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About Assignment 5 (Task 1)
Written on 22.11.2021 13:43 by Sven Rahmann
Dear all,
we had an error in assignment 5 task 1: The entries of the random matrix were given as +1 or -1, but they should be + or - 1 / sqrt(d). The sheet has been updated last Friday. But if you solved the problem with the original formulation (+-1), this is also fine. You can simply re-scale the solution accordingly.
To give you some background, this type of "random projection" is important in practice. By multiplying with a random matrix of a well-chosen type (such as in this task), you can project points from n-dimensional space into d-dimensional space (where d is much smaller than n) and approximately keep lengths and distances unchanged (in expectation).