For more on this topic, see the post.The eigenvectors can be sorted by the eigenvalues in descending order to provide a ranking of the components or axes of the new subspace for A.If all eigenvalues have a similar value, then we know that the existing representation may already be reasonably compressed or dense and that the projection may offer little. ![]() Values, vectors = eig(V)The eigenvectors represent the directions or components for the reduced subspace of B, whereas the eigenvalues represent the magnitudes for the directions. ![]() Let’s walk through the steps of this operation. Principal Component AnalysisPrincipal Component Analysis, or PCA for short, is a method for reducing the dimensionality of data.It can be thought of as a projection method where data with m-columns (features) is projected into a subspace with m or fewer columns, whilst retaining the essence of the original data.The PCA method can be described and implemented using the tools of linear algebra.PCA is an operation applied to a dataset, represented by an n x m matrix A that results in a projection of A which we will call B.
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