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    <p><code>x(t)</code> is the original voice from one channel/microphone. </p> <p><code>X = repmat(sum(x.*x,1),size(x,1),1).*x)*x'</code> is an estimation of the power spectrum of <code>x(t)</code>. Although <code>X' = X</code>, the intervals between rows and columns are not the same at all. Each row represents the time of the signal, while each column is frequency. I guess this is an estimation and simplification of a more strict expression called <a href="http://www.mathworks.com/help/signal/ref/spectrogram.html">spectrogram</a>. </p> <p><a href="http://en.wikipedia.org/wiki/Singular_value_decomposition">Singular Value Decomposition</a> on spectrogram is used to factorize the signal into different components based on spectrum information. Diagonal values in <code>s</code> are the magnitude of different spectrum components. The rows in <code>u</code> and columns in <code>v'</code> are the orthogonal vectors that map the frequency component with the corresponding magnitude to <code>X</code> space.</p> <p>I don't have voice data to test, but in my understanding, by means of SVD, the components fall into the similar orthogonal vectors are hopefully be clustered with the help of unsupervised learning. Say, if the first 2 diagonal magnitudes from s are clustered, then <code>u*s_new*v'</code> will form the one-person-voice, where <code>s_new</code> is the same of <code>s</code> except all the elements at <code>(3:end,3:end)</code> are eliminated.</p> <p>Two articles about the <a href="http://orbit.dtu.dk/fedora/objects/orbit:82321/datastreams/file_4737044/content">sound-formed matrix</a> and <a href="http://airccse.org/journal/ijnlc/papers/2113ijnlc02.pdf">SVD</a> are for your reference.</p>
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    1. POcocktail party algorithm SVD implementation ... in one line of code?
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    1. COgregS, mathematically an n-by-2 matrix x can still form an X with the repmat operation. However, the spectrogram can only show channel each time. So I think it makes more sense to use n-by-1 x each time, and treat the problem as a linear regression (two matrix equations). Another two possible approachs are (i) to average two channels as n-by-2 x; or (ii) binding them together to construct an 2*n-by-2 x.
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    2. COyou are very welcome to update your experimental progress!
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    3. COgregS, I reconsidered your question. It may work if you implement repmat on a n-by-2 x. Physically it can be viewed as an average of power from two channels at each time, and each frequency.
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