The goal of PCA is to produce the most useful possible 2 or 3-dimensional projection of a high-dimensional data set-most useful in that the smallest amount of information is lost by the projection. Human minds are good at recognizing patterns in two dimensions and to some extent in three, but are essentially useless in higher dimensions. Principal component analysis (PCA), an algorithm for helping us understand large-dimensional data sets, has become very useful in science (for example, a search in Nature for the year 2020 picks it up in 124 different articles). Very often, especially in applications to the life sciences, useful low-dimensional projections exist and allow humans to grasp a data set that would otherwise be inscrutable. ![]() Principal Component Analysis: Three Examples and some Theory
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