This problem goes through a simple numerical example to help you get familiar with PCA: Given...

  

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This problem goes through a simple numerical example to help you get familiar with PCA: Given a data set x = {x() R}^_ of N points in a two-dimensional feature space with sample covariance matrix given by l=1 - [ C = 6 2 26 " we perform principal component analysis (PCA) to obtain the principal components. If we use the two principal components with the largest eigenvalues obtained by PCA to project X linearly onto another space spanned by the principal components, what is the maximum percentage of total variance that can be explained by the two principal components together? Justify your answer. This problem goes through a simple numerical example to help you get familiar with PCA: Given a data set x = {x() R}^_ of N points in a two-dimensional feature space with sample covariance matrix given by l=1 - [ C = 6 2 26 " we perform principal component analysis (PCA) to obtain the principal components. If we use the two principal components with the largest eigenvalues obtained by PCA to project X linearly onto another space spanned by the principal components, what is the maximum percentage of total variance that can be explained by the two principal components together? Justify your answer.