Thanks for this -- it's a very nice explainer about the statistical techniques.
Yes, I see that PC1 looks like a good measure of sandwichness. But I'd like to make one point: The location of your PC1=0 point is an artifact of the set of objects that you put in your dataset. If you were to add 10 different "proper sandwiches", then the PC1=0 point would shift to the left somewhat, possibly changing the egg salad sandwich from a "yes" to a "no". And if you were to include more barely-sandwich-like foods and not-sandwich-like-at-all foods, then the PC1=0 point would shift to the right (hmm, and maybe also mess up the clean meaning of PC1=sandwichness...).
As your analysis stands, do you think it might be fairer to say that a line near your PC1=~0 demarcates "proper sandwiches" from "quasi-sandwiches"?
Your analysis may have little impact on the hardliners who say "Dude, everything's a sandwich. I'm a sandwich. The world is a sandwich!" But I'm in favor of choosing words as useful tools for categorizing the unavoidably complicated and fuzzy details of the world. And this quantification helps with that. Choosing useful demarcation point(s) along the PC1 axis still seems subjective, and that's okay!
p.s. I'm curious about the whole chili pepper tucked into that hot dog! Is that a thing?
... Well, I see a partial rebuttal to my complaints about choosing the dataset -- First you did the k=2 clustering (and clustering is somewhat resistant to the addition of extra near-duplicate data points) and then from that clustering, you simply observed that the 2 clusters border near PC1=~0.
This is correct, I’m basing the classification off the clustering. If the k=3 cluster had shown a better demarcation I would have had to use a more complex formula. As it is, PC1 = 0 is a pretty good proxy for the cluster boundary, so I just used that for simplicity.
Of course! The method is totally general. Ooh I love “is cereal a soup.” My gut says that it would not cluster with soups as it is too different, but I’d have to do the math.
Thanks for this -- it's a very nice explainer about the statistical techniques.
Yes, I see that PC1 looks like a good measure of sandwichness. But I'd like to make one point: The location of your PC1=0 point is an artifact of the set of objects that you put in your dataset. If you were to add 10 different "proper sandwiches", then the PC1=0 point would shift to the left somewhat, possibly changing the egg salad sandwich from a "yes" to a "no". And if you were to include more barely-sandwich-like foods and not-sandwich-like-at-all foods, then the PC1=0 point would shift to the right (hmm, and maybe also mess up the clean meaning of PC1=sandwichness...).
As your analysis stands, do you think it might be fairer to say that a line near your PC1=~0 demarcates "proper sandwiches" from "quasi-sandwiches"?
Your analysis may have little impact on the hardliners who say "Dude, everything's a sandwich. I'm a sandwich. The world is a sandwich!" But I'm in favor of choosing words as useful tools for categorizing the unavoidably complicated and fuzzy details of the world. And this quantification helps with that. Choosing useful demarcation point(s) along the PC1 axis still seems subjective, and that's okay!
p.s. I'm curious about the whole chili pepper tucked into that hot dog! Is that a thing?
... Well, I see a partial rebuttal to my complaints about choosing the dataset -- First you did the k=2 clustering (and clustering is somewhat resistant to the addition of extra near-duplicate data points) and then from that clustering, you simply observed that the 2 clusters border near PC1=~0.
This is correct, I’m basing the classification off the clustering. If the k=3 cluster had shown a better demarcation I would have had to use a more complex formula. As it is, PC1 = 0 is a pretty good proxy for the cluster boundary, so I just used that for simplicity.
And the chili pepper is Chicago Style!
I like this approach a lot. Could be applied to other controversial questions like "is cereal soup?" or the definition of "salad"
Of course! The method is totally general. Ooh I love “is cereal a soup.” My gut says that it would not cluster with soups as it is too different, but I’d have to do the math.