𝗛𝗼𝘄 𝗶𝘀 𝘁𝗵𝗲 𝗳𝗶𝗿𝘀𝘁 𝗽𝗿𝗶𝗻𝗰𝗶𝗽𝗹𝗲 𝗰𝗼𝗺𝗽𝗼𝗻𝗲𝗻𝘁 𝗮𝘅𝗶𝘀 𝘀𝗲𝗹𝗲𝗰𝘁𝗲𝗱 𝗶𝗻 𝗣𝗖𝗔? In Principal Component Analysis (PCA) we look to summarize a large set of 𝗰𝗼𝗿𝗿𝗲𝗹𝗮𝘁𝗲𝗱 𝘃𝗮𝗿𝗶𝗮𝗯𝗹𝗲𝘀 (basically a high dimensional data) into a smaller number of representative variables, called the 𝗽𝗿𝗶𝗻𝗰𝗶𝗽𝗮𝗹 𝗰𝗼𝗺𝗽𝗼𝗻𝗲𝗻𝘁𝘀, that explains most of the variability in the original set. The 𝗳𝗶𝗿𝘀𝘁 𝗽𝗿𝗶𝗻𝗰𝗶𝗽𝗮𝗹 𝗰𝗼𝗺𝗽𝗼𝗻𝗲𝗻𝘁 axis is selected in a way such that it 𝗲𝘅𝗽𝗹𝗮𝗶𝗻𝘀 𝗺𝗼𝘀𝘁 of the variation in the data and is closest to all n observations.
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