![]() 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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