![]() The first answer is that you are looking for some wine properties (characteristics) that strongly differ across wines. You: I guess I can give two different answers to this question. What do you actually mean when you say that these new PCA characteristics "summarize" the list of wines? Mother: Hmmm, this certainly sounds good, but I am not sure I understand. In fact, PCA finds the best possible characteristics, the ones that summarize the list of wines as well as only possible (among all conceivable linear combinations). Of course, these new characteristics are constructed using the old ones for example, a new characteristic might be computed as wine age minus wine acidity level or some other combination (we call them linear combinations). Instead, it constructs some new characteristics that turn out to summarize our list of wines well. You: Excellent question, granny! No, PCA is not selecting some characteristics and discarding the others. Grandmother: This is interesting! So this PCA thing checks what characteristics are redundant and discards them? If so, we should be able to summarize each wine with fewer characteristics! This is what PCA does. But many of them will measure related properties and so will be redundant. We can compose a whole list of different characteristics of each wine in our cellar. We can describe each wine by its colour, how strong it is, how old it is, and so on. Look, we have some wine bottles standing here on the table. You: Ah, it's just a method of summarizing some data. Great-grandmother: I heard you are studying "Pee-See-Ay". Each time the next person is less of a layman. ![]() First, you explain it to your great-grandmother then to your grandmother then to your mother then to your spouse finally, to your daughter (a mathematician). Imagine a big family dinner where everybody starts asking you about PCA.
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