Problem 42676. Histogram of histogram

Created by Peng Liu

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{"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>Histogram of histogram (HoH) is a useful measure concerning the distribution of random data, which has diverse applications in data science, statistics, information theory, etc.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>In this problem, given an n-by-m array x of integer numbers {1,2,...,S}, return the HoH along every column of x: f = HoH(x). An example for n = 5, m = 4, and S = 6 follows.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Input</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ x = [1 2 2 3\n 2 3 3 6\n 1 3 1 1\n 6 3 2 5\n 2 2 4 2]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Histogram</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ h = [2 0 1 1\n 2 2 2 1\n 0 3 1 1\n 0 0 1 0\n 0 0 0 1\n 1 0 0 1]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>where the r-th (r=1,...,S) row of h is the histogram bin counts for number r along every column of x.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>HoH</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ f = [1 0 3 5\n 2 1 1 0\n 0 1 0 0]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>where f is a max(h(:))-by-m matrix, with the p-th row representing the histogram of number p along every column of h.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Hint</w:t></w:r><w:r><w:t> : A straightforward reference scheme to obtain f could be:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ h = histc(x,1:max(x(:)),1); \n f = histc(h,1:max(h(:)),1);]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This is simple but inefficient in terms of both performance and memory (It will crash for the last test case). Note that the ultimate goal is to find f (HoH); thus, it is not necessary to go through exactly the same h as described above. Try your best to improve your code in terms of both</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>speed</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>memory</w:t></w:r><w:r><w:t>. Your score will be based on the</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>speed</w:t></w:r><w:r><w:t> of your code.</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>"}]}

Histogram of histogram (HoH) is a useful measure concerning the distribution of random data, which has diverse applications in data science, statistics, information theory, etc.In this problem, given an n-by-m array x of integer numbers {1,2,...,S}, return the HoH along every column of x: f = HoH(x). An example for n = 5, m = 4, and S = 6 follows.Input<pre> x = [1 2 2 3
 2 3 3 6
 1 3 1 1
 6 3 2 5
 2 2 4 2]</pre>Histogram<pre> h = [2 0 1 1
 2 2 2 1
 0 3 1 1
 0 0 1 0
 0 0 0 1
 1 0 0 1]</pre>where the r-th (r=1,...,S) row of h is the histogram bin counts for number r along every column of x.HoH<pre> f = [1 0 3 5
 2 1 1 0
 0 1 0 0]</pre>where f is a max(h(:))-by-m matrix, with the p-th row representing the histogram of number p along every column of h.Hint : A straightforward reference scheme to obtain f could be:<pre> h = histc(x,1:max(x(:)),1); 
 f = histc(h,1:max(h(:)),1);</pre>This is simple but inefficient in terms of both performance and memory (It will crash for the last test case). Note that the ultimate goal is to find f (HoH); thus, it is not necessary to go through exactly the same h as described above. Try your best to improve your code in terms of both speed and memory. Your score will be based on the speed of your code.

Histogram of histogram (HoH) is a useful measure concerning the distribution of random data, which has diverse applications in data science, statistics, information theory, etc.

In this problem, given an n-by-m array x of integer numbers {1,2,...,S}, return the HoH along every column of x: f = HoH(x). An example for n = 5, m = 4, and S = 6 follows.

*Input*

x = [1  2  2  3
                      2  3  3  6
                      1  3  1  1
                      6  3  2  5
                      2  2  4  2]

*Histogram*

h = [2  0  1  1
                      2  2  2  1
                      0  3  1  1
                      0  0  1  0
                      0  0  0  1
                      1  0  0  1]

where the r-th (r=1,...,S) row of h is the histogram bin counts for number r along every column of x.

*HoH*

f = [1  0  3  5
                      2  1  1  0
                      0  1  0  0]

where f is a max(h(:))-by-m matrix, with the p-th row representing the histogram of number p along every column of h.

*Hint* : A straightforward reference scheme to obtain f could be:

h = histc(x,1:max(x(:)),1);         
    f = histc(h,1:max(h(:)),1);

This is simple but inefficient in terms of both performance and memory (It will crash for the last test case). Note that the ultimate goal is to find f (HoH); thus, it is not necessary to go through exactly the same h as described above. Try your best to improve your code in terms of both *speed* and *memory*. Your score will be based on the *speed* of your code.

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Last Solution submitted on Apr 02, 2023

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Dennis Gimlin on 4 Sep 2020

I've tried multiple schemes, some are faster than histc, but not fast enough. Hint?

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Problem 42676. Histogram of histogram

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