Problem 42504. Data Regularization
Provided is an m-by-n integer data matrix A whose elements are drawn arbitrarily from a set S = [1,2,3,...,S] for any large integer number S > 1. The "arbitrary" manner of drawing integer numbers implies that each column of A might contain only a subset of integer numbers from S. Our objective is to regularize the data in A subject to the following rules:
For each column in A,
- The smallest number or numbers (if there are more than one such number) are mapped to 1;
- The 2nd-smallest number or numbers (if there are more than one such number) are mapped to 2;
- The k th-smallest number or numbers (if there are more than one such number) are mapped to k .
For example, S = [1:8] with S = 8. Suppose the input data matrix A is
A = [2 6 5 3 5 6 3 7]
Then the output matrix B is
B = [1 2 3 1 3 2 2 3]
Please try to avoid for or while loops. Vectorized code will be more appreciated.
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