I felt most the analogies lacking, so here goes. I'd tell my grandma, "the PCA for a loaf of bread is actually listed right on the back, cleverly labeled 'Ingre

I felt most the analogies lacking, so here goes. I'd tell my grandma, "the PCA for a loaf of bread is actually listed right on the back, cleverly labeled 'Ingredients'." If I took some sort of microscope to a loaf of bread and saw exactly how many atoms of each element were in that loaf, the ingredients would be the eigenvectors and the ratios of ingredients would be the eigenvalues. (Each ingredient has a very specific and unique combination of elements, leaving a certain signature) It all depends on the data, though, because that's how you frame reality. Maybe I look through the microscope a hundred times for a hundred different loaves, and maybe each ingredient-list might start to look like a datapoint. So now the patterns change. Here's where it gets interesting, because the very notion of what the eigenvectors are gets blurry. What used to be distinct (flour and sugar) now basically show up everywhere together. They blend into the walls. Every loaf is going to be on average the same. Now there's 1 main pattern, the average-loaf-of-bread, and several trailing patterns, like extra-raisins or extra-sunflower-seeds. But remember the one thing special about eigenvectors: in the model, they're mathematically independent. So if two things are dependent, they will be globbed by the same eigenvector. The pattern extra-raisins might come up in a loaf full of cranberries (as long they are chemically similar). If grandma is still listening, I'd wrap up: PCA reduces complex but uniform data to mathematically independent patterns or ingredients. The eigenvectors are the patterns and the eigenvalues are the ratios.