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This is truly fantastic. Excuse me for being daft, but how do you transform back into 'what does this mean'? For instance, in ex 3, we see that N. Ireland is

This is truly fantastic. Excuse me for being daft, but how do you transform back into 'what does this mean'? For instance, in ex 3, we see that N. Ireland is an outlier. It wasn't obvious to me that the cause was potatoes and fruit. How does PCA help you with the fundamental meaning?

scribu 12y ago
That's the main drawback of PCA - the principal components are linear combinations of all the original features. An attempt to remedy this is callled Sparse PCA (you can look it up on Google Scholar), in which the principal components are combinations of only a few features. This allows you to figure out which features are not important.
icegreentea 12y ago
They kind of skipped a step. What you would do is then look at what the first principle axis is. In this particular case, it would be a 17-D vector, each element corresponding a food type. You would then look at which elements (food types) have the greatest magnitude. In a toy example, imagine we had a 5D case where we have beer, cereal, fruit, beef, chicken, and salad, and we found out that the first principle axis is {0.3, 0.1, -0.5, 0.0. 0.2} (in the same order). Then the cause of the change would be due to primarily fruit and beer consumption.
- gus_massa 12y ago
  I was looking for the same information. The article has a link to pdf with a more deep discussion of this case, and the explanation and the values of the weight of each product. http://people.maths.ox.ac.uk/richardsonm/SignalProcPCA.pdf http://people.maths.ox.ac.uk/richardsonm/SignalProcPCA.pdf From the figure 4, after rescaling and rounding the coefficients The pc1 that separate N Ireland is approximately: PC1 = FreshPotatoes + SoftDrinks/2 - FreshFruits/2 - AlcoholicDrinks/2 The pc2 that separate the other three countries is approximately: PC2 = FreshPotatoes - SoftDrinks
abfan1127 12y ago
It be helpful to learn about eigenanalysis (at least it was for me). PCA leverages the ideas of vector spaces that I found eigenanalysis to clarify.

scribu 12y ago

That's the main drawback of PCA - the principal components are linear combinations of all the original features. An attempt to remedy this is callled Sparse PCA (you can look it up on Google Scholar), in which the principal components are combinations of only a few features. This allows you to figure out which features are not important.

icegreentea 12y ago

They kind of skipped a step. What you would do is then look at what the first principle axis is. In this particular case, it would be a 17-D vector, each element corresponding a food type. You would then look at which elements (food types) have the greatest magnitude. In a toy example, imagine we had a 5D case where we have beer, cereal, fruit, beef, chicken, and salad, and we found out that the first principle axis is {0.3, 0.1, -0.5, 0.0. 0.2} (in the same order). Then the cause of the change would be due to primarily fruit and beer consumption.

gus_massa 12y ago
I was looking for the same information. The article has a link to pdf with a more deep discussion of this case, and the explanation and the values of the weight of each product. http://people.maths.ox.ac.uk/richardsonm/SignalProcPCA.pdf http://people.maths.ox.ac.uk/richardsonm/SignalProcPCA.pdf From the figure 4, after rescaling and rounding the coefficients The pc1 that separate N Ireland is approximately: PC1 = FreshPotatoes + SoftDrinks/2 - FreshFruits/2 - AlcoholicDrinks/2 The pc2 that separate the other three countries is approximately: PC2 = FreshPotatoes - SoftDrinks

abfan1127 12y ago

It be helpful to learn about eigenanalysis (at least it was for me). PCA leverages the ideas of vector spaces that I found eigenanalysis to clarify.