y agoAnother good one: http://www.ams.org/featurecolumn/archive/svd.html http://www.ams.org/featurecolumn/archive/svd.html and its HN thread: http://news.ycombinator.com/item?id=736618 http://news.ycombinator.com/item?id=736618
- pz 17y agoeveryone loves to reference the SVD because the concepts are principled and intuitive. but i've found that, as often as it is brought up in conversation, its rarely used in practice. anyone here used SVD in a production setting?
- KonaB 17y agoRarely used in practice??? Dude, are you being facetious?? SVD is the sledgehammer that cracks any problem you come up against...
- cf 17y agoDon't most people use NNMF instead these days?
- sweis 17y agoI messed around with analyzing US senate votes using a SVD several years ago: http://saweis.net/svd/ http://saweis.net/svd/
- roundsquare 17y agoWow, this is really great. The data seems to to support the claim that politics has gotten more divisive over the past 2 decades. (I get unreasonably happy when data actually supports a broad claim). Very creative way to show this. Have you thought about going further back? I'd be curious to see this on voting records as far back as possible, just to see what trends might have happened.