cess are called principal componentsas they are the main directions of variance in the data in generalthere are as many principal components as original features figure - transformation of data with pca the second plot (top rightshows the same databut now rotated so that the first principal component aligns with the -axis and the second principal component aligns with the -axis before the rotationthe mean was subtracted from the dataso that the transformed data is centered around zero in the rotated representation found by pcathe two axes are uncorrelatedmeaning that the correlation matrix of the data in this representation is zero except for the diagonal we can use pca for dimensionality reduction by retaining only some of the principal components in this examplewe might keep only the first principal componentas dimensionality reductionfeature extractionand manifold learning