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POMuPad in Matlab
 

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  1. POMuPad in Matlab
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    <p>I have a simple question want to use MuPad in Matlab to calculate it. I spent about 1 hour to calc it using my pen and paper, however it's interesting for me if it can be solved using MuPad.</p> <p>I have n numbers, clustered in two groups (p and q), each of them with a mean (Mp and Mq). I have a measure called SSE (sum of square error) that calculates the sum of the squared distances between any number in a group to its mean <code>(sum (x[i]-Mp)^2 + sum (x[j]-Mq)^2</code> where i loops on first group and j loops on the second). My question is about the value of the measure if I exchange the position of two records from their original group to the neighbor group <code>( q &lt;= xq,xp =&gt; p )</code>. Please note that the means of the groups are changed also after the exchange. The final formula (based on pen and paper) is as follows:</p> <pre><code>d = xq - xp deltaSSE = SSE1 - SSE2 = d(d (np + nq)/(np nq) -2 (Mq-Mp)) </code></pre> <p>where np and nq are the number of records in groups, xq and xp are the two records are considered for exchange the position, Mq and Mp are corresponding means (before exchange).</p> <p>The most important problem I have with MuPad, is about the number of records in groups (it is always below 10).</p> <p>Thank you for your help.</p> <p><hr/> Example about the formula above: you have two groups "1 2 3" and "4 5 6". The SSE of such clustering is 1^2+0^2+1^2 + 1^2+0^2+1^2 = 4. Now I'm interested to know what is the SSE if I exchange the place of 3 and 6, without the complete calculation. based on the formula above, d=6-3=3, np=nq=3,Mp=(1+2+3)/3=2 and Mq=(4+5+6)/3=5, so deltaSSE = 3(3(3+3)/(3*3)-2(5-2))=-12, i.e the new SSE is 4+12=16. My question is about how to represent clusters of numbers without knowing the exact number of them in MuPad. The Simple form where the number of elements in groups are known, can be solved easily in MuPad. </p>
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    1. COWhy use symbolics here? Are you developing an algorithm for later implementation in `C` or `Fortran`. Why not use just MATLAB and its awesomely fast numerics?
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    2. COThe computation above requires O(1) calculation, but the complete calculation requires O(n). This mean about 1000 times speed up for my case.
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    3. COUnless there some crazy simplifications going on, I don't understand why you want to use MuPad. Anyhow, what is the problem exactly in implementing the calculation you want. Can you give an example?
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