This limits the number of possible basisPCA can find. One important fact: PCA returns a new basis which is a linear combination of the original basis. Remember that a basis is a set of linearly independent vectors, that, in a linear combination, can represent every vector (they form a coordinate system). In this sense, PCA computes the most meaningful basis to express our data. PCA is an orthogonal linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on. Wikipedia: >Principal component analysis (PCA) is a mathematical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The tutorial shows the necessary steps to perform the dimension reduction of Principal Component Analysis (PCA) A (not entirely successful) example of image processing and reduction.
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