1. Load the image dog.jpg and compute the economy SVD. 2. Compute the relative reconstruction error...

 

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1. Load the image dog.jpg and compute the economy SVD. 2. Compute the relative reconstruction error of the truncated SVD in the Frobenius norm as a function of the rank r. Hint: The python command for frobenius norm of a matrix is scipy.linalg.norm (). In Matlab, use norm (X, 'fro'). 3. Square this error to compute the fraction of missing variance as a function of r. 4. Plot the quantities computed in (b) and (c) along with the cumulative sum of singular values as a function of r. 5. Find the rank r where the reconstruction captures 99% of the total variance. Compare this with the rank r where the reconstruction captures 99% in the Frobenius norm and with the rank r that captures 99% of the cumulative sum of singular values. 1. Load the image dog.jpg and compute the economy SVD. 2. Compute the relative reconstruction error of the truncated SVD in the Frobenius norm as a function of the rank r. Hint: The python command for frobenius norm of a matrix is scipy.linalg.norm (). In Matlab, use norm (X, 'fro'). 3. Square this error to compute the fraction of missing variance as a function of r. 4. Plot the quantities computed in (b) and (c) along with the cumulative sum of singular values as a function of r. 5. Find the rank r where the reconstruction captures 99% of the total variance. Compare this with the rank r where the reconstruction captures 99% in the Frobenius norm and with the rank r that captures 99% of the cumulative sum of singular values.