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I found this line confusing: > The printed lines above show that both algorithms capture more than 50% of the variance exhibited in the data using only 4 of th

by wjn0 8y ago

I found this line confusing: > The printed lines above show that both algorithms capture more than 50% of the variance exhibited in the data using only 4 of the 50 stocks. Based on the sklearn PCA documentation [1] this has nothing to do with the coefficients on individual stocks, and for PCA should read more like: "[...] capture more than 50% of the variance exhibited in the data using only 4 components [...]" which is not the same thing. 1. http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html http://scikit-learn.org/stable/modules/generated/sklearn.dec...

pacbard 8y ago
Not really. PCA extract components (or factors) using individual items (in this case, each stock). OP points out that those 4 stocks strongly load (large amount of their variation used to calculate the component) on the PCA first component. I would interpret those variances explained more like a way to make sense of the component (maybe stocks of tech companies load on it) rather than a “quality” of extractoin measure. Usually, correlation matrix eigenvalues can be used to get a sense of how well the PCA is performing and how many dimensions are present in the raw data.
- wjn0 8y ago
  The idea (ranking stocks by sum of the absolute value of the coefficients) is valid, but that line of code (variance explained by each component) doesn't do that.
  - efavdb 8y ago
    I think your criticism is right. In that line I was thinking about the feature selector, which does pull out 4 of the individual stocks -- these capture more than 50% of the variance in the full set. As you pointed out, that description isn't quite right for the PCA line, which uses four hybrid components.
makmanalp 8y ago
To expand upon this, in PCA, different components have "loadings" not on single variables but on many variables (a.k.a. columns), which are often highly correlated with each other.

by wjn0 8y ago

pacbard 8y ago

Not really. PCA extract components (or factors) using individual items (in this case, each stock). OP points out that those 4 stocks strongly load (large amount of their variation used to calculate the component) on the PCA first component. I would interpret those variances explained more like a way to make sense of the component (maybe stocks of tech companies load on it) rather than a “quality” of extractoin measure. Usually, correlation matrix eigenvalues can be used to get a sense of how well the PCA is performing and how many dimensions are present in the raw data.

wjn0 8y ago
The idea (ranking stocks by sum of the absolute value of the coefficients) is valid, but that line of code (variance explained by each component) doesn't do that.
- efavdb 8y ago
  I think your criticism is right. In that line I was thinking about the feature selector, which does pull out 4 of the individual stocks -- these capture more than 50% of the variance in the full set. As you pointed out, that description isn't quite right for the PCA line, which uses four hybrid components.

makmanalp 8y ago

To expand upon this, in PCA, different components have "loadings" not on single variables but on many variables (a.k.a. columns), which are often highly correlated with each other.