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I'm working on an algorithm for determining the principal components of data. It works, but the convergence criterion uses the symbol $\Delta$ in a way in which I'm not familiar with. It's in step 3 of the picture below, and is used elsewhere in the algorithm that this is part of so I need to figure it out! $s$ is a vector, which may not be clear in the picture below.

Any help will be much appreciated.

enter image description here

Peter Greaves
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  • $\Delta_n$ seems to be a metric defined by the authors. Where did you find this algorithm? – Alex Silva Oct 24 '16 at 13:08
  • It seems to be the "difference" between $s^{(j+1)}$ and $s^{(j)}$ where the index $n$ in $\Delta_n$ depends on the fact that the "vectors" u, t nad s have $n$ coordinates. – Mauro ALLEGRANZA Oct 24 '16 at 13:09
  • Thanks @MauroALLEGRANZA, Would I take the sum of the absolute differences to get a scalar quantity or is it the maximum value of $n$? To compound the confusion, $s$ is a $n$ by 2 matrix. – Peter Greaves Oct 24 '16 at 13:25
  • It must be a scalar : $(1 - \ldots)$. – Mauro ALLEGRANZA Oct 24 '16 at 13:33
  • Intuitively, if the process converges, the quantity $\Delta_n$ for step $(j+1)$ must be "quite equal" to the same quantity for step $(j)$; thus their ratio approximates $1$ and this is the criteria to stop the iterations : "when the ratio is different from $1$ of less than a certain threshold". – Mauro ALLEGRANZA Oct 24 '16 at 13:35

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