11/7/2023 0 Comments Pca column2) between data and their projection and is equivalent to carrying out multiple linear regression 3, 4 on the projected data against each variable of the original data. The PC selection process has the effect of maximizing the correlation ( r 2) (ref. This requirement of no correlation means that the maximum number of PCs possible is either the number of samples or the number of features, whichever is smaller. For example, projection onto PC1 is uncorrelated with projection onto PC2, and we can think of the PCs as geometrically orthogonal. The second (and subsequent) PCs are selected similarly, with the additional requirement that they be uncorrelated with all previous PCs. By minimizing this distance, we also maximize the variance of the projected points, σ 2 ( Fig. The first PC is chosen to minimize the total distance between the data and their projection onto the PC ( Fig. PCA reduces data by geometrically projecting them onto lower dimensions called principal components (PCs), with the goal of finding the best summary of the data using a limited number of PCs.
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