Question: data science- low dimensional representation of data exam practice question Problem 1. Assume we have 1000 data points .1, $2, . . . , 100o

data science- low dimensional representation of data exam practice question

Problem 1. Assume we have 1000 data points .1, $2, . . . , 100o E R50. We know that the singular values of the data matrix are given as o1 = 10, 02 = 9, 03 = 8, . .. , 010 = 1, 011 = 0, . . . . We would like to find a low dimensional representation of the data points in a way that at least 50% of the energy of the data is kept. What is the minimum value of the dimension that we can use for the low-dimensional representation of the data

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