Timeline for How would you preprocess data for SVD? [closed]
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| Jun 18 at 19:37 | history | closed | whuber♦ | Needs details or clarity | |
| Jun 18 at 19:03 | history | edited | kjetil b halvorsen♦ |
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| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
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| Jan 22, 2013 at 21:44 | comment | added | whuber♦ | OK, thanks: I see now what you're looking for. But I am still wondering how you intend to interpret the results, because I think that ought to determine whether you standardize or recenter the data first. A good analogue is the distinction, where $n=m$, between the correlation coefficient (where $X$ and $Y$ are standardized) and the cosine similarity (where $X$ and $Y$ are normalized to unit length but not recentered): both are valid measures of association but the choice depends on the nature of the data and the intended interpretation. | |
| Jan 22, 2013 at 21:37 | comment | added | SVDer | It is not an SVD on XY', it is an SVD on a sum of matrices of the form $x_i*y_i'$. Note the expectation! (reminds a little bit of PCA, where you compute $E[XX']$.) | |
| Jan 22, 2013 at 21:32 | comment | added | whuber♦ | When you do SVD on $XY'$, which has rank at most one, there will be at most one nonzero singular value. If by "empirical version" you mean that realizations of $XY'$ are observed with noise in the coefficients, then--unless that noise is huge--once again there will be a single large singular value and the rest should be close to zero. In neither case does that singular value appear to tell you anything directly about "correlation" of $X$ and $Y$, so I am quite curious about what you might mean by correlation (at least when $n\ne m$) and how this calculation would measure it. | |
| Jan 22, 2013 at 21:29 | history | edited | SVDer | CC BY-SA 3.0 |
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| Jan 22, 2013 at 21:28 | comment | added | SVDer | SVD is used here to project X and Y into a lower-dimensional space where X and Y are most correlated. The singular values are used to decide how correlated X and Y are (the larger they are, the more information there is about Y from X and vice versa). | |
| Jan 22, 2013 at 21:19 | comment | added | whuber♦ | It all depends on why you are computing the SVD. What's the purpose? How will you use or interpret the results? | |
| Jan 22, 2013 at 21:14 | history | asked | SVDer | CC BY-SA 3.0 |