Problem 42504. Data Regularization

Created by Peng Liu

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Provided is an m-by-n integer data matrix A whose elements are drawn arbitrarily from a set</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>S</w:t></w:r><w:r><w:t> = [1,2,3,...,S] for any large integer number S &gt; 1. The \"arbitrary\" manner of drawing integer numbers implies that each column of A might contain only a subset of integer numbers from</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>S</w:t></w:r><w:r><w:t>. Our objective is to regularize the data in A subject to the following rules:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For each column in A,</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>The smallest number or numbers (if there are more than one such number) are mapped to 1;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>The 2nd-smallest number or numbers (if there are more than one such number) are mapped to 2;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>The</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>k</w:t></w:r><w:r><w:t> th-smallest number or numbers (if there are more than one such number) are mapped to</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>k</w:t></w:r><w:r><w:t> .</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For example,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>S</w:t></w:r><w:r><w:t> = [1:8] with S = 8. Suppose the input data matrix A is</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[A = [2 6\n 5 3\n 5 6\n 3 7]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Then the output matrix B is</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[B = [1 2 \n 3 1\n 3 2\n 2 3]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Please try to avoid for or while loops. Vectorized code will be more appreciated.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

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 &gt; 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,<ul><li>The smallest number or numbers (if there are more than one such number) are mapped to 1;</li><li>The 2nd-smallest number or numbers (if there are more than one such number) are mapped to 2;</li><li>The k th-smallest number or numbers (if there are more than one such number) are mapped to k .</li></ul>For example, S = [1:8] with S = 8. Suppose the input data matrix A is<pre class="language-matlab">A = [2 6
 5 3
 5 6
 3 7]
</pre>Then the output matrix B is<pre class="language-matlab">B = [1 2 
 3 1
 3 2
 2 3]
</pre>Please try to avoid for or while loops. Vectorized code will be more appreciated.

Solve

Solution Stats

119 Solutions
33 Solvers

Last Solution submitted on Jun 10, 2021

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Asif Newaz on 12 May 2020

without loop makes it quite difficult..is there any particular built-in function to do this?

Rafael S.T. Vieira on 29 Jun 2020

You do know that Matlab most certainly uses while and for loops to multiply matrices internally. The vectorized solution is probably faster because of parallelization and other optimization tricks, which we could also implement with the proper toolboxes.

Rafael S.T. Vieira on 29 Jun 2020

And please add an space to strfind, or else It will find fors and whiles inside comments and even parameter names. I was using a parameter "Uniform" of the function cellfun and it took me a while to realize why it was failing the first test.

Solution Comments

Solution 714294

1 Comment

1 Comment

Peng Liu on 13 Aug 2015

very nice idea!

Solution 713866

1 Comment

1 Comment

Peng Liu on 12 Aug 2015

The first truly vectorized solution I've seen here without using for, while, cellfun, arrayfun, etc.

Problem Recent Solvers33

Problem Tags

integer matrix vectorization

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 42504. Data Regularization

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers33

Suggested Problems

More from this Author30

Problem Tags

Community Treasure Hunt

Problem 42504. Data Regularization

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers33

Suggested Problems

More from this Author30

Problem Tags

Community Treasure Hunt

Players