representing X, R, X = 54 10 Consider the observations (a) Compute the unit length...

  

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representing X, € R², X = 54 10 Consider the observations (a) Compute the unit length principal components of X. (b) Use PCA to approximate the data using one dimension. Derive the equation for a new, X, E R², observation and its approximation. (c) Plot the 4 samples in X. Draw the directions of two eigenvectors and the projections of all the sample points on the both eigenvectors. Label all samples precisely. (d) Calculate the variance of the projections on the principle component direction (i.e., the eigenvector with the largest eigenvalue) as well as the projections on the second eigenvector. Which variance is larger? Justify your answer. representing X, € R², X = 54 10 Consider the observations (a) Compute the unit length principal components of X. (b) Use PCA to approximate the data using one dimension. Derive the equation for a new, X, E R², observation and its approximation. (c) Plot the 4 samples in X. Draw the directions of two eigenvectors and the projections of all the sample points on the both eigenvectors. Label all samples precisely. (d) Calculate the variance of the projections on the principle component direction (i.e., the eigenvector with the largest eigenvalue) as well as the projections on the second eigenvector. Which variance is larger? Justify your answer.

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a Compute the unit length principal components of X To find the principal co... View the full answer